Talk:Logical connective

8641:

footnote for readers about the possible subjective interpretations from the unprecise natural language word "either...or" to a precise mathematical logic concept (i.e. a logical connective). At least, we shall make the column elements in this row consistent with each other and error free. IMHO, the current edition (with the inconsistency between "inclusive disjuction" and "⊕" introduced by the revision "06:56, 16 December 2020‎", and the none logic gate term "Logical disjunction" introduced by the revision "11:54, 26 February 2021‎") may cause confusions for readers unfamiliar with this topic.

5913: 264: 254: 233: 7772:, and everything else, because that's not a topic that anyone actually writes about in the literature. Each logical system has its own syntax that includes particular connectives, so an article that tried to come up with a general definition of "logical connective" would be original research. On the other hand, many books (including Enderton's book in the references) cover the topic of arbitrary truth-functional logical connectives. That is an important topic for us to cover, and it's what this article is intended to discuss. — Carl 200: 5881: 463: 5951: 5942: 1410:/operator. Wondering if this was done with consensus, if connective is the best word (relation?, operation?), etc. And I also want to know if this is to be the overview article, are all linkages based in use of the term "logical operation/operator" (the convention until now, apparently) are going to be addressed. Seems like this was done out of process, and needs to be moved back, with "connective" being an alternative boldface term. Regards, - 191: 6037: 5956: 365: 338: 4947: 4766: 4602: 4395: 4142: 4041: 3939: 3751: 3561: 3460: 3358: 3189: 2999: 2839: 2630: 2517: 2114: 1937: 1778: 8186: 8149: 375: 7313:

concerns me is the “non-preserving” group as they have not been described as such in the lit. I put it as a catch all, to the others that don't have a preserving property. Also, should the first group be “True and False Preserving” or should it be “True and/or False preserving”. Maybe this should be stated differently. I can’t find a source for how the two properties combine.

495: 6221:

non-standard formats here is it hinders other editors changing the article. Anything like that should be avoided if at all possible I believe. It probably does make some articles less good but Knowledge is supposed to be collaborative and overall it seems to work out well. In this particular case there is a reasonable alternative which is quite satisfactory for the job.

1509:

Once you start going beyond that, going into detail, as to the (potentially infinite) possibilities that exist for something to be a "logical connective" within a given language, then the article will be doomed to be unfinished, and, I think, you confuse the reader. Apologies if I angered anyone, I can tell you've put a lot of work into it.

5388:, for instance. Invariably, I would like to see a canonically worded account which gives some idea where in the big scheme of things the topic resides, beginning with the immediately next level of abstraction. X is a type of Y. "Oh, what's a 'Y'?" "Well just click on 'Y'." Explanations are sufficiently easy to get that we are able to 5214:

logic falsity is much more often taken as basic than negation. An important reason is that without explicit constants the set of connectives is not stricly speaking functionally complete, there is no way of defining constant functions without variables. In any case, these doubts may only apply to the question of

8632:

2. The symbol "⊕" seems the logical connective "exclusive disjunction", or the logic gate "XOR". Shall it be "∨" if we go with the interpret of "either...or" as "inclusive disjunction"? Or shall we change the other columns for this row, since they ("inclusive disjuction", "⊕") are not consistent if I

8130:

The following excerpt from the article is completely incoherent. "Is some new technology (such as reversible computing, clockless logic, or quantum dots computing) "functionally complete", in that it can be used to build computers that can do all the sorts of computation that CMOS-based computers can

8110:

It is possible to define logical operators in terms of only conjunction (and) and negation (not). I have added this for disjunction (or) as it is common, well known and occasionally useful to be able to do this for disjunction in particular, and shows how each operator can be formed in its most basic

8074:

of classical logic. I can understand that many readers expects "logical connective" to be a rough synonymous of "logical operator over 0 and 1" as they maybe just learned in their digital logic course, but this is not the only way to refer to the "digital logic" meaning since for instance "two-valued

8065:

I am not happy with the hatnote that indeed clarifies that this page is about logical connectives in (two-valued) classical propositional logic, but that leaves no room for non two-valued interpretations of logical connectives. In particular, that leaves no room neither for discussing the use of this

7857:

So instead of naming this article "truth-functional {0,1}-valued logical connectives" we just call it "logical connectives". That seems to match with the COMMONNAMES advice: people who are looking for modal logic will know that's what they want, while people who are interested in the connectives they

7721:

I don't understand why you keep linking to books. Could you just come out and say whatever argument you're trying to make? Both books you have linked seem to use the word "operator" for the modal symbols, which is the word I used above and is the word I am used to for modal operators. This article is

6707:

As someone coming from constructive logic and computer science, I am used to a much broader definition of "logical connective" than what is implied by this article. Although there is a brief mention of finite-valued logic in the section on arity, most of the article is heavily biased towards boolean

6226:

As to the funny colouring all I can say is tha sometimes more is less, it is an unnecessary distraction tha doesn't add anything wen explained. The gif for the Thue-Morse sequence seems fine though, it doesn't try to substitute for part of that article and though I'm not keen on things jumping around

5618:

Even though I wrote some of the new lede, I tend to agree with Lambiam. I was trying to preserve as much of the earlier lede as possible, and it identified the logical connective with its truth table, which is certainly one way to go. If nobody else has already fixed this, I'll take a shot later on

5568:

For example, in "x = 0 AND y = 1", "AND" is a logical connective that combines the two statements "x = 0" and "y = 1" to a single compound statement. The same connective can also be denoted by the symbols "&" and "∧", as in "x = 0 ∧ y = 1". For this example, the compound statement is true only if

5199:

I appreciate that you now edit in a constructive way, instead of reverting. I think direct editing in this way can be more productive than discussing everything first on the talk page. I am more or less happy with the current version, except for one point below, which you continue to push for reasons

5059:

I'm sure you can find a book that describe T and F as nullary connectives but that description does not appear in any of the textbooks or research papers I use regularly, and is in any case a construction that would only appeal to a research mathematician who already knows everything in this article.

4995:

This sentence could only be read by a mathematician or upper division math major, who would already know what a logical connective was. The beginner will not understand "logical constant" or "syntactic operation", and may also stumble over "well-formed formula", all concepts usually introduced after

1660:

I doubt very much that the readers to whom such a table may be useful can actually interpret it. In the first column, it is unclear what the arity of the symbols is. I've never seen ⌋, ⌊, ⌈ or ⌉ used as logical connectives, and they are not explained otherwise in the article. They are also not listed

8648:

Thanks for pointing this out. I've trimmed the list and added some information above it. As for exclusive disjunction, it's not so much that it's subjective in the sense of different people having different opinions. It's more that disjunction can get different interpretations in different syntactic

7339:

Are these properties discussed in any standard textbook? I am more familiar with the mathematical logic literature, where I don't think I have seen this sort of preservation property having much interest. I guess I am asking why this information is worth including; it's clearly true, but I don't see

5535:

I don't like the new lede, which appears to conflate the connectives (which are symbols, living in the world of syntax) with truth functions (which are values, living in the semantic world). This may not be the intention, but the wording is very unclear. What is the antecedent to which the word "it"

4979:

for example. But logic, and logical connectives, are basic to math and computer science, and so this article should be aimed at the introductory level. For that reason, I think it is best to begin the article with the five most commonly used logical connectives (I can site a dozen books that begin

884:

provided by Gregbard, I figured out what is intended - that if you look at a particular 16 element sublattice of the Lindenbaum algebra of propositional logic, it gives you a way to rank the logical strength of the operators based on the partial ordering of the Lindenbaum algebra. But the link does

5764:

if you want to try again. I think an article covering the following information might be encyclopedic: the basic difference between search engines proper and web directories, the difference between "simple" (one-line) and "advanced" (web form) search interfaces. And then also differences in support

5414:

The problem with "logical constant" is that it is bad terminology in the first place. Calling quantifiers and connectives "constants" in a context where constants in a much more normal sense also play a role is incredibly bizarre, unpractical, and only serves to confuse people who are not initiated

5213:

The statement "but the connectives that are always true or always false are usually omitted, leaving 14 connectives in actual use" is patently absurd. The constant for falsity is very widely used, many calculi take implication and falsity as the only connectives, for example. Also in intuitionistic

800:

Thank you Arthur_Rubin, I'm sorry for my tone in my frustration. I think you can see that the diagram may have taken some time and effort. What I had in mind was that the diagram represents an interesting four dimensional relationship. I think it is informative on the logical connective concept. I

7504:

to wiki's purpose. Without this, wiki would be a copying machine and none of us would be allowed to talk here. The truth is preserved in verification however, as these preservation properties demonstrate, it is also transformed by the applied logical connectives. Ultimate, wiki is about verified

6360:

I respectfully disagree. See the Knowledge entries for Karnaugh Map and Truth Table, both of which treat them as distinctly different concepts. I think that this Logical Connective Knowledge entry should be consistant with the Karnaugh Map and Truth Table Knowledge entries. Otherwise, I think that

5444:

The article is describing logical connectives (a) as they occur in natural language (as by words like and and or, and also (b) as they occur in logic and represented by our familiar symbols. I think that is a worthy aim, but I am just wondering if the article is clear on this and not confusing to

1508:

of time over this article, and care about it deeply: however, do you not think that you have perhaps taken the subject too broadly? I mean that a clear and succinct definition of a logical connective given at the beginning with examples of the main truth functional connectives would be sufficient.

8621:

1, The interpretation of the word "either...or..." may be subjective. To me, this word applies to two exclusive terms which belong to the same system to categorize things. On the other hand, it is not uncommon that people use "inclusive disjunction" interpretations (esp. when it is convenient and

6889:

This article was originally very limited, covering only truth-functional connectives in formal languages. At some point, I believe User:Philogo began to add some text about natural-language connectives. This is a good thing to add, but unfortunately it is outside the knowledge of many mathematics

6397:

The diagrams happen to be Karnaugh maps, but that does not mean that they are not truth tables. Truth table is simply an assignment of truth values of a Boolean function to all possible combinations of truth values of its input, the layout of the table is completely irrelevant if you are going to

6203:

Tables are used by blind people every day of the week. The complaint blind people have about tables is if they are used purely for formatting rather than as tables. If they are used for the purpose for which they are intended they work very well. Even tables with colspans and rowspans are good if

5419:

to understand. The term "logical constant" is obsolete; it does not contribute to making anything easier, and it can be easily replaced by "logical symbol", which has the same meaning except that it also includes the variables. There is no need to spread bad terminology all over the encyclopedia.

5383:

Then we have a basic difference of opinion on how articles should be organized. I think that we should always attempt to identify the next level of abstraction early in the lead. "A set is an abstract object." "An algorithm is a type of effective method." This is especially justified on Knowledge

757:

You are correct. The operators have different qualities in different n-ary logic. They could be interpreted as a totally different thing with a different set of pages for the ternary operators, for instance. Perhaps it would be better to just include a section on the different "versions" of n-ary

8376:

Now I lean to creation of completely new design. Please, propose colors and proportions. My proposal is to retain orthogonally intersecting circles from Lipedia's design, with not so thick outline, filled with a color m.b. slightly lighter than proposed earlier (say, #9000FF ) but darker than in

8640:

4, This row went through a couple of revisions in history. I believe it might be due to the issue of different subjective interpretations of the word "either...or..." as described in the first doubt. This suggests that we might be better off removing the row completely. Or we shall put an extra

7312:

Good question, the table is a summary of properties that are well established in the literature and all ready in the article. I believe these properties say something about preserving validity. It serves as a summary here, how these groupings are applied requires a statement and a source. What

6716:

is a logical connective! It combines two sentences to form a new sentence, and its meaning is uniquely determined by the meaning of those subsentences—you just can't model the meaning of those sentences by boolean truth values. Perhaps much of the material in this article should be moved to a

5846:

Fully agree. And more than that I think editors should try and put information into WP in a form where it an be edited easily by others. It is supposed to be a collaborative effort, doing this sort of thing would lock out editors who might know more about the subject matter. Even if it was well

7847:

The common meaning of "logical connective" is essentially "a connective in propositional logic", that is, the type of connective that corresponds to a digital logic gate. Modal logic and other nonclassical logics are very specialized topics, but many undergraduates in mathematics and computer

6214:

Knowledge doesn't use imagemaps or Flash or Java in a core way in the edited content. If you want to get people to adopt imagemaps as another standard I believe you start at the village pump. Otherwise the best I think one could do with it is use it as ancillary help which could be included or

1808:

It is an improvement in clarity. It is a bit unfortunate that such a harsh red was used for the Venn diagram, and the colour key "red = true/included, white = false/excluded" is not the most intuitive. I'd further suggest to separate "Notation" into "Notation" and "Equivalent formulas", giving

8265:. If the background remains white, I do not object against blue, azure, violet, or even black. Let Lipedia explain what means "no rational reason" himself (if he feels that further explanations are needed), and, as a homework personally to Dmcq, try to explain what would be wrong with yellow. 6220:

Have a look at Knowledge's main pages, it doesn't use imagemaps to direct to the various subjects does it? In a place like Google's effort at an encyclopaedia where individual editors are responsible for their own patch I'm sure there wouldn't be any problem. The problem with just sticking in

5759:

it deserves its own article (I am not sure), then certainly the domain of application must be part of the title. Given the wider scope of the former article (quotation marks and wildcards are "orthogonal" concepts, completely unrelated to boolean operators except that in computer science they

5336:

Logical constant seems to me to be seminal to the concept. I was surprised to find it buried lower down. I find the distinction you make fascinating, but I'm wondering if it isn't pretty trivial or should be an early lead distinction to cover. In formal logic a logical connective is a logical

1556:

There's no reason to restrict to two formulae, right? Certainly, the common logical connectives are all unary or binary, but one could define a truth-functional connective to operate on three WFFs and it would still be a truth-functional connective. Shouldn't it say "one or more well-formed

8047:

that is not really related to them being connectives (quantifiers are also important) but which should be covered in that article rather than this one. Phrases such as "whereupon" and "that is" are not really "logical" connectives, unless you think natural language is a sort of logic. — Carl

6151:

The truth tables in the imagemap are arranged in a linear way, which is strange because a truth table ought to be a square. The current version of the page has square truth tables. I have no idea how to read the truth tables in the imagemap (that is, which order the truth values are arranged

8700:

Different people use the same terms differently. I prefer to have operator be something that ranges over 0-ary logical constants (i.e., true/false in bivalent classical logic); 1-ary operators including unary modalities and negation; 2-ary operators including binary logical connectives and

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0)" if we use a categorization system using both x and y variables. Is "exclusive disjunction" more applicable than "inclusive disjunction", or vice versa? Or shall we delete this row completely since this depends on subjective interpretations of the natural language word "either...or..."?

8042:

I am happy with the hatnote that clarifies this page is about logical connectives in classical (propositional) logic. There is no general concept of "logical connective" in an arbitrary logic that we could write about; the syntax varies so much, all we would be able to do is make a list of

8527:

In the section "natural language", I removed from the table a line incorrectly stating that "only if" is the converse implication. To the contrary, "P only if Q" means the implication, P implies Q. As I am in a hurry - this implies error prone - I have not introduced a corrected version.

889:

of incoming to outgoing arrows is important - the Hasse diagram hides the transitivity of the partial order. Lacking any evidence that this method of ranking strengths is in the literature, or an important fact about the logical connectives, I'm moving the section to the talk page. — Carl

8636:

3. The 4th column, i.e. "Logical gate", shall use a term for logical gate. So the term for this row shall be "OR" (a logic gate term) if "inclusive disjunction" (a logical / boolean connective term), or "XOR" if "exclusive disjunction". It seems the term issue only occurs in the 5th row

7505:

validity with logical connectives. Knowledge, isn't about valid truths, disputes are often settled by source attribution to the cited subject and specific context. (Sorry, I can't address "a random selection of trivial information" that seems uncivil and off track for now). Thanks

8396:

I created the original images that served this purpose. They were replaced by these red ones. The original ones I made had circles which were labeled. So I would support any replacement, however the images themselves should be labeled with circles "A" and "B" (or preferably "P" and

7858:

just learned in their digital logic course will not expect to find modal logic. They certainly won't expect an article on the philosophical arguments about what a logical constant is, like the SEP article you quoted. That article is not about the same topic as this article. — Carl

1523:

I have added some more examples and renderings into symbols, intended to give a better overview for the reader before he/she dives into the depths of this article. Also removed example of causal relation on the ground that such, though interesting, is not a truth-functional

6477:

There are more important problems with the text you inserted, though. The first is the sentence "Logical connective symbols can be defined by means of an interpretative function and a functionally complete set of truth-functions (Gamut 1991)." It does not makes sense to

5008:

This is simply untrue, at least without considerably more discussion. What is true is that if A is a well-formed formula and B is a well-formed formula and # is a binary logical connective, then (A)#(B) is a well-formed formula. But this is too technical for the lede.

8075:

logical operators" would be as relevant if not more. On the other side, I don't know other common names for what logicians call "logical connective" (i.e. a formal symbol to build new formulas by composition). What can be done to solve the problem? For instance,

1423:"Connective" seems a politically neutral term to me (as a formalist). Relation and Operator seem to have specific interpretation of the connective in mind. A specific interpretation helps in introductory examples. But hauling a specific interpretation into the 7767:

Another way to say it is that this article is about the truth-functional connectives relevant to propositional logic. We can't write an article about every possible type of logical connective including modal operators, infinitary quantifiers, the operators from

645:

Since I'm on the topic, this article could do with a lot of improving, eg. remove presumption that logic = Boolean logic, introduce slightly more high-powered mathematical analysis, such as lattice of expressiveness of sets of logical operators, and so on. ----

2357:

I'm posting this here for a look-over before I put it into the main article. I spent a lot of time squinting my eyes and tipping my head doing these one after another, so they may be ripe with errors. Please check it with fresh eyes and edit as appropriate.

5176:

Knowledge is arrived at by consensus. An unwillingness to talk is not a good way to arrive at a consensus. I've taken the time to listen to your points and respond to them, and I'm busy, too. I've tried to address your points, and Philogo's points as well.

5755:. It's a synonym for logical connective, and also for boolean function, although as with all synonyms there are minor variations in usage and connotations. The very special application of this concept to search engines is at most marginally encyclopedic, and 5544:"? In any case, the formulation chosen is very convoluted and hard to understand, and such a heavy emphasis on truth functions is not needed or desirable. I think we should go back to earlier approaches and propose the following for the very first sentence: 2394:

Sorry if I switched the template on you while you were working on them. I thinking lining them up in two columns opposite their negations expresses what the colors in the table were expressing just as well, but it's be a little bit friendlier on the eyes.

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to a reliable source to be valid, (making it objective in place of purely subjective). Is all exactly un-sourced material in-valid? No, because there is subjective common sense about truth preservation and partial truths in the verification for validity

6807:

Perhaps the article should have a small section saying there are other logics which don't follow the rules but I think this article is right to be at the straightforward propositional logic level. No need to muddle it up with things like quantum logic.

7801:

McGee's strategy is to invoke semantic notions instead of modal ones: he suggests that “ connective is a logical connective if and only if it follows from the meaning of the connective that it is invariant under arbitrary bijections” (McGee 1996, 578)

6058:

or whatever. I take that very serious. But in these cases a table containing wikipedia math symbols would be not useful as well. Thus a good solution for all kinds of users is to keep the imagemap template in the article, and to add a note like this:

2220:. There is example code there that demonstrates how to fill in all the pieces. I think we can simply replace the table and Venn diagrams with 16 of those. (So if any formatting needs to be changed, we can change it once instead of 16 times.) — Carl 5712:

What happened to my article? Whoever deleted it obviously doesn't know the difference between philosophy and networking technology in search engines. I'm putting it back up, and if someone has an issue with it, I'd like a thorough explaination.

1644:

I changed the colors in the truth-table to alternating shades of white/light gray. I understand that the colors were there as an illustrative tool, but it really made the table muddy. Maybe there's another way we can present that information.

861:

I'm quite familiar with Lindenbaum-Tarski algebras. Why not just say what you mean in the article, that the "strength" is just the ordering of this algebra (oriented with F on top), or that the figure is a Hasse diagram of the lattice? — Carl

6779:. In the usage I've been exposed to, a "logical connective" can basically be any way of combining propositions, so long as its meaning can be defined compositionally. Note that I count modal operators as logical connectives (and there are a 7495:. Sorry to repeat myself. It seems folks dealing in the abstract don't realty care about validity however, it's a must for real applications with a purpose. The article has neglected validity. For example: a wiki sentence must be verified 1969:

A blue or green color for the filled in areas would be more intuitive to me - red means "no" in my mind, so it's weird to have the T cells colored red. If we want to put text on top of the color, it might need to be somewhat lighter. — Carl

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I am not very convinced those are relevant to an article on logical connectives; it seems like a stretch. I will look more closely tomorrow, but I would appreciate hearing why those sources actually support the table in question. — Carl

5120:

Is a reader who does not know want "trig. function" means, likely to know what sin, tan and cos are? Then how would he be any the wiser. Explanation by example only works of the examples are more familiar than the term to be explained.

8283:

I have never found the red very aesthetically pleasing, we had a violet shade before that was calmer. If there is a worry about having too many images on commons, you could just change the color on the images and re-upload them. — Carl

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the "non-persistent" term (p 26). Furthermore, the application is that initial binary (true, false) requirement for a sentence changes to 3, 4 or higher order logic. These properties appear to be very relevant for the transition from

5814:

It's no longer possible to easily tell which row corresponds to which connective. In the table on the left, the truth values are presented in some weird order instead of being in a truth table. And the Venn diagrams are no longer

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was (maybe a child, or person with limited English.) Would you tell them (a) it is a marsupual? (b) an animal that hops about carrying its young in a pouch? The purpose of writing is to communicate. --Philogo 23:01, 30 May 2008

5107:

In logic, the five standard logical connectives are the binary connectives, "AND", "OR", "IMPLIES", and "BICONDITIONAL", which connect two logical statements, and the unary connective "NOT", which modifies one logical statement.

5033:

This will strike a lay reader as meaningless and a mathematician as wrong. (A mathematician would want something like "An n-ary logical connective can be seen as a function which maps n-tuples of truth values to truth values.")

5015:"If a logical connective is applied to sentences then the result is a compound sentence, and the truth-value of the resulting compound sentence is determined uniquely by the truth-values of the sentences to which it was applied." 6890:

editors, including myself, so we can't really help with that. I believe there is a significant amount of additional material that could be added, modal connectives and other non-truth-functional connectives included. — Carl

4974:

A Knowledge article, especially the first paragraph, should be readable by the average, intelligent person, who has no training in the area under discussion. Exceptions are allowed in the case of highly technical articles,

8672: 7656:

Non-truth-functional connectives are not usually called "logical connectives". This is the usual terminology from propositional logic, Boolean logic, etc. It is rare for such books to mention modal operators at all. — Carl

5672:

doesn't have any references, and I hadn't heard that term before I stumbled on our article. If my understanding is correct, for people distinguishing them a Venn diagram can solely represent a set-valued expression such as

5046:

Again, a comment unnecessary for a mathematician and opaque to a non-mathematician. Since the most common logical connectives are either unary or binary, it is hardly necessary to get into n-ary connectives in the lede.

8579:

2 slightly different symbols are used: with the slash either *after* the arrow or in the *middle* of it (this second, IMO preferable symbol appears in the "redundancy - 2 symbols" section) Confused me for a minute, anyway

7848:

science learn about logical connectives either in the context of Boolean logic for computing, a course in mathematical proof where they learn the mathematical meanings of 'and' and 'or', or a basic course in formal logic.

6543:

The article appears to me to be somewhat ambigous in its use of the term "logical connective"/"truth-functional connective" A logical conenective/truth-functional connective appears to mean variously (a) a symbol such as

6144:

I will not be able to discuss this at length over the next few days because of travel, but I will leave my thoughts here. I greatly prefer the current version of the page over the one with the imagemap and Hasse diagram.

7790:

I think the problem is that you have adopted McGee's definition (you should have told me where it was coming from instead of complaining about the inline tags). I was able to figure this out from the SEP article on this

5773:), quotation marks, wildcards, Latin diacritics and special letters (é = è = ê = ë = e, ü = ue, ß = ss?), non-Latin alphabets, support for exact word groups (e.g. marked by quotation marks; but what does "exact" mean?), 6320: 5319:

logic, which this article is not necessarily about. In any case, it's stated further down within the lead. (IMHO, it should be moved still further down, probably into another article, but that's just my opinion.) —

8585: 531:

In mathematical systems, there are operators and comparators. For example, in the familiar algebra of real numbers we have +, -, divide, * and others as binary operators, along with "=", "<", etc. as comparators.

7486:

This is a tough crowd, but I expect so in binary logic (smile) LC's are about truth and false sentences, these particular properties focus on how truth is preserved. From my perspective of true and false relevance,

7368:

Let me see if I can find an appropriate statement from this source or others. It seems like preserving validity is objectivity valid and non-preserving is subjective validation. The issue crosses over from logic to

8436: 6668:&c. (The ambiguity is perhaps akin to confusing/confounding numbers and numerals, or the plus-sign with the fucntion sum.) Eg. we should be clear when we are talking about (i) a negation sign or symbol, like 2184:

It seems better to me to make a template that incorporates the code above, so that the article source itself looks like {{logicalconnective|...}} instead of being full of messy table code. I'll work on that. — Carl

8022:

Stop the presses. Greg and I agree. (Seriously, in this instance, Greg expresses the issue better than I did. The additional comment is about non-truth-functional connectives, rather than a disguised comment on

6402:

for the layout used here. As Carl pointed out, these diagrams are usually called truth tables in the literature, whereas Karnaugh maps are only referred to in very specialized contexts (integrated circuit design).

6155:

The colors in the rows of the imagemap don't have any meaning to me. I'm sure they are there for a reason, but I don't want readers to have to think for a long time to figure out what the article is trying to tell

5222:

binary connectives, and pragmatically speaking, they are much more useful then many other of the 16. I can't imagine any sane source which would deny constants to be binary connectives, yet include the connectives

5072:

After being careful about arity above, you now omit the word "binary" which is essential here. Without "binary", the "finitely" is wrong. With "binary", the word "finitely" should be replace by the word "two".

5053:"Commonly used connectives include the binary connectives conjunction (and), disjunction (or), implication, and biconditional, the unary connective negation (not), and the nullary connectives truth and falsity." 8236:

I think the 'no rational reason' really means can you provide a reason for sticking in green instead of red? Why not blue of black or yellow or purple or orage or pink? Or what's particularly wrong with red?

1446:

In two-valued logic there are 4 unary operators, 16 binary operators, and 256 ternary operators. In three valued logic there are 9 unary operators, 19683 binary operators, and 7625597484987 ternary operators.

4989:"In logic, a logical connective, also called a truth-functional connective, logical operator or propositional operator, is a logical constant which represents a syntactic operation on well-formed formulas." 1454:

In two-valued logic, there are 4 unary operators, 16 binary operators, and 256 ternary operators. In three-valued logic, there are 27 unary operators, 19 683 binary operators, and 7 625 597 484 987 ternary

8481:

Sure, there is no rational reason to add another bunch of Venn diagrams to Commons. But since Lipedia likes his red diagrams, these diagrams should be preserved, so, I will add another bunch of diagrams.

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The text also says, "Let I be an interpretative function, from sentences onto {true,false}," and then go on to say "I(~)=I(¬)=fnot", but "~" on its own is not a sentence, so it makes no sense to say I(~).

814:

I have never seen this diagram before and have no idea how it measures logical strength, as it appears to be relatively arbitrarily labeled and oriented. Do you know a reference that discusses it? — Carl

5821:

Editors do not typically move their mouse around to find out what the article is saying; they read the text to find out. Moreover, when the article is printed, any information from the image map is lost.

5481:, represented by words or by symbols. The atomic statements may be in natural language or in a more symbolic form. As I see it, the differences between the following compound statements are superficial: 527:

This article and some of its relatives suffer from the lumping of operators and comparators into one big category, unfortunately called operators. You can blame computer languages on this if you wish.

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I don't see any reason we can't have a section toward the bottom about non-truth functional connectives. I don't think we need to split it either. Please let's all just get along in the same article.

7878: 147: 7914:(but not actually appearing there) into this article. I don't see a reason to do so. If there were an appropriate article or section to contrast this to, I wouldn't oppose a note to that effect. 5159:

version of the lead. The previous lead has been there for many months, and people were happy with it. Instead, I have modified your text point by point where I've seen serious issues with it. —

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I don't believe that pointing out that these can be expressed in different ways, for instance, as a relation, is needless complication, nor does it miss any point which is being communicated.

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in the table, and the silver cube in the diagram. (These are interesting links to other regions of mathematics, and could even be mentioned in a "see also" section at the end of the article.)

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I also think that the random smattering of tags on the article isn't helpful. Just putting the POV tag at the top of the article is enough to indicate you have some issues with it. — Carl

786:

section is an arbitrary representation of the operators, which probably requires a reference, as well. If you can explain what you (Greybard) had in mind, I'll work on polishing them. —

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Yes, that's exactly what I said: the meaning of "so" depends on the meaning of its subsentences. I did not know how broadly we are construing "truth value", which is why I used the term

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The introduction states: "A logical connective is a logical constant used to connect two or more formulas" But only one sentence later, it states: "Common connectives include negation"

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How's that? I tried to fix it so that "one or two" is no longer present, and so that it all makes sense. I don't think I changed any of the meaning, just made it clearer and neater.

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becomes probelematic when discussing non-classical logics. "Connective", being a purely syntatic term in English, seem appropriately agnostic to me, and I think is the right choice.

8462:. Don't forget to delete the illustrations from them (I'm sure CBM will like that) or to upload some 3-circle diagrams in the new color. And don't forget to remove anything red from 5155:

Rick, I have neither the time nor desire to getting involved in a lengthy discussion, especially given your attitude that you only show the willingness to discuss after reverting to

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I added a line beneath the Venn diagrams crediting the source for their arrangement, which Greg Bard mentioned above ("'Sets' and 'Logical strength' sections") in a link he titled

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bimodalities (i.e., 2-ary modal operators); and then one typically might have finite and infinite quantifiers, which generally needs some kind of set or type theory to axiomatise.

6123: 6060: 5079:"A particular logical system will only employ some basic set connectives to construct well-formed formulas, and treat the other connectives as defined in terms of the basic ones." 7377:. Haven't found a table source or these specific statement sourced. It could be this belongs in a new separate article about the "Logical Connective Preservation Properties". 4860: 3691: 3058: 2724: 7050: 4832: 4542: 4452: 4308: 4280: 3620: 3129: 2752: 2352: 8440: 8105: 4980:

that way if you want me to, but I imagine anyone else reading this could do the same), instead of leaping into the question of the infinitely many n-ary logical connectives.

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On my analysis above, connectives are usually binary, and if I want to be more general I use the language "logical operator". That differs from the scheme in this article. —

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of the sentences, not just their truth values, boolean or not. I don't know of an example from a constructive logic where it makes sense. Perhaps you could elaborate? —

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I have boldy added some content at the beginning rather than discussing here first. Feel free to edit or del it if you disagree with it.--Philogo 18:57, 30 May 2008 (UTC)

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The value in pointing out that it is a function is that for any input, it returns one and only one truth-value. That property isn't present in the more general relation.

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It's OK for me, although you're right that the purple color does look a little flowery. I changed the colors of the rest of the box, and now I think it looks fine. — Carl

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I thought the project would be too small for a formal wikiproject. There's just 16 of them. However, co-operation is needed from several disparate areas. I'd like to see:

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It's true. However everything arity greater than 2 can be expressed in terms of just binary connectives. I also think there may be a name for some of them, for instance:

7894: 7154: 6666: 6626: 6582: 6302: 4887: 4253: 1351: 978: 583: 7623: 6970: 6688:(ii) the negation function. We should be clear whether it is the symbols or the functions whcih are propery called logical connectives/truth-functional connectives.-- 6173:

I have never found the ordering of connectives this way to be of interest in propositional logic. I've never seen a textbook that discussed this ordering, for example.

5761: 4996:"logical connective". Also, there is no need to put all the synonyms into the first sentence, where they are stumbling blocks for the beginner. They can come later. 2697: 2257:

It looks fine to me. As you can see below, much lighter colours still give a quite perceptible difference with white, but the "T" is sufficiently legible as it is. --

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I'm also moving this section from the article. It's quite unclear to me what these sets are supposed to represent. It was tagged as possible OR for some time. — Carl

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on Knowledge. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the

6265: 7885:. So, I see no option but to split this page. It's ridiculous to include two different notions in the same article and revert sourced attempts to distinguish them. 5955: 8779: 8116: 8060: 6492:

Also, I don't believe the terminology "interpretive function" is common in the literature, and I'm not sure this section needs to be in the article at all. — Carl

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Venn diagrams in white and red are more usual, because books with two ink colors were done rather in black and red than in black and light blue. Some examples:

1665:. In the next column, why are "false" and "true" replicated four times, while P is all alone on its line? The last column must surely be totally mysterious. -- 1494: 7607: 5449:

As a professional logician, I can't answer questions as to clarity. As a professional philosopher, neither can Greg. Any ideas where we can go from here? —

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To Colonel Marksman: The term "boolean operator" clearly originates in mathematics; more exactly from the area of it in which most things are associated with

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into this arcane terminology. In mathematics it's generally accepted that the subject is already hard enough and that we should do whatever we can to make it

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Mammal: the class of verterbrate animal that bears its young live and suckles them Eg. Dog, Cow, Kangaroo. Compare other vertebrebrates: Reptile, Fish, Bird.

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areas of Venn diagrams are highlighted. Red causes awareness, and that's also the reason for the use in anti-logos - not any symbolic meaning of this color.

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I think that looks good. I'll go through and change the colors for all the rest of the Venn diagrams tonight and toss them into the article in this format.

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except that it uses a strange (to me) notation in place of OR and NAND and so on. What are the curlicues and rotated question marks etc in that diagram?

5027:"Consequently, a logical connective can be seen as a function which maps the truth-values of the sentences to which it is applied to either true or false." 1551: 433: 8331: 6452: 5978:

in the table, they are explained to me bit by bit. Please do not underestimate, that this can be helpful for people, who do not already know the subject.

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But is not a comparator that which takes two arguments and gives a boolean? Therefore, can a logical operator not be thought of as a kind of comparator?

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Do what you want in the article, but please keep my red and white files out of this. If you want to upload something new you may overwrite the files in

6008:. When I touch the odd bit connectives in the diagram, I can see that the 1 bit connectives are conjunctions and the 3 bit connectives are disjunctions 8784: 8432: 5950: 1662: 1480:

to format numbers into groups of three digits. Bless the SI, but this seems problematic in cases where the number reaches a line break. Some kind of

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Nevermind. It seems very few people call these things Johnston diagrams, I have trouble finding mention of said diagram on the web or in logic books.

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This would have the advantage of combining the Venn diagrams into the table, and should be more clear about the information being presented. — Carl

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do? If it can implement the NAND operator, only then is it functionally complete." I would correct it, but I honestly cannot make sense of this.

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I think EditorPerson53 has a point actually.. but instead of writing about in the talk page, just be bold and update the intro text :P · · ·

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The reference to software compilers in the Order of precedence section seems abrupt and out of context. Maybe the section should be expanded?

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about truth-functional logic connectives, not about modal logic, and it would be out of place to try to cover modal logic in this article.

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Why drag me into this question like this? If there are clarifications to be made, lets be grateful to identify them and leave it at that.

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I like this idea. I could go through and change the reds in all the Venn diagrams. Do you think I should also invert the color scheme?

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has the color I was talking about - a light violet. The darker violet, for me, doesn't have much contrast with the black border. — Carl

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which seems a much better title to me and is also far better developed, it has for instance ... drumroll please maestro ... references.

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by the same editor who earlier tried to push a huge table containing a similar graphic (without the "masonic" symbols) into the article

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a connective via a function - a connective is a symbol. Maybe you mean you can interpret a connective via an interpretive function?

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This article uses Harvard style refs, not footnotes. So you need to add the refs at the end and insert the citation in parentheses.

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connectives in this logic, and this logic, and this logic. On the other hand there is a lot of philosophy discussion on arbitrary

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Hi, I would like to offer this table for inclusion in the properties section. Any comments or modifications are welcome. Thanks

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I see that Arthur has deleted the fact that logical connectives are a type of logical constant. Does that make any sense at all?

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Need some help from knowledgeable Knowledge fellows since I'm far from an expert in this topic (or I won't read this article).

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to form a compound statement, whose truth value is then determined by the truth values of the individual component statements.

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The thought in your first sentence has occurred to me as well. But the table doesn't really seem to belong there, either.

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it as having much interest. But if it is mentioned in the literature then I would not object to including it here. — Carl

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connectives. There is no way in hell how constant binary functions could be excluded from the 16 binary connectives. They

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I deleted the "Logical strength" section because I couldn't figure out what it was trying to say. I now realize that the

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I agree with Noam's suggestion. A more dramatic bias towards classical propositional logic has happened in the case of

5021:

Before this discussion should come a discussion of truth values. Also "applied to" is vague, and easily misunderstood.

141: 8819: 8112: 7544: 689:, properties (including theorems that demonstrate the properties), symbols (preferably from all the above disciplines). 30: 5929: 5928: 5309: 5002:"The formula that results from applying a logical connective to well-formed formulas is a well-formed formula itself." 8132: 6628:&c when used as to represent a truth-function (c) a truth-function that can be represented by a a symbol such as 6399: 6378:

Could you explain exactly why the tables in this article should be called Karnaugh maps and not truth tables? — Carl

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A) the logical, grammatical, mathematic, and computer science applications all on the same page for the same concept.

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In all of these cases I propose that what's on the left be merged into the article on the right, as is the case with

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be the same as "Logical connective". (If you're talking about something else, you'll have to be more specific.) —

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used in a reasonable fashion. Reading the maths in wiki is done by turning off maths formatting in the preferences.

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The diagram is upside-down compared to the corresponding lattice of the Lindenbaum algebra of propositional logic.

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What if each row of the table was replaced with a box? Here is a very rough idea of what I am thinking of. — Carl

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with green-coloured ones. Also I think that the border should be removed from SVGs: we can use table borders.

6697: 5920: 5888: 5066:"All logical connectives can be constructed from finitely many of them, negation and conjunction for example." 8500:

My suggestion was to overwrite these unused blue files. Of course with diagrams without the annoying border.

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constant, in informal logic there is a sense in which logical connectives aren't logical constants? Be well,

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Would some kind ed look at and make work my non-functioning ref in the first sentence of this new section.--

6054:

It is true, that articles should also be accessible to blind people, and for plain text uses, may it be for

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The number of lines aiming away from the operator divided by the number of lines aimed toward is the ratio.

5917: 5901: 929: 724: 663: 213: 8650: 8537: 5927: 5895: 4500: 4472: 4320: 4186: 1528: 6863: 6767:. Backing up a bit, perhaps what I should have first suggested is that we modify the lede. Instead of, 5923: 5887: 5643:

rather than Venn diagrams. I'd change in on the article but I can't find the table template -- thoughts?

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Agreed in general. Two-penny's worth. The opening sensne of any aricel is very imprtant. This one begins:

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not actually discuss that, I had to fill in the details myself. Moreover, I can't see any reason why the

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removed without destroying an article, the sort of thing much of the material in Knowledge Commons does.

6093:

The information displayed in the Hasse diagram can be shown by a simple list of conclusions like these:

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Hmmm. Some of these in (C) are the same as binary operators, but not as ternary/poly-ary operaters. —

8734: 8378: 6305:, and I think it's safe to assume that there is a consensus that the link should be removed. Thanks. -- 5893: 5824:

The Hasse diagram conveys no useful information about logical connectives. It should simply be removed.

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I think it is always good to come with an example as soon as possible, and the next sentence might be:

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the reader, assuming as we should that they are new to this subject.--Philogo 23:12, 30 May 2008 (UTC)

2217: 839:. Along with this information, I'm looking for articles by Zellweger, Shea. There is relevant info at 553: 5885: 5862: 4845: 3676: 3043: 2709: 535:

In logic systems, this distinction is also made. Consider for example what comparator is used in the

8156:

I removed the paragraph. It didn't make sense, and it didn't appear to add anything to the article.

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Step back from this. Suppose you wondered what a "trig. function" was. You turn to Wiki and it says:

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usage of "logical connective". And even if you want Knowledge to follow McGee, that would mean that

7453:, as opposed to monotonicity, affineness, self-duality, or any other properties defining a clone in 8690: 8088: 7928: 7215: 6769:

The truth value of the compound is uniquely determined by the truth values of the simpler sentences

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It's very hard to read the image. It tries to compress too much information into too small an area.

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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In general, there's just too much information and not enough navigation packed into the imagemap.

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had any momentum, it would be a natural place to try to reach consensus over the logic articles.

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These Venns (without the unnecesseary blue margin) are already used in the single articles like

7566: 7271: 7083: 4673: 3793: 2764: 8084: 8031: 7947: 7927:, but I'll have to get back to that, later. I believe that article would be better split into 6871: 6751: 6417:

The tables in this article look like truth tables (a) to me (b) and as exampled in the article

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So what would you call them? Illogical connectives? Perhaps this article should be renamed to

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The imagemap doesn't allow readers to select their own fonts, unlike the current text version.

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is a symbol (usually denoted as a word or a special logical symbol) that connects a number of

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If this article is intended to be read by somebody who wants to know something or more about

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The imagemap can't be edited in any easy way, unlike the current text version of the article

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Then I think we should list the five most common connectives, and finish off the lede with:

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The ratio of implications between operators is demonstrated by the directional lines in the

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I have proposed that this page be the centerpiece of a series of articles on the operators.

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Change red to violet by script and upload updated versions with links to this discussion;

7967:. Try redirecting it here. And read something besides math books, it'll do you some good. 7223: 7115: 7011: 6979: 6831: 6671: 6631: 6591: 6547: 6209:

Knowledge already has a way of finding out about things. This is by marking them as links.

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And I have no problem with this sentence, if you would like to restore it to the article.

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EJ and I disagree about what the lede should contain. I would like to discuss that here.

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Either negation is not a connective, or a connective need not join two or more formulas.

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for that matter? To me the table looks like a random selection of trivial information. —

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Interestingly, the same diagram (Image:Logictesseract.jpg) is already on wikipedia under

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for instance. I have the impression the definitions in the lead are not really sourced.

6276:

These are secret free-masonic symbols. Your head will explode if you read them aloud. —

5921: 2377:. I copied yours in. I also changed the template to fix some alignment problems. — Carl 1504:

I don't mean to be impertenent or anything, as it is very clear that you have all spent

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Reading the lead, I'd say that the article describes logical connectives as they occur

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when the meaning of the compound is determined by the meaning of the simpler sentences

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Where is this talked about in the literature please? What is its application? Thanks

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Red doesn't have any "negative" meaning when there is no green in the same context:

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article could be streamlined to only discuss logical connectives in general terms?

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I've read that diagrams like the ones depicted in this article are actually called

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such a source, it is highly nonstandard, and very misleading to potential users. —

4966: 2374: 701: 505: 8654: 6421:. I propose we agree any preferred terminology in the (as yet empty) section of -- 6325:

The summary says it all. To someone who knows what they are doing -- please fix.

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I don't see the difference between "logical connective" and "connective (logic)".

7461: 7454: 7402: 6792: 6730: 6407: 6280: 5661: 5648: 1510: 1411: 253: 232: 8242: 7990: 7943:). At least, your edits there all relate to some topic with the same name. — 7638:

Shouldn't this article talk about those too? Are those not called logical? See

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Contradiction between definition of connective and negation being a connective

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page with a short (see: validity) in this article. Thanks for the feedback.

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So, in absence of further objections, tomorrow I proceed to following steps:

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doesn't show the places to avoid when you are searching for Israel (compare

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Karnaugh maps (2-variable k-map) are incorrectly referred to as Truth Tables

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Doubts of the table in Section "In language", Subsection "Natural language"

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unary operators for three-valued logic, not 9. Will someone check my math?

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the proper terminology, even if it stands in need of explanation itself.

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short in natural languages), for example, "the solution is either x: -->

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What are you talking about? "Boolean operator" and "Boolean operators"

5688:, whereas a Johnston diagrams depict propositional expressions, such as 5609:

I don't see anything else that urgently needs to be put in the lede. --

4983:

Here, line by line, are the problems I had with the other introduction:

462: 8529: 7458: 6788: 6726: 6404: 6277: 5657: 5644: 5040:"There are infinitely many logical connectives, 22n for every arity n." 1428: 606: 393: 392:, a collaborative effort to improve the coverage of content related to 6433:

is no longer empty but collaborators are urgently required. (Hans?)--

6024: 5760:

sometimes appear in similar contexts) I suggest using a title such as

5132:--Philogo 13:36, 30 May 2008 (UTC) --Philogo 13:36, 30 May 2008 (UTC) 8238: 8204:

There is no rational reason to add another bunch of Venn diagrams to

7986: 7907: 7298: 6809: 6708:

logic. I'm especially disturbed that this bias even sneaks into the

6228: 5997: 5983: 5848: 5774: 5385: 2396: 2359: 2338: 2203: 2171: 2128: 1956: 1646: 1626: 1590: 1558: 1473:

Consistency: "X-valued" should use always either use a hyphen or not.

1106: 923: 8618:

I have a few doubts in the 5th row, i.e. the word "either...or...".

8356: 8083:. Could it be possible to exploit the difference of meaning between 7939:(which apparently has some present content, at least in the article 1572:

Zero or more, if you want to pursue that in full generality. — Carl

880:

I'm removing the "relative strength of operators" section. Based on

8362: 8287: 8258: 8255: 8051: 7861: 7775: 7748: 7660: 7527: 7492: 7428: 7370: 7343: 7219: 6893: 6495: 6381: 6345: 6184: 5831: 2380: 2223: 2188: 2156: 1973: 1790: 1679: 1575: 1086: 893: 865: 818: 713: 639: 7879:

Reverted again by the math department, thus page needs to be split

6148:

The current version already has the Venn diagrams and truth tables

7562:. So 0/false should be next to the matrice's orgin, not 1/true. 6874:

is meant to be just that, so I have to think about merging it. —

6055: 6036: 5260: 5160: 8087:(the connective interpreted on some domain) and connective (the 7491:. The other properties are interesting however, these relate to 6342:

They are commonly called truth tables in the literature. — Carl

6010:(without cropping the article with text about details like this) 8381:, and without any foreign elements such as borders or margins. 5975: 1101:

The logical operators can be expressed in terms of sets (where

6431:

Knowledge:WikiProject Logic/Standards for notation#Terminology

5996:

are helpful representations, of what the connectives actually

5818:

It's completely inaccessible for users with images turned off.

2127:

Is that sort of color scheme alright, or is that too flowery?

8337:

Replace mentioning of red with violet in wikis, if necessary.

7923:

edits are inappropriate, due to the various mergers, such as

7374: 5807:

I don't favor the giant imagemap, for the following reasons:

5549: 536: 5968:

what I like about the representation above is the following:

523:

There are unary operators, binary operators, and comparators

8706:

We absolutely should be consistent within each article. If

8185: 7694:

Besides, your statement doesn't hold for modal logic texts

7554:, because the index elements of a matrix should be ordered 4946: 4765: 4601: 4394: 4141: 4040: 3938: 3750: 3560: 3459: 3357: 3188: 2998: 2838: 2629: 2516: 2113: 1936: 1777: 1111: 934: 620: 364: 337: 7608:

Knowledge:WikiProject Logic/Standards for notation#Symbols

2373:

I was afraid that might happen - I also made a version at

593:

We have the following pairs of boolean/logical operators:

8251: 1470:

Punctuation: introductory phrases should end with commas.

937:

The relative strength of the 16 binary logical operators:

670:

Knowledge:WikiProject_Council/Proposals#Logical_Operators

628: 7612:

It is raining if I am indoors (Q P) <- fail fix it

6028:

The odd bit connectives in the table are ordered in the

5116:

The three standard trig. functions ar sin, tan and cos.

8486:

does not satisfy me because of thick annoying borders.

6400:

truth table#Condensed truth tables for binary operators

2353:

List of connectives with truth tables and Venn diagrams

539:({T, F}, and, xor). It is isomorphic to the field F2. 8106:

Logical operators in terms of conjunction and negation

7365:

These properties are about validity. See this source

6066:

The lines in this table should simply look like this:

5484:

Socrates' dying implies that Socrates is not immortal.

1450:

Call me crazy, but I think it should read as follows:

160: 7820:

should have its separate article, not redirect here!

7274: 7250: 7226: 7190: 7166: 7142: 7118: 7086: 7062: 7038: 7014: 6982: 6958: 6674: 6654: 6634: 6614: 6594: 6570: 6550: 6126:, if you agree that it makes sense. I think it does. 5668:

Can you identify where you read this? The article on

4875: 4848: 4820: 4676: 4649: 4530: 4503: 4475: 4440: 4323: 4296: 4268: 4241: 4215: 4189: 3849: 3822: 3796: 3679: 3634: 3608: 3278: 3242: 3117: 3072: 3046: 2927: 2767: 2740: 2712: 2685: 2559: 2446: 1375: 1339: 1313: 1203: 1161: 1135: 993: 966: 370: 281:, a collaborative effort to improve the coverage of 259: 15: 8649:configurations and discourse contexts. I recommend 8341:I do not intend to make other changes to SVGs now. 8332:

commons:Category:Violet and white Johnston diagrams

8183:I propose to replace red-coloured diagrams such as 8091:

properly speaking) to satisfy all needs at best? --

7578: 7489:

these are the most relevant properties for validity

8458:Since a year there are the property sections like 8328:Replace "Category:Red and white Johnston diagrams" 8111:alphabet. Would it be useful to add it to others? 7981:That article seems redundant when there's already 7280: 7256: 7232: 7196: 7172: 7148: 7124: 7092: 7068: 7044: 7020: 6988: 6964: 6680: 6660: 6640: 6620: 6600: 6576: 6556: 6170:The Hasse diagram has a separate set of problems. 5371:. Thus e.g. suppose a person did not know what a 5124:It is better to give give the examples after. Eg: 4881: 4854: 4826: 4682: 4655: 4536: 4509: 4481: 4446: 4329: 4302: 4274: 4247: 4221: 4195: 3855: 3828: 3802: 3685: 3640: 3614: 3284: 3248: 3123: 3078: 3052: 2933: 2773: 2746: 2718: 2691: 2565: 2452: 2202:Sure, thanks. I'll do the images in the meantime. 1663:Knowledge:WikiProject Logic/Standards for notation 1381: 1345: 1319: 1209: 1167: 1141: 999: 972: 8484:commons:Category:Blue and white Johnston diagrams 8418:commons:Category:Blue and white Johnston diagrams 8315:commons:Category:0 and 1 circle Johnston diagrams 7912:grammatical conjunction#Coordinating conjunctions 5619:today, working along the lines Lambiam suggests. 5255:, and distinguish between → and ←. Even if there 1406:This was moved (renamed) a couple weeks ago from 909: 8751: 8319:commons:Category:Red and white Johnston diagrams 6110:If the statement "Q" is true, the statements "P 5577:Other terms in use for "logical connective" are 589:Merging boolean operators with logical operators 33:for general discussion of the article's subject. 8780:Knowledge level-5 vital articles in Mathematics 8543:This depends on how to write it down. “Only if 5915: 5883: 801:have to go for a moment, I'll have more later. 8624:0", althou it is equivalent to "either (x: --> 7963:the entire Knowledge. Someone already created 5516:only to improve readability by the lay reader. 5487:Died(Socrates) IMPLIES NOT Immortal(Socrates). 5278:I agree. Your recent edit is an improvement. 1114:Set Theoretic Definitions of Logical Operators 8637:("either...or..."), all other rows are fine. 7526:Ok, I talked myself into placing this on the 5744:To Arthur Rubin: He is clearly talking about 5359:, then telling them that it is (if it is) a 542:In short, this page needs a major overhaul. 174: 8447:red is used to highlight the prime numbers. 1438:Changes to "Arity" section (major and minor) 8222:So, just change the color and upload over? 8066:very same concept of logical connective in 6453:Truth functions and Interpretation function 6101:Q" is true, the statements "P", "Q" and "P 188: 8072:non-necessarily two-valued interpretations 6227:it does seem to be doing a competent job. 6063:you find this information in plain text." 5869:Copied from the WikiProject Math talk page 8785:Start-Class vital articles in Mathematics 8206:commons:Category:Vector Johnston diagrams 7903:. You appear to be trying to merge some 5367:were more familiar to them than the term 1153:{ ∅ , { ∅ } , { { ∅ } } , { ∅ , { ∅ } } } 6035: 6023: 8770:Knowledge vital articles in Mathematics 8582:2A00:23C6:B211:D100:2598:1B13:2DDC:B828 5490:Socrates died → ¬ Socrates is immortal. 8752: 8627:0 AND y<=0), or (x<=0 AND y: --> 6588:a truth-function (b) a symbol such as 6016:Last but not least: I like the silver 5847:designed I would still be against it. 5493:Died(Socrates) → ¬ Immortal(Socrates). 5363:would only be informative if the term 1442:The "Arity" section currently begins: 402:about philosophy content on Knowledge. 8595:About the Order of precedence section 6771:, I would just write something like, 6429:) 13:02, 1 April 2009 (UTC) PS It 5508:I agree with Lambiam. The lede uses 4898: 4717: 4553: 4510:{\displaystyle \not \leftrightarrow } 4482:{\displaystyle \not \leftrightarrow } 4346: 4330:{\displaystyle \not \leftrightarrow } 4196:{\displaystyle \not \leftrightarrow } 4093: 3992: 3890: 3702: 3512: 3411: 3309: 3140: 2950: 2790: 2581: 2468: 2065: 1888: 1729: 1195:{ { ∅ } , { { ∅ } } , { ∅ , { ∅ } } } 7794: 7729:with a different meaning that here. 5138:Point taken. I'll make the change. 509: 489: 386:This article is within the scope of 275:This article is within the scope of 184: 7937:formal semantics (natural language) 7933:formal semantics (computer science) 5992:shows all possible deductions. The 218:It is of interest to the following 23:for discussing improvements to the 13: 8805:Mid-importance Philosophy articles 8775:Start-Class level-5 vital articles 7449:What's so special about these two 7227: 7119: 7015: 6675: 6635: 6595: 6551: 5911: 5879: 5315:They're only logical constants in 2447: 1552:"two or more well-formed formulae" 1162: 1136: 461: 14: 8831: 8795:Mid-priority mathematics articles 8633:understand this issue correctly. 7549:I've slightly changed the table 6509:Fixed as you suggested. NB typo: 6398:visualize it. In particular, see 6290:It looks like a very bad case of 6250:is to a Hasse diagram similar to 6243:External link to obscure notation 4855:{\displaystyle \not \rightarrow } 3686:{\displaystyle \not \rightarrow } 3053:{\displaystyle \not \rightarrow } 2719:{\displaystyle \not \rightarrow } 1231:{ ∅ , { { ∅ } } , { ∅ , { ∅ } } } 295:Knowledge:WikiProject Mathematics 8790:Start-Class mathematics articles 8765:Knowledge level-5 vital articles 8427:doesn't show which territory is 8254:is inappropriate because of its 8184: 8147: 7634:Non-truth-functional connectives 7045:{\displaystyle \leftrightarrow } 5954: 5949: 5940: 5777:, support for parentheses (e.g. 5384:since people can easily look up 5200:which I do not quite understand. 4945: 4827:{\displaystyle \not \leftarrow } 4764: 4600: 4537:{\displaystyle \leftrightarrow } 4447:{\displaystyle \leftrightarrow } 4393: 4303:{\displaystyle \leftrightarrow } 4275:{\displaystyle \leftrightarrow } 4140: 4039: 3937: 3749: 3615:{\displaystyle \not \leftarrow } 3559: 3458: 3356: 3187: 3124:{\displaystyle \not \leftarrow } 2997: 2837: 2747:{\displaystyle \not \leftarrow } 2628: 2515: 2112: 1935: 1776: 851:. I will keep looking. Be well, 493: 408:Knowledge:WikiProject Philosophy 373: 363: 336: 298:Template:WikiProject Mathematics 262: 252: 231: 198: 189: 45:Click here to start a new topic. 8800:Start-Class Philosophy articles 8263:commons:Category:SVG Anti logos 7321:) 16:21, 1 November 2009 (UTC) 6740:Well, no. "So" depends on the 6251: 616:and the three-way equivalence: 500:This article was nominated for 428:This article has been rated as 411:Template:WikiProject Philosophy 315:This article has been rated as 8412:Please stay away from my files 7275: 7251: 7087: 7063: 7039: 6835:Boolean satisfiability problem 6124:Logical connectives text table 5569:both component statements are. 5060:An article should be useful. 4677: 4531: 4441: 4297: 4269: 3797: 2768: 1547:11:26, 28 September 2007 (UTC) 1529:13:05, 20 September 2007 (UTC) 910:Relative strength of operators 681:B) similar sections including 562:00:32, 25 September 2007 (UTC) 1: 8815:Mid-importance logic articles 8575:NIMPLY / Material implication 8551:” – the converse implication 7812:But this is nowhere near the 7628:19:17, 16 February 2011 (UTC) 7173:{\displaystyle \nrightarrow } 6908:Preservation properties table 6315:17:47, 11 December 2008 (UTC) 6284:13:29, 11 December 2008 (UTC) 6270:10:33, 11 December 2008 (UTC) 6237:13:56, 26 November 2008 (UTC) 6194:13:39, 26 November 2008 (UTC) 6139:12:19, 26 November 2008 (UTC) 5857:19:52, 19 November 2008 (UTC) 5841:21:01, 18 November 2008 (UTC) 5795:20:39, 16 November 2008 (UTC) 5740:14:50, 16 November 2008 (UTC) 5723:08:55, 16 November 2008 (UTC) 3641:{\displaystyle \not \subset } 3079:{\displaystyle \not \supset } 1514:12:29, 8 September 2007 (UTC) 1495:06:45, 4 September 2007 (UTC) 1279:{ ∅ , { ∅ } , { ∅ , { ∅ } } } 1275:- Converse nonimplication (⊄) 1263:{ { { ∅ } } , { ∅ , { ∅ } } } 1227:- Material nonimplication (⊅) 930:Image:Logical-connectives.gif 289:and see a list of open tasks. 42:Put new text under old text. 8743:18:03, 7 February 2022 (UTC) 8725:01:26, 7 February 2022 (UTC) 8695:22:31, 6 February 2022 (UTC) 8609:19:54, 28 October 2020 (UTC) 7540:16:16, 5 November 2009 (UTC) 7515:20:21, 4 November 2009 (UTC) 7478:12:16, 4 November 2009 (UTC) 7465:11:18, 4 November 2009 (UTC) 7438:02:22, 4 November 2009 (UTC) 7387:22:17, 3 November 2009 (UTC) 7353:11:58, 3 November 2009 (UTC) 7331:16:25, 1 November 2009 (UTC) 7307:09:49, 1 November 2009 (UTC) 7197:{\displaystyle \nleftarrow } 7136:Exclusive disjunction (XOR, 7069:{\displaystyle \rightarrow } 6922:05:18, 1 November 2009 (UTC) 5765:for boolean operators (e.g. 4222:{\displaystyle \not \equiv } 1320:{\displaystyle \not \equiv } 1000:{\displaystyle \not \equiv } 692:C) several merges including 584:22:38, 6 February 2022 (UTC) 7: 8590:07:52, 5 October 2020 (UTC) 8261:, see numerous examples in 7281:{\displaystyle \downarrow } 7244:Alternative denial (NAND, 7093:{\displaystyle \leftarrow } 6870:. I've just realised that 6864:Satisfiability and validity 6833:, but now is a redirect to 6710:section on natural language 5603:truth-functional connective 4683:{\displaystyle \leftarrow } 3803:{\displaystyle \leftarrow } 2774:{\displaystyle \downarrow } 1432:15:38, 31 August 2007 (UTC) 1096:17:01, 28 August 2007 (UTC) 508:in the past. The result of 50:New to Knowledge? Welcome! 10: 8836: 8810:Start-Class logic articles 8760:Start-Class vital articles 8667:23:49, 11 March 2021 (UTC) 8510:19:46, 24 April 2012 (UTC) 8496:18:58, 24 April 2012 (UTC) 8476:15:54, 24 April 2012 (UTC) 8407:20:37, 24 April 2012 (UTC) 8391:18:58, 24 April 2012 (UTC) 8379:commons:File:Set union.png 8372:13:02, 24 April 2012 (UTC) 8351:12:13, 24 April 2012 (UTC) 8297:11:02, 24 April 2012 (UTC) 8275:10:33, 24 April 2012 (UTC) 8247:10:11, 24 April 2012 (UTC) 8232:09:16, 24 April 2012 (UTC) 8218:08:26, 24 April 2012 (UTC) 8101:20:47, 17 April 2011 (UTC) 7871:17:41, 30 March 2011 (UTC) 7830:17:20, 30 March 2011 (UTC) 7785:16:34, 30 March 2011 (UTC) 7758:16:22, 30 March 2011 (UTC) 7739:17:20, 30 March 2011 (UTC) 7709:16:13, 30 March 2011 (UTC) 7690:16:03, 30 March 2011 (UTC) 7670:15:57, 30 March 2011 (UTC) 7651:14:57, 30 March 2011 (UTC) 7545:Small changes in the table 7184:Converse nonimplication ( 6952:Logical conjunction (AND, 6947:True and false preserving: 6373:22:23, 31 March 2009 (UTC) 6355:00:24, 25 March 2009 (UTC) 6337:22:58, 24 March 2009 (UTC) 6122:I can create this subpage 6040:...and form a cube in the 5908: 5653:09:20, 1 August 2008 (UTC) 2347:00:07, 31 March 2008 (UTC) 2332:23:01, 30 March 2008 (UTC) 2262:16:59, 31 March 2008 (UTC) 2233:16:13, 31 March 2008 (UTC) 2218:Template:Logicalconnective 2212:16:10, 31 March 2008 (UTC) 2198:15:57, 31 March 2008 (UTC) 2180:15:55, 31 March 2008 (UTC) 2166:15:22, 31 March 2008 (UTC) 2137:04:02, 31 March 2008 (UTC) 1983:01:34, 31 March 2008 (UTC) 1965:00:09, 31 March 2008 (UTC) 1951:22:14, 30 March 2008 (UTC) 1800:18:17, 30 March 2008 (UTC) 1689:14:20, 30 March 2008 (UTC) 1670:13:47, 30 March 2008 (UTC) 1655:18:48, 29 March 2008 (UTC) 1635:23:07, 24 March 2008 (UTC) 1620:21:13, 24 March 2008 (UTC) 1599:22:47, 24 March 2008 (UTC) 1585:19:09, 24 March 2008 (UTC) 1567:18:45, 24 March 2008 (UTC) 1418:02:19, 6 August 2007 (UTC) 1281:- Converse implication (⊂) 1233:- Material implication (⊃) 903:15:11, 5 August 2007 (UTC) 875:03:41, 4 August 2007 (UTC) 856:11:08, 1 August 2007 (UTC) 434:project's importance scale 8820:Logic task force articles 8680:This is a contradiction. 8569:15:05, 20 July 2019 (UTC) 8538:14:54, 20 July 2019 (UTC) 8313:Download all images from 8199:12:38, 9 March 2012 (UTC) 8173:18:49, 28 July 2011 (UTC) 8141:18:04, 28 July 2011 (UTC) 8061:11:51, 5 April 2011 (UTC) 8035:01:27, 5 April 2011 (UTC) 8018:00:50, 5 April 2011 (UTC) 7995:00:43, 5 April 2011 (UTC) 7977:23:54, 4 April 2011 (UTC) 7951:23:37, 4 April 2011 (UTC) 7895:23:00, 4 April 2011 (UTC) 7257:{\displaystyle \uparrow } 6976:Logical disjunction (OR, 6903:12:32, 25 June 2009 (UTC) 6884:20:35, 26 June 2009 (UTC) 6855:19:29, 26 June 2009 (UTC) 6818:10:30, 25 June 2009 (UTC) 6797:03:25, 25 June 2009 (UTC) 6755:20:25, 24 June 2009 (UTC) 6735:16:21, 24 June 2009 (UTC) 6698:14:06, 2 April 2009 (UTC) 6531:13:37, 2 April 2009 (UTC) 6505:02:14, 2 April 2009 (UTC) 6467:22:35, 1 April 2009 (UTC) 6443:22:37, 1 April 2009 (UTC) 6411:12:59, 1 April 2009 (UTC) 6391:05:19, 1 April 2009 (UTC) 6248:One of the external links 6049:Concerning accessibility: 5769:), other operators (e.g. 4977:Ascending chain condition 4915: 4900: 4734: 4719: 4570: 4555: 4363: 4348: 4110: 4095: 4009: 3994: 3907: 3892: 3719: 3704: 3529: 3514: 3428: 3413: 3326: 3311: 3157: 3142: 2967: 2952: 2807: 2792: 2598: 2583: 2485: 2470: 2405:02:21, 1 April 2008 (UTC) 2390:02:14, 1 April 2008 (UTC) 2368:01:28, 1 April 2008 (UTC) 2216:The template is done, at 2082: 2067: 1994: 1905: 1890: 1817: 1746: 1731: 1696: 1609:If P then Q, otherwise R. 1534:Venn diagrams arrangement 1361:{ ∅ , { ∅ } , { { ∅ } } } 1307:- Exclusive disjunction ( 1295:{ { ∅ } , { ∅ , { ∅ } } } 845:Lindenbaum-Tarski algebra 828:10:52, 29 July 2007 (UTC) 806:04:04, 29 July 2007 (UTC) 795:02:34, 29 July 2007 (UTC) 763:20:47, 28 June 2007 (UTC) 749:20:29, 28 June 2007 (UTC) 735:05:31, 28 June 2007 (UTC) 650:21:04, 11 Mar 2005 (UTC) 469: 444: 440: 427: 358: 314: 247: 226: 80:Be welcoming to newcomers 8657:if you wanna read more. 7929:formal semantics (logic) 7597:17:15, 19 May 2010 (UTC) 7558:, as it is done e.g. in 5762:Search engine interfaces 5629:13:38, 2 June 2008 (UTC) 5614:03:16, 2 June 2008 (UTC) 5526:16:38, 31 May 2008 (UTC) 5503:08:13, 31 May 2008 (UTC) 5471:00:17, 31 May 2008 (UTC) 5457:00:11, 31 May 2008 (UTC) 5430:21:00, 31 May 2008 (UTC) 5402:00:14, 31 May 2008 (UTC) 5347:22:45, 30 May 2008 (UTC) 5328:22:04, 30 May 2008 (UTC) 5310:21:34, 30 May 2008 (UTC) 5288:14:50, 30 May 2008 (UTC) 5269:14:28, 30 May 2008 (UTC) 5187:14:18, 30 May 2008 (UTC) 5169:14:15, 30 May 2008 (UTC) 5148:13:58, 30 May 2008 (UTC) 5097:13:14, 30 May 2008 (UTC) 3829:{\displaystyle \subset } 3249:{\displaystyle \supset } 659:03:58, 28 May 2005 (UTC) 321:project's priority scale 8518:(see comments above)-GB 8121:16:15, 5 May 2011 (UTC) 8025:grammatical conjunction 7983:Grammatical conjunction 7935:(not yet written), and 7567:University of Leicester 7149:{\displaystyle \oplus } 7080:Converse implication ( 6932:Preservation properties 6661:{\displaystyle \wedge } 6621:{\displaystyle \wedge } 6577:{\displaystyle \wedge } 6361:this entry is helpful. 6080:converse nonimplication 6076:material nonimplication 4882:{\displaystyle \wedge } 4248:{\displaystyle \oplus } 3578:Converse nonimplication 3016:Material nonimplication 2318:expressed as a relation 1460:Mathematics: there are 1346:{\displaystyle \equiv } 973:{\displaystyle \equiv } 847:, and maybe someday at 445:Associated task forces: 278:WikiProject Mathematics 8179:Style of Venn diagrams 7959:Fortunately you don't 7571:University of Illinois 7282: 7258: 7234: 7198: 7174: 7150: 7126: 7107:False preserving only: 7094: 7070: 7046: 7022: 6990: 6966: 6965:{\displaystyle \land } 6872:interpretation (logic) 6682: 6662: 6642: 6622: 6602: 6578: 6558: 6045: 6033: 5934: 5905: 5595:propositional operator 5130: 5118: 5110: 4883: 4856: 4828: 4684: 4657: 4538: 4511: 4483: 4448: 4331: 4304: 4276: 4249: 4223: 4197: 3857: 3830: 3804: 3687: 3642: 3616: 3286: 3250: 3125: 3080: 3054: 2935: 2775: 2748: 2720: 2693: 2692:{\displaystyle \land } 2567: 2454: 1457: 1448: 1396: 1383: 1382:{\displaystyle \land } 1347: 1321: 1211: 1169: 1143: 1080: 1001: 974: 704:; different pages for 466: 389:WikiProject Philosophy 75:avoid personal attacks 8735:Omnissiahs hierophant 8464:Logical biconditional 8420:, which are unused. 7575:The Geometry of Logic 7283: 7259: 7235: 7233:{\displaystyle \neg } 7199: 7175: 7151: 7127: 7125:{\displaystyle \bot } 7095: 7071: 7047: 7032:Biconditional (XNOR, 7023: 7021:{\displaystyle \top } 7003:True preserving only: 6991: 6989:{\displaystyle \lor } 6967: 6683: 6681:{\displaystyle \neg } 6663: 6643: 6641:{\displaystyle \neg } 6623: 6603: 6601:{\displaystyle \neg } 6579: 6559: 6557:{\displaystyle \neg } 6301:. This was discussed 6039: 6027: 5933: 5904: 5599:sentential connective 5126: 5114: 5105: 4938:{{{truthtable-11}}} 4935:{{{truthtable-10}}} 4927:{{{truthtable-01}}} 4924:{{{truthtable-00}}} 4884: 4857: 4829: 4757:{{{truthtable-11}}} 4754:{{{truthtable-10}}} 4746:{{{truthtable-01}}} 4743:{{{truthtable-00}}} 4685: 4658: 4656:{\displaystyle \lor } 4593:{{{truthtable-11}}} 4590:{{{truthtable-10}}} 4582:{{{truthtable-01}}} 4579:{{{truthtable-00}}} 4539: 4512: 4484: 4449: 4386:{{{truthtable-11}}} 4383:{{{truthtable-10}}} 4375:{{{truthtable-01}}} 4372:{{{truthtable-00}}} 4332: 4305: 4277: 4250: 4224: 4198: 4159:Exclusive disjunction 4133:{{{truthtable-11}}} 4130:{{{truthtable-10}}} 4122:{{{truthtable-01}}} 4119:{{{truthtable-00}}} 4032:{{{truthtable-11}}} 4029:{{{truthtable-10}}} 4021:{{{truthtable-01}}} 4018:{{{truthtable-00}}} 3930:{{{truthtable-11}}} 3927:{{{truthtable-10}}} 3919:{{{truthtable-01}}} 3916:{{{truthtable-00}}} 3858: 3856:{\displaystyle \lor } 3831: 3805: 3742:{{{truthtable-11}}} 3739:{{{truthtable-10}}} 3731:{{{truthtable-01}}} 3728:{{{truthtable-00}}} 3688: 3643: 3617: 3552:{{{truthtable-11}}} 3549:{{{truthtable-10}}} 3541:{{{truthtable-01}}} 3538:{{{truthtable-00}}} 3451:{{{truthtable-11}}} 3448:{{{truthtable-10}}} 3440:{{{truthtable-01}}} 3437:{{{truthtable-00}}} 3349:{{{truthtable-11}}} 3346:{{{truthtable-10}}} 3338:{{{truthtable-01}}} 3335:{{{truthtable-00}}} 3287: 3285:{\displaystyle \lor } 3251: 3180:{{{truthtable-11}}} 3177:{{{truthtable-10}}} 3169:{{{truthtable-01}}} 3166:{{{truthtable-00}}} 3126: 3081: 3055: 2990:{{{truthtable-11}}} 2987:{{{truthtable-10}}} 2979:{{{truthtable-01}}} 2976:{{{truthtable-00}}} 2936: 2934:{\displaystyle \lor } 2830:{{{truthtable-11}}} 2827:{{{truthtable-10}}} 2819:{{{truthtable-01}}} 2816:{{{truthtable-00}}} 2776: 2749: 2721: 2694: 2621:{{{truthtable-11}}} 2618:{{{truthtable-10}}} 2610:{{{truthtable-01}}} 2607:{{{truthtable-00}}} 2568: 2508:{{{truthtable-11}}} 2505:{{{truthtable-10}}} 2497:{{{truthtable-01}}} 2494:{{{truthtable-00}}} 2455: 2453:{\displaystyle \bot } 1452: 1444: 1384: 1348: 1331:{ ∅ , { ∅ , { ∅ } } } 1322: 1305:{ { ∅ } , { { ∅ } } } 1212: 1210:{\displaystyle \vee } 1170: 1168:{\displaystyle \top } 1144: 1142:{\displaystyle \bot } 1099: 1002: 975: 906: 698:logical biconditional 465: 205:level-5 vital article 100:Neutral point of view 8068:intuitionistic logic 7965:discourse connective 7919:I also believe your 7272: 7248: 7224: 7188: 7164: 7140: 7116: 7084: 7060: 7036: 7012: 6980: 6956: 6717:separate article on 6672: 6652: 6632: 6612: 6592: 6568: 6548: 6116:material implication 6097:If the statement "P 6042:rhombic dodecahedral 4873: 4846: 4818: 4674: 4647: 4528: 4501: 4473: 4438: 4321: 4294: 4266: 4239: 4213: 4187: 3847: 3820: 3794: 3766:Converse implication 3677: 3632: 3606: 3276: 3240: 3204:Material implication 3115: 3070: 3044: 2925: 2765: 2738: 2710: 2683: 2557: 2444: 1478:SI recommends spaces 1373: 1337: 1311: 1201: 1159: 1133: 991: 964: 664:wikiproject proposed 654:Why was this moved? 301:mathematics articles 105:No original research 7584:Logical conjunction 7268:Joint denial (NOR, 6787:that do likewise). 6292:"original research" 6131:Boolean hexadecimal 6030:Thue-Morse sequence 6018:Thue-Morse sequence 5369:Logical connectives 5357:Logical connectives 4783: 4621: 4412: 4161: 4061: 3961: 3768: 3580: 3480: 3380: 3206: 3018: 2856: 2649: 2534: 2421: 1482:thousands separator 1116: 939: 758:xor, for instance. 625:Logical equivalence 414:Philosophy articles 8081:logical connective 7818:connective (logic) 7727:logical connective 7676:connective (logic) 7278: 7254: 7230: 7194: 7170: 7146: 7122: 7090: 7066: 7042: 7018: 6986: 6962: 6938:Logical connective 6723:Logical connective 6678: 6658: 6638: 6618: 6598: 6574: 6554: 6046: 6034: 5935: 5906: 5554:logical connective 4961: 4879: 4852: 4824: 4779: 4680: 4653: 4617: 4534: 4507: 4479: 4444: 4408: 4327: 4300: 4272: 4245: 4219: 4193: 4157: 4054: 3954: 3853: 3826: 3800: 3764: 3683: 3638: 3612: 3576: 3473: 3373: 3282: 3246: 3202: 3121: 3076: 3050: 3014: 2931: 2854:Alternative denial 2852: 2771: 2744: 2716: 2689: 2645: 2563: 2530: 2450: 2417: 1996:Alternative denial 1819:Alternative denial 1698:Alternative denial 1379: 1343: 1317: 1207: 1165: 1139: 1112: 1079: 997: 970: 935: 467: 399:general discussion 270:Mathematics portal 214:content assessment 86:dispute resolution 47: 25:Logical connective 8723: 8370: 8295: 8079:is a redirect to 8059: 8045:logical constants 7869: 7809: 7808: 7783: 7756: 7725:Because they use 7668: 7618:comment added by 7602:Standard Notation 7556:lexicographically 7436: 7351: 7293: 7292: 7160:Nonimplication ( 6901: 6882: 6853: 6719:Boolean operators 6503: 6389: 6353: 6260:comment added by 6192: 6118:Q" are also true. 6011: 5974:When I touch the 5962: 5961: 5839: 5708:Boolean Operators 5670:Johnston diagrams 5641:Johnston diagrams 5587:logical operation 5583:logical connector 5463:Pontiff Greg Bard 5394:Pontiff Greg Bard 5339:Pontiff Greg Bard 5302:Pontiff Greg Bard 4960: 4959: 4953: 4952: 4942: 4941: 4772: 4771: 4761: 4760: 4608: 4607: 4597: 4596: 4401: 4400: 4390: 4389: 4148: 4147: 4137: 4136: 4047: 4046: 4036: 4035: 3945: 3944: 3934: 3933: 3757: 3756: 3746: 3745: 3567: 3566: 3556: 3555: 3466: 3465: 3455: 3454: 3364: 3363: 3353: 3352: 3195: 3194: 3184: 3183: 3005: 3004: 2994: 2993: 2845: 2844: 2834: 2833: 2636: 2635: 2625: 2624: 2566:{\displaystyle T} 2523: 2522: 2512: 2511: 2411: 2388: 2324:Pontiff Greg Bard 2315: 2314: 2231: 2196: 2164: 2120: 2119: 2109: 2108: 1981: 1943: 1942: 1932: 1931: 1825:Notation 1798: 1784: 1783: 1773: 1772: 1687: 1612:Pontiff Greg Bard 1583: 1408:logical operation 1395: 1394: 1367:{ { ∅ , { ∅ } } } 1333:- Biconditional ( 1289:{ ∅ , { { ∅ } } } 1129:- Contradiction ( 1094: 1078: 1077: 933: 901: 873: 849:Geometry of logic 826: 564: 548:comment added by 520: 519: 488: 487: 484: 483: 480: 479: 476: 475: 381:Philosophy portal 331: 330: 327: 326: 183: 182: 66:Assume good faith 43: 8827: 8719: 8360: 8285: 8188: 8171: 8155: 8151: 8150: 8077:logical operator 8049: 7941:formal semantics 7921:formal semantics 7910:associated with 7859: 7795: 7773: 7746: 7658: 7630: 7426: 7407:zero order logic 7341: 7287: 7285: 7284: 7279: 7263: 7261: 7260: 7255: 7239: 7237: 7236: 7231: 7203: 7201: 7200: 7195: 7179: 7177: 7176: 7171: 7155: 7153: 7152: 7147: 7131: 7129: 7128: 7123: 7112:Contradiction ( 7099: 7097: 7096: 7091: 7075: 7073: 7072: 7067: 7051: 7049: 7048: 7043: 7027: 7025: 7024: 7019: 6995: 6993: 6992: 6987: 6971: 6969: 6968: 6963: 6928: 6927: 6891: 6878: 6849: 6837:. Fortunately, 6781:gazillion papers 6773:A connective is 6687: 6685: 6684: 6679: 6667: 6665: 6664: 6659: 6647: 6645: 6644: 6639: 6627: 6625: 6624: 6619: 6607: 6605: 6604: 6599: 6583: 6581: 6580: 6575: 6563: 6561: 6560: 6555: 6517:function not an 6493: 6379: 6343: 6294:to me. This was 6272: 6182: 6105:Q" are alo true. 6078:not Q) = (not P 6009: 5958: 5953: 5944: 5914: 5882: 5876: 5875: 5829: 5715:Colonel Marksman 5702: 5687: 5591:logical operator 5579:Boolean operator 5390:go ahead and use 5365:logical constant 5361:logical constant 5296:Logical constant 4949: 4896: 4895: 4888: 4886: 4885: 4880: 4861: 4859: 4858: 4853: 4833: 4831: 4830: 4825: 4784: 4778: 4768: 4715: 4714: 4689: 4687: 4686: 4681: 4662: 4660: 4659: 4654: 4622: 4616: 4604: 4551: 4550: 4543: 4541: 4540: 4535: 4516: 4514: 4513: 4508: 4488: 4486: 4485: 4480: 4453: 4451: 4450: 4445: 4413: 4407: 4397: 4344: 4343: 4336: 4334: 4333: 4328: 4309: 4307: 4306: 4301: 4281: 4279: 4278: 4273: 4254: 4252: 4251: 4246: 4228: 4226: 4225: 4220: 4202: 4200: 4199: 4194: 4162: 4156: 4144: 4091: 4090: 4062: 4053: 4043: 3990: 3989: 3962: 3953: 3941: 3888: 3887: 3862: 3860: 3859: 3854: 3835: 3833: 3832: 3827: 3809: 3807: 3806: 3801: 3769: 3763: 3753: 3700: 3699: 3692: 3690: 3689: 3684: 3647: 3645: 3644: 3639: 3621: 3619: 3618: 3613: 3581: 3575: 3563: 3510: 3509: 3481: 3472: 3462: 3409: 3408: 3381: 3372: 3360: 3307: 3306: 3291: 3289: 3288: 3283: 3255: 3253: 3252: 3247: 3207: 3201: 3191: 3138: 3137: 3130: 3128: 3127: 3122: 3085: 3083: 3082: 3077: 3059: 3057: 3056: 3051: 3019: 3013: 3001: 2948: 2947: 2940: 2938: 2937: 2932: 2857: 2851: 2841: 2788: 2787: 2780: 2778: 2777: 2772: 2753: 2751: 2750: 2745: 2725: 2723: 2722: 2717: 2698: 2696: 2695: 2690: 2650: 2644: 2632: 2579: 2578: 2572: 2570: 2569: 2564: 2535: 2529: 2519: 2466: 2465: 2459: 2457: 2456: 2451: 2422: 2416: 2413: 2412: 2378: 2375:User:CBM/Sandbox 2273: 2272: 2221: 2186: 2154: 2116: 2063: 2062: 1992: 1991: 1971: 1939: 1886: 1885: 1828:Equivalent 1815: 1814: 1788: 1780: 1727: 1726: 1694: 1693: 1677: 1573: 1484:would be useful. 1388: 1386: 1385: 1380: 1369:- Conjunction ( 1352: 1350: 1349: 1344: 1326: 1324: 1323: 1318: 1216: 1214: 1213: 1208: 1174: 1172: 1171: 1166: 1148: 1146: 1145: 1140: 1117: 1084: 1006: 1004: 1003: 998: 979: 977: 976: 971: 940: 921: 891: 863: 816: 776:Logical strength 702:logical equality 573: 570:Richard B. Frost 550:Richard B. Frost 543: 506:Logical constant 497: 496: 490: 452: 442: 441: 416: 415: 412: 409: 406: 383: 378: 377: 376: 367: 360: 359: 354: 351: 340: 333: 332: 303: 302: 299: 296: 293: 272: 267: 266: 256: 249: 248: 243: 235: 228: 227: 211: 202: 201: 194: 193: 185: 179: 178: 164: 95:Article policies 16: 8835: 8834: 8830: 8829: 8828: 8826: 8825: 8824: 8750: 8749: 8716:Charles Stewart 8675: 8616: 8597: 8577: 8525: 8414: 8307: 8181: 8169: 8157: 8148: 8146: 8128: 8108: 7881: 7636: 7613: 7604: 7579:S. H. Cullinane 7547: 7273: 7270: 7269: 7249: 7246: 7245: 7225: 7222: 7221: 7211:Non-preserving: 7189: 7186: 7185: 7165: 7162: 7161: 7141: 7138: 7137: 7117: 7114: 7113: 7085: 7082: 7081: 7061: 7058: 7057: 7037: 7034: 7033: 7013: 7010: 7009: 6981: 6978: 6977: 6957: 6954: 6953: 6910: 6876:Charles Stewart 6862:— I've created 6847:Charles Stewart 6705: 6673: 6670: 6669: 6653: 6650: 6649: 6633: 6630: 6629: 6613: 6610: 6609: 6593: 6590: 6589: 6569: 6566: 6565: 6549: 6546: 6545: 6541: 6455: 6323: 6255: 6245: 5932: 5912: 5903: 5880: 5865: 5805: 5783:a AND (b OR C)) 5710: 5689: 5674: 5655: 5636: 5533: 5442: 5440:moment of doubt 5298: 4969: 4874: 4871: 4870: 4847: 4844: 4843: 4819: 4816: 4815: 4675: 4672: 4671: 4648: 4645: 4644: 4529: 4526: 4525: 4502: 4499: 4498: 4474: 4471: 4470: 4439: 4436: 4435: 4322: 4319: 4318: 4295: 4292: 4291: 4267: 4264: 4263: 4240: 4237: 4236: 4214: 4211: 4210: 4188: 4185: 4184: 3848: 3845: 3844: 3821: 3818: 3817: 3795: 3792: 3791: 3678: 3675: 3674: 3633: 3630: 3629: 3607: 3604: 3603: 3277: 3274: 3273: 3241: 3238: 3237: 3116: 3113: 3112: 3071: 3068: 3067: 3045: 3042: 3041: 2926: 2923: 2922: 2766: 2763: 2762: 2739: 2736: 2735: 2711: 2708: 2707: 2684: 2681: 2680: 2558: 2555: 2554: 2445: 2442: 2441: 2355: 2320: 1809:something like: 1642: 1554: 1540:Finite Geometry 1536: 1521: 1502: 1476:Number format: 1440: 1404: 1374: 1371: 1370: 1363:- NAND (↑ or |) 1338: 1335: 1334: 1312: 1309: 1308: 1202: 1199: 1198: 1160: 1157: 1156: 1134: 1131: 1130: 1105:represents the 992: 989: 988: 965: 962: 961: 915: 913: 912: 841:Finite Geometry 780: 666: 648:Charles Stewart 591: 567: 525: 494: 450: 413: 410: 407: 404: 403: 379: 374: 372: 352: 346: 300: 297: 294: 291: 290: 268: 261: 241: 212:on Knowledge's 209: 199: 121: 116: 115: 114: 91: 61: 12: 11: 5: 8833: 8823: 8822: 8817: 8812: 8807: 8802: 8797: 8792: 8787: 8782: 8777: 8772: 8767: 8762: 8748: 8747: 8746: 8745: 8728: 8727: 8711: 8703: 8702: 8687:EditorPerson53 8674: 8671: 8670: 8669: 8626:0), or (x: --> 8615: 8612: 8596: 8593: 8576: 8573: 8572: 8571: 8524: 8521: 8520: 8519: 8515: 8514: 8513: 8512: 8413: 8410: 8394: 8393: 8374: 8339: 8338: 8335: 8325: 8322: 8306: 8303: 8302: 8301: 8300: 8299: 8281: 8280: 8279: 8278: 8277: 8180: 8177: 8176: 8175: 8165: 8160:Justin W Smith 8127: 8124: 8107: 8104: 8040: 8039: 8038: 8037: 8002: 8001: 8000: 7999: 7998: 7997: 7954: 7953: 7916: 7915: 7880: 7877: 7876: 7875: 7874: 7873: 7852: 7851: 7850: 7849: 7842: 7841: 7840: 7839: 7833: 7832: 7807: 7806: 7803: 7799: 7793: 7792: 7765: 7764: 7763: 7762: 7761: 7760: 7743: 7742: 7741: 7714: 7713: 7712: 7711: 7692: 7635: 7632: 7620:85.231.122.178 7603: 7600: 7587: 7581: 7546: 7543: 7524: 7523: 7522: 7521: 7520: 7519: 7518: 7517: 7455:Post's lattice 7447: 7446: 7445: 7444: 7443: 7442: 7441: 7440: 7415: 7414: 7413: 7412: 7411: 7410: 7401:This applies 7394: 7393: 7392: 7391: 7390: 7389: 7358: 7357: 7356: 7355: 7334: 7333: 7295: 7294: 7291: 7290: 7277: 7253: 7229: 7213: 7207: 7206: 7193: 7169: 7145: 7121: 7109: 7103: 7102: 7089: 7065: 7056:Implication ( 7041: 7017: 7005: 6999: 6998: 6985: 6961: 6949: 6943: 6942: 6934: 6909: 6906: 6887: 6886: 6857: 6828:satisfiability 6823: 6822: 6821: 6820: 6802: 6801: 6800: 6799: 6758: 6757: 6704: 6701: 6677: 6657: 6637: 6617: 6597: 6573: 6553: 6540: 6537: 6536: 6535: 6534: 6533: 6515:interpretation 6489: 6488: 6484: 6483: 6474: 6473: 6454: 6451: 6450: 6449: 6448: 6447: 6446: 6445: 6394: 6393: 6358: 6357: 6322: 6319: 6318: 6317: 6287: 6286: 6244: 6241: 6240: 6239: 6223: 6222: 6217: 6216: 6211: 6210: 6206: 6205: 6199: 6197: 6196: 6179: 6178: 6177: 6174: 6168: 6167: 6166: 6163: 6160: 6157: 6153: 6149: 6120: 6119: 6107: 6106: 6091: 6090: 6051: 6044:Hasse diagram. 6022: 6021: 6014: 6013: 5980: 5979: 5970: 5960: 5959: 5947: 5945: 5937: 5936: 5909: 5907: 5874: 5873: 5864: 5861: 5860: 5859: 5826: 5825: 5822: 5819: 5816: 5812: 5804: 5803:Giant imagemap 5801: 5800: 5799: 5798: 5797: 5779:(a AND b) or C 5749: 5709: 5706: 5705: 5704: 5638: 5635: 5632: 5607: 5606: 5571: 5570: 5562: 5561: 5542:truth-function 5532: 5529: 5506: 5505: 5496: 5495: 5494: 5491: 5488: 5485: 5475: 5474: 5473: 5441: 5438: 5437: 5436: 5435: 5434: 5433: 5432: 5407: 5406: 5405: 5404: 5378: 5377: 5352: 5351: 5350: 5349: 5331: 5330: 5297: 5294: 5276: 5275: 5274: 5273: 5272: 5271: 5206: 5205: 5204: 5203: 5202: 5201: 5192: 5191: 5190: 5189: 5153: 5152: 5151: 5150: 5104: 5103: 5083: 5082: 5081: 5080: 5070: 5069: 5068: 5067: 5057: 5056: 5055: 5054: 5044: 5043: 5042: 5041: 5031: 5030: 5029: 5028: 5019: 5018: 5017: 5016: 5006: 5005: 5004: 5003: 4993: 4992: 4991: 4990: 4968: 4965: 4963: 4958: 4957: 4955: 4951: 4950: 4943: 4940: 4939: 4936: 4933: 4929: 4928: 4925: 4922: 4919: 4913: 4912: 4909: 4905: 4904: 4899: 4893: 4878: 4865: 4851: 4838: 4823: 4810: 4800: 4799: 4796: 4793: 4791: 4788: 4776: 4774: 4770: 4769: 4762: 4759: 4758: 4755: 4752: 4748: 4747: 4744: 4741: 4738: 4732: 4731: 4728: 4724: 4723: 4718: 4712: 4703: 4694: 4679: 4666: 4652: 4638: 4637: 4634: 4631: 4629: 4626: 4613: 4612: 4610: 4606: 4605: 4598: 4595: 4594: 4591: 4588: 4584: 4583: 4580: 4577: 4574: 4568: 4567: 4564: 4560: 4559: 4554: 4548: 4533: 4520: 4506: 4493: 4478: 4465: 4457: 4443: 4429: 4428: 4425: 4422: 4420: 4417: 4405: 4403: 4399: 4398: 4391: 4388: 4387: 4384: 4381: 4377: 4376: 4373: 4370: 4367: 4361: 4360: 4357: 4353: 4352: 4347: 4341: 4326: 4313: 4299: 4286: 4271: 4258: 4244: 4232: 4218: 4206: 4192: 4178: 4177: 4174: 4171: 4169: 4166: 4153: 4152: 4150: 4146: 4145: 4138: 4135: 4134: 4131: 4128: 4124: 4123: 4120: 4117: 4114: 4108: 4107: 4104: 4100: 4099: 4094: 4088: 4085: 4078: 4077: 4074: 4071: 4069: 4066: 4051: 4049: 4045: 4044: 4037: 4034: 4033: 4030: 4027: 4023: 4022: 4019: 4016: 4013: 4007: 4006: 4003: 3999: 3998: 3993: 3987: 3984: 3978: 3977: 3974: 3971: 3969: 3966: 3950: 3949: 3947: 3943: 3942: 3935: 3932: 3931: 3928: 3925: 3921: 3920: 3917: 3914: 3911: 3905: 3904: 3901: 3897: 3896: 3891: 3885: 3876: 3867: 3852: 3839: 3825: 3813: 3799: 3785: 3784: 3781: 3778: 3776: 3773: 3761: 3759: 3755: 3754: 3747: 3744: 3743: 3740: 3737: 3733: 3732: 3729: 3726: 3723: 3717: 3716: 3713: 3709: 3708: 3703: 3697: 3682: 3669: 3660: 3651: 3637: 3625: 3611: 3597: 3596: 3593: 3590: 3588: 3585: 3572: 3571: 3569: 3565: 3564: 3557: 3554: 3553: 3550: 3547: 3543: 3542: 3539: 3536: 3533: 3527: 3526: 3523: 3519: 3518: 3513: 3507: 3504: 3497: 3496: 3493: 3490: 3488: 3485: 3470: 3468: 3464: 3463: 3456: 3453: 3452: 3449: 3446: 3442: 3441: 3438: 3435: 3432: 3426: 3425: 3422: 3418: 3417: 3412: 3406: 3403: 3397: 3396: 3393: 3390: 3388: 3385: 3369: 3368: 3366: 3362: 3361: 3354: 3351: 3350: 3347: 3344: 3340: 3339: 3336: 3333: 3330: 3324: 3323: 3320: 3316: 3315: 3310: 3304: 3295: 3281: 3268: 3259: 3245: 3233: 3223: 3222: 3219: 3216: 3214: 3211: 3199: 3197: 3193: 3192: 3185: 3182: 3181: 3178: 3175: 3171: 3170: 3167: 3164: 3161: 3155: 3154: 3151: 3147: 3146: 3141: 3135: 3120: 3107: 3098: 3089: 3075: 3063: 3049: 3035: 3034: 3031: 3028: 3026: 3023: 3010: 3009: 3007: 3003: 3002: 2995: 2992: 2991: 2988: 2985: 2981: 2980: 2977: 2974: 2971: 2965: 2964: 2961: 2957: 2956: 2951: 2945: 2930: 2917: 2908: 2899: 2891: 2883: 2873: 2872: 2869: 2866: 2864: 2861: 2849: 2847: 2843: 2842: 2835: 2832: 2831: 2828: 2825: 2821: 2820: 2817: 2814: 2811: 2805: 2804: 2801: 2797: 2796: 2791: 2785: 2770: 2757: 2743: 2730: 2715: 2702: 2688: 2676: 2666: 2665: 2662: 2659: 2657: 2654: 2641: 2640: 2638: 2634: 2633: 2626: 2623: 2622: 2619: 2616: 2612: 2611: 2608: 2605: 2602: 2596: 2595: 2592: 2588: 2587: 2582: 2576: 2573: 2562: 2551: 2550: 2547: 2544: 2542: 2539: 2527: 2525: 2521: 2520: 2513: 2510: 2509: 2506: 2503: 2499: 2498: 2495: 2492: 2489: 2483: 2482: 2479: 2475: 2474: 2469: 2463: 2460: 2449: 2438: 2437: 2434: 2431: 2429: 2426: 2410: 2409: 2408: 2407: 2354: 2351: 2350: 2349: 2319: 2316: 2313: 2312: 2309: 2307: 2304: 2302: 2299: 2297: 2294: 2292: 2289: 2287: 2284: 2282: 2279: 2277: 2271: 2270: 2269: 2268: 2267: 2266: 2265: 2264: 2248: 2247: 2246: 2245: 2244: 2243: 2242: 2241: 2240: 2239: 2238: 2237: 2236: 2235: 2214: 2144: 2143: 2142: 2141: 2140: 2139: 2118: 2117: 2110: 2107: 2106: 2103: 2100: 2096: 2095: 2092: 2089: 2086: 2080: 2079: 2076: 2072: 2071: 2066: 2060: 2051: 2042: 2033: 2025: 2015: 2014: 2011: 2008: 2006: 2003: 1999: 1998: 1990: 1989: 1988: 1987: 1986: 1985: 1941: 1940: 1933: 1930: 1929: 1926: 1923: 1919: 1918: 1915: 1912: 1909: 1903: 1902: 1899: 1895: 1894: 1889: 1883: 1874: 1865: 1856: 1848: 1838: 1837: 1834: 1831: 1829: 1826: 1822: 1821: 1813: 1812: 1811: 1810: 1803: 1802: 1782: 1781: 1774: 1771: 1770: 1767: 1764: 1760: 1759: 1756: 1753: 1750: 1744: 1743: 1740: 1736: 1735: 1730: 1724: 1722: 1720: 1718: 1716: 1712: 1711: 1708: 1705: 1701: 1700: 1692: 1691: 1673: 1672: 1641: 1638: 1623: 1622: 1604: 1603: 1602: 1601: 1589:Right, right. 1553: 1550: 1535: 1532: 1520: 1517: 1501: 1498: 1488: 1487: 1486: 1485: 1474: 1471: 1465: 1463: 1439: 1436: 1435: 1434: 1403: 1400: 1398: 1393: 1392: 1390: 1378: 1364: 1357: 1356: 1354: 1342: 1328: 1316: 1301: 1300: 1298: 1292: 1285: 1284: 1282: 1276: 1269: 1268: 1266: 1260: 1237: 1236: 1234: 1228: 1221: 1220: 1218: 1206: 1192: 1179: 1178: 1176: 1164: 1150: 1138: 1123: 1122: 1120: 1082: 1076: 1075: 1072: 1069: 1066: 1063: 1060: 1057: 1054: 1051: 1048: 1045: 1042: 1039: 1036: 1033: 1030: 1026: 1025: 1022: 1019: 1016: 1013: 1010: 1007: 996: 986: 983: 980: 969: 959: 956: 953: 950: 947: 944: 911: 908: 907: 878: 877: 833: 832: 831: 830: 809: 808: 779: 769: 768: 767: 766: 765: 752: 751: 729: 728: 717: 694:If and only if 690: 679: 665: 662: 652: 632: 631: 614: 613: 604: 590: 587: 576:EditorPerson53 524: 521: 518: 517: 510:the discussion 498: 486: 485: 482: 481: 478: 477: 474: 473: 468: 458: 457: 455: 453: 447: 446: 438: 437: 430:Mid-importance 426: 420: 419: 417: 385: 384: 368: 356: 355: 353:Mid‑importance 341: 329: 328: 325: 324: 313: 307: 306: 304: 287:the discussion 274: 273: 257: 245: 244: 236: 224: 223: 217: 195: 181: 180: 118: 117: 113: 112: 107: 102: 93: 92: 90: 89: 82: 77: 68: 62: 60: 59: 48: 39: 38: 35: 34: 28: 9: 6: 4: 3: 2: 8832: 8821: 8818: 8816: 8813: 8811: 8808: 8806: 8803: 8801: 8798: 8796: 8793: 8791: 8788: 8786: 8783: 8781: 8778: 8776: 8773: 8771: 8768: 8766: 8763: 8761: 8758: 8757: 8755: 8744: 8740: 8736: 8732: 8731: 8730: 8729: 8726: 8722: 8718: 8717: 8712: 8709: 8705: 8704: 8699: 8698: 8697: 8696: 8692: 8688: 8684: 8681: 8678: 8668: 8664: 8660: 8656: 8652: 8647: 8646: 8645: 8642: 8638: 8634: 8630: 8619: 8611: 8610: 8606: 8602: 8592: 8591: 8587: 8583: 8570: 8566: 8562: 8559:, certainly. 8558: 8554: 8550: 8546: 8542: 8541: 8540: 8539: 8535: 8531: 8517: 8516: 8511: 8507: 8503: 8499: 8498: 8497: 8493: 8489: 8485: 8480: 8479: 8478: 8477: 8473: 8469: 8465: 8461: 8456: 8454: 8450: 8446: 8442: 8438: 8437:this category 8434: 8431:the USA, and 8430: 8426: 8421: 8419: 8409: 8408: 8404: 8400: 8392: 8388: 8384: 8380: 8375: 8373: 8368: 8364: 8358: 8355: 8354: 8353: 8352: 8348: 8344: 8336: 8333: 8329: 8326: 8323: 8320: 8316: 8312: 8311: 8310: 8298: 8293: 8289: 8282: 8276: 8272: 8268: 8264: 8260: 8257: 8253: 8250: 8249: 8248: 8244: 8240: 8235: 8234: 8233: 8229: 8225: 8221: 8220: 8219: 8215: 8211: 8207: 8203: 8202: 8201: 8200: 8196: 8192: 8187: 8174: 8170: 8168: 8162: 8161: 8154: 8145: 8144: 8143: 8142: 8138: 8134: 8123: 8122: 8118: 8114: 8103: 8102: 8098: 8094: 8093:Hugo Herbelin 8090: 8086: 8082: 8078: 8073: 8069: 8063: 8062: 8057: 8053: 8046: 8036: 8033: 8030: 8026: 8021: 8020: 8019: 8015: 8011: 8007: 8004: 8003: 7996: 7992: 7988: 7984: 7980: 7979: 7978: 7974: 7970: 7966: 7962: 7958: 7957: 7956: 7955: 7952: 7949: 7946: 7942: 7938: 7934: 7930: 7926: 7925:formal theory 7922: 7918: 7917: 7913: 7909: 7906: 7902: 7899: 7898: 7897: 7896: 7892: 7888: 7884: 7872: 7867: 7863: 7856: 7855: 7854: 7853: 7846: 7845: 7844: 7843: 7837: 7836: 7835: 7834: 7831: 7827: 7823: 7819: 7815: 7814:WP:COMMONNAME 7811: 7810: 7804: 7800: 7797: 7796: 7789: 7788: 7787: 7786: 7781: 7777: 7771: 7759: 7754: 7750: 7744: 7740: 7736: 7732: 7728: 7724: 7723: 7720: 7719: 7718: 7717: 7716: 7715: 7710: 7706: 7702: 7698: 7696: 7693: 7691: 7687: 7683: 7680: 7677: 7673: 7672: 7671: 7666: 7662: 7655: 7654: 7653: 7652: 7648: 7644: 7640: 7631: 7629: 7625: 7621: 7617: 7610: 7609: 7599: 7598: 7594: 7590: 7585: 7580: 7576: 7572: 7568: 7563: 7561: 7560:Karnaugh maps 7557: 7553: 7551: 7542: 7541: 7537: 7533: 7532:Zulu Papa 5 ☆ 7529: 7516: 7512: 7508: 7507:Zulu Papa 5 ☆ 7503: 7498: 7494: 7490: 7485: 7484: 7483: 7482: 7481: 7480: 7479: 7476: 7473: 7469: 7468: 7467: 7466: 7463: 7460: 7456: 7452: 7439: 7434: 7430: 7423: 7422: 7421: 7420: 7419: 7418: 7417: 7416: 7408: 7403: 7400: 7399: 7398: 7397: 7396: 7395: 7388: 7384: 7380: 7379:Zulu Papa 5 ☆ 7376: 7372: 7367: 7364: 7363: 7362: 7361: 7360: 7359: 7354: 7349: 7345: 7338: 7337: 7336: 7335: 7332: 7328: 7324: 7323:Zulu Papa 5 ☆ 7320: 7316: 7315:Zulu Papa 5 ☆ 7311: 7310: 7309: 7308: 7304: 7300: 7289: 7265: 7241: 7217: 7214: 7212: 7209: 7208: 7205: 7191: 7181: 7167: 7157: 7143: 7133: 7110: 7108: 7105: 7104: 7101: 7077: 7053: 7029: 7006: 7004: 7001: 7000: 6997: 6983: 6973: 6959: 6950: 6948: 6945: 6944: 6941: 6939: 6935: 6933: 6930: 6929: 6926: 6925: 6924: 6923: 6919: 6915: 6914:Zulu Papa 5 ☆ 6905: 6904: 6899: 6895: 6885: 6881: 6877: 6873: 6869: 6865: 6861: 6858: 6856: 6852: 6848: 6844: 6843:unsatisfiable 6840: 6836: 6832: 6829: 6825: 6824: 6819: 6815: 6811: 6806: 6805: 6804: 6803: 6798: 6794: 6790: 6786: 6782: 6778: 6776: 6775:compositional 6770: 6766: 6762: 6761: 6760: 6759: 6756: 6753: 6750: 6746: 6743: 6739: 6738: 6737: 6736: 6732: 6728: 6724: 6720: 6715: 6712:. Of course 6711: 6700: 6699: 6695: 6691: 6655: 6615: 6587: 6584:&c which 6571: 6532: 6528: 6524: 6520: 6516: 6512: 6508: 6507: 6506: 6501: 6497: 6491: 6490: 6486: 6485: 6481: 6476: 6475: 6471: 6470: 6469: 6468: 6464: 6460: 6444: 6440: 6436: 6432: 6428: 6424: 6420: 6416: 6415: 6414: 6413: 6412: 6409: 6406: 6401: 6396: 6395: 6392: 6387: 6383: 6377: 6376: 6375: 6374: 6370: 6366: 6362: 6356: 6351: 6347: 6341: 6340: 6339: 6338: 6334: 6330: 6326: 6316: 6312: 6308: 6304: 6300: 6297: 6293: 6289: 6288: 6285: 6282: 6279: 6275: 6274: 6273: 6271: 6267: 6263: 6262:69.227.129.30 6259: 6253: 6252:the one above 6249: 6238: 6234: 6230: 6225: 6224: 6219: 6218: 6213: 6212: 6208: 6207: 6202: 6201: 6200: 6195: 6190: 6186: 6180: 6175: 6172: 6171: 6169: 6164: 6161: 6158: 6154: 6150: 6147: 6146: 6143: 6142: 6141: 6140: 6136: 6132: 6127: 6125: 6117: 6113: 6109: 6108: 6104: 6100: 6096: 6095: 6094: 6089: 6085: 6081: 6077: 6073: 6069: 6068: 6067: 6064: 6062: 6057: 6052: 6050: 6043: 6038: 6031: 6026: 6019: 6015: 6007: 6006: 6001: 6000: 5995: 5994:Venn diagrams 5991: 5990:Hasse diagram 5988: 5985: 5981: 5977: 5973: 5972: 5971: 5969: 5965: 5957: 5952: 5948: 5946: 5943: 5939: 5938: 5910: 5878: 5877: 5872: 5870: 5867: 5866: 5858: 5854: 5850: 5845: 5844: 5843: 5842: 5837: 5833: 5823: 5820: 5817: 5813: 5810: 5809: 5808: 5796: 5792: 5788: 5784: 5780: 5776: 5772: 5768: 5763: 5758: 5754: 5750: 5747: 5743: 5742: 5741: 5738: 5735: 5731: 5727: 5726: 5725: 5724: 5720: 5716: 5700: 5696: 5692: 5685: 5681: 5677: 5671: 5667: 5666: 5665: 5663: 5659: 5654: 5650: 5646: 5642: 5634:Venn Diagrams 5631: 5630: 5626: 5622: 5616: 5615: 5612: 5604: 5600: 5596: 5592: 5588: 5584: 5580: 5576: 5575: 5574: 5567: 5566: 5565: 5559: 5555: 5551: 5547: 5546: 5545: 5543: 5539: 5528: 5527: 5523: 5519: 5515: 5511: 5504: 5501: 5497: 5492: 5489: 5486: 5483: 5482: 5480: 5476: 5472: 5468: 5464: 5460: 5459: 5458: 5455: 5452: 5448: 5447: 5446: 5431: 5427: 5423: 5418: 5413: 5412: 5411: 5410: 5409: 5408: 5403: 5399: 5395: 5391: 5387: 5382: 5381: 5380: 5379: 5374: 5370: 5366: 5362: 5358: 5354: 5353: 5348: 5344: 5340: 5335: 5334: 5333: 5332: 5329: 5326: 5323: 5318: 5314: 5313: 5312: 5311: 5307: 5303: 5293: 5290: 5289: 5285: 5281: 5270: 5266: 5262: 5258: 5254: 5250: 5246: 5242: 5238: 5234: 5230: 5226: 5221: 5217: 5212: 5211: 5210: 5209: 5208: 5207: 5198: 5197: 5196: 5195: 5194: 5193: 5188: 5184: 5180: 5175: 5174: 5173: 5172: 5171: 5170: 5166: 5162: 5158: 5149: 5145: 5141: 5137: 5136: 5135: 5134: 5133: 5129: 5125: 5122: 5117: 5113: 5109: 5101: 5100: 5099: 5098: 5094: 5090: 5086: 5078: 5077: 5076: 5075: 5074: 5065: 5064: 5063: 5062: 5061: 5052: 5051: 5050: 5049: 5048: 5039: 5038: 5037: 5036: 5035: 5026: 5025: 5024: 5023: 5022: 5014: 5013: 5012: 5011: 5010: 5001: 5000: 4999: 4998: 4997: 4988: 4987: 4986: 4985: 4984: 4981: 4978: 4972: 4964: 4956: 4948: 4944: 4937: 4934: 4931: 4930: 4926: 4923: 4920: 4918: 4914: 4910: 4907: 4906: 4903: 4897: 4894: 4892: 4876: 4869: 4864: 4849: 4842: 4837: 4821: 4814: 4811: 4809: 4805: 4802: 4801: 4798:Venn diagram 4797: 4794: 4789: 4786: 4785: 4782: 4777: 4775: 4767: 4763: 4756: 4753: 4750: 4749: 4745: 4742: 4739: 4737: 4733: 4729: 4726: 4725: 4722: 4716: 4713: 4711: 4707: 4702: 4698: 4693: 4670: 4667: 4665: 4650: 4643: 4640: 4639: 4636:Venn diagram 4635: 4632: 4627: 4624: 4623: 4620: 4615: 4614: 4611: 4603: 4599: 4592: 4589: 4586: 4585: 4581: 4578: 4575: 4573: 4569: 4565: 4562: 4561: 4558: 4552: 4549: 4547: 4524: 4519: 4504: 4497: 4492: 4476: 4469: 4466: 4464: 4460: 4456: 4434: 4431: 4430: 4427:Venn diagram 4426: 4423: 4418: 4415: 4414: 4411: 4410:Biconditional 4406: 4404: 4396: 4392: 4385: 4382: 4379: 4378: 4374: 4371: 4368: 4366: 4362: 4358: 4355: 4354: 4351: 4345: 4342: 4340: 4324: 4317: 4312: 4290: 4285: 4262: 4259: 4257: 4242: 4235: 4231: 4216: 4209: 4205: 4190: 4183: 4180: 4179: 4176:Venn diagram 4175: 4172: 4167: 4164: 4163: 4160: 4155: 4154: 4151: 4143: 4139: 4132: 4129: 4126: 4125: 4121: 4118: 4115: 4113: 4109: 4105: 4102: 4101: 4098: 4092: 4089: 4086: 4084: 4080: 4079: 4076:Venn diagram 4075: 4072: 4067: 4064: 4063: 4060: 4059: 4052: 4050: 4042: 4038: 4031: 4028: 4025: 4024: 4020: 4017: 4014: 4012: 4008: 4004: 4001: 4000: 3997: 3991: 3988: 3985: 3983: 3980: 3979: 3976:Venn diagram 3975: 3972: 3967: 3964: 3963: 3960: 3959: 3952: 3951: 3948: 3940: 3936: 3929: 3926: 3923: 3922: 3918: 3915: 3912: 3910: 3906: 3902: 3899: 3898: 3895: 3889: 3886: 3884: 3880: 3875: 3871: 3866: 3850: 3843: 3840: 3838: 3823: 3816: 3812: 3790: 3787: 3786: 3783:Venn diagram 3782: 3779: 3774: 3771: 3770: 3767: 3762: 3760: 3752: 3748: 3741: 3738: 3735: 3734: 3730: 3727: 3724: 3722: 3718: 3714: 3711: 3710: 3707: 3701: 3698: 3696: 3680: 3673: 3668: 3664: 3659: 3655: 3652: 3650: 3635: 3628: 3624: 3609: 3602: 3599: 3598: 3595:Venn diagram 3594: 3591: 3586: 3583: 3582: 3579: 3574: 3573: 3570: 3562: 3558: 3551: 3548: 3545: 3544: 3540: 3537: 3534: 3532: 3528: 3524: 3521: 3520: 3517: 3511: 3508: 3505: 3503: 3499: 3498: 3495:Venn diagram 3494: 3491: 3486: 3483: 3482: 3479: 3478: 3471: 3469: 3461: 3457: 3450: 3447: 3444: 3443: 3439: 3436: 3433: 3431: 3427: 3423: 3420: 3419: 3416: 3410: 3407: 3404: 3402: 3399: 3398: 3395:Venn diagram 3394: 3391: 3386: 3383: 3382: 3379: 3378: 3371: 3370: 3367: 3359: 3355: 3348: 3345: 3342: 3341: 3337: 3334: 3331: 3329: 3325: 3321: 3318: 3317: 3314: 3308: 3305: 3303: 3299: 3294: 3279: 3272: 3267: 3263: 3260: 3258: 3243: 3236: 3232: 3228: 3225: 3224: 3221:Venn diagram 3220: 3217: 3212: 3209: 3208: 3205: 3200: 3198: 3190: 3186: 3179: 3176: 3173: 3172: 3168: 3165: 3162: 3160: 3156: 3152: 3149: 3148: 3145: 3139: 3136: 3134: 3118: 3111: 3106: 3102: 3097: 3093: 3090: 3088: 3073: 3066: 3062: 3047: 3040: 3037: 3036: 3033:Venn diagram 3032: 3029: 3024: 3021: 3020: 3017: 3012: 3011: 3008: 3000: 2996: 2989: 2986: 2983: 2982: 2978: 2975: 2972: 2970: 2966: 2962: 2959: 2958: 2955: 2949: 2946: 2944: 2928: 2921: 2916: 2912: 2907: 2903: 2900: 2898: 2894: 2890: 2886: 2882: 2878: 2875: 2874: 2871:Venn diagram 2870: 2867: 2862: 2859: 2858: 2855: 2850: 2848: 2840: 2836: 2829: 2826: 2823: 2822: 2818: 2815: 2812: 2810: 2806: 2802: 2799: 2798: 2795: 2789: 2786: 2784: 2761: 2756: 2741: 2734: 2729: 2713: 2706: 2703: 2701: 2686: 2679: 2675: 2671: 2668: 2667: 2664:Venn diagram 2663: 2660: 2655: 2652: 2651: 2648: 2643: 2642: 2639: 2631: 2627: 2620: 2617: 2614: 2613: 2609: 2606: 2603: 2601: 2597: 2593: 2590: 2589: 2586: 2580: 2577: 2574: 2560: 2553: 2552: 2549:Venn diagram 2548: 2545: 2540: 2537: 2536: 2533: 2528: 2526: 2518: 2514: 2507: 2504: 2501: 2500: 2496: 2493: 2490: 2488: 2484: 2480: 2477: 2476: 2473: 2467: 2464: 2461: 2440: 2439: 2436:Venn diagram 2435: 2432: 2427: 2424: 2423: 2420: 2419:Contradiction 2415: 2414: 2406: 2402: 2398: 2393: 2392: 2391: 2386: 2382: 2376: 2372: 2371: 2370: 2369: 2365: 2361: 2348: 2344: 2340: 2336: 2335: 2334: 2333: 2329: 2325: 2310: 2308: 2305: 2303: 2300: 2298: 2295: 2293: 2290: 2288: 2285: 2283: 2280: 2278: 2275: 2274: 2263: 2260: 2256: 2255: 2254: 2253: 2252: 2251: 2250: 2249: 2234: 2229: 2225: 2219: 2215: 2213: 2209: 2205: 2201: 2200: 2199: 2194: 2190: 2183: 2182: 2181: 2177: 2173: 2169: 2168: 2167: 2162: 2158: 2152: 2151: 2150: 2149: 2148: 2147: 2146: 2145: 2138: 2134: 2130: 2126: 2125: 2124: 2123: 2122: 2121: 2115: 2111: 2104: 2101: 2098: 2097: 2093: 2090: 2087: 2085: 2081: 2077: 2074: 2073: 2070: 2064: 2061: 2059: 2055: 2050: 2046: 2041: 2037: 2034: 2032: 2028: 2024: 2020: 2017: 2016: 2013:Venn diagram 2012: 2009: 2004: 2001: 2000: 1997: 1993: 1984: 1979: 1975: 1968: 1967: 1966: 1962: 1958: 1954: 1953: 1952: 1949: 1945: 1944: 1938: 1934: 1927: 1924: 1921: 1920: 1916: 1913: 1910: 1908: 1904: 1900: 1897: 1896: 1893: 1887: 1884: 1882: 1878: 1873: 1869: 1864: 1860: 1857: 1855: 1851: 1847: 1843: 1840: 1839: 1836:Venn diagram 1835: 1832: 1827: 1824: 1823: 1820: 1816: 1807: 1806: 1805: 1804: 1801: 1796: 1792: 1786: 1785: 1779: 1775: 1768: 1765: 1762: 1761: 1757: 1754: 1751: 1749: 1745: 1741: 1738: 1737: 1734: 1728: 1725: 1714: 1713: 1710:Venn diagram 1709: 1706: 1703: 1702: 1699: 1695: 1690: 1685: 1681: 1675: 1674: 1671: 1668: 1664: 1659: 1658: 1657: 1656: 1652: 1648: 1637: 1636: 1632: 1628: 1621: 1617: 1613: 1610: 1606: 1605: 1600: 1596: 1592: 1588: 1587: 1586: 1581: 1577: 1571: 1570: 1569: 1568: 1564: 1560: 1549: 1548: 1545: 1541: 1531: 1530: 1527: 1524:connective.-- 1516: 1515: 1512: 1507: 1497: 1496: 1493: 1483: 1479: 1475: 1472: 1469: 1468: 1466: 1461: 1459: 1458: 1456: 1451: 1447: 1443: 1433: 1430: 1426: 1422: 1421: 1420: 1419: 1416: 1413: 1409: 1399: 1391: 1376: 1368: 1365: 1362: 1359: 1358: 1355: 1340: 1332: 1329: 1314: 1306: 1303: 1302: 1299: 1296: 1293: 1290: 1287: 1286: 1283: 1280: 1277: 1274: 1273:{ { { ∅ } } } 1271: 1270: 1267: 1264: 1261: 1258: 1255: 1252: 1249: 1245: 1242: 1239: 1238: 1235: 1232: 1229: 1226: 1223: 1222: 1219: 1204: 1196: 1193: 1190: 1187: 1184: 1181: 1180: 1177: 1155:- Tautology ( 1154: 1151: 1128: 1125: 1124: 1121: 1119: 1118: 1115: 1110: 1108: 1104: 1098: 1097: 1092: 1088: 1073: 1070: 1067: 1064: 1061: 1058: 1055: 1052: 1049: 1046: 1043: 1040: 1037: 1034: 1031: 1028: 1027: 1023: 1020: 1017: 1014: 1011: 1008: 994: 987: 984: 981: 967: 960: 957: 954: 951: 948: 945: 942: 941: 938: 932: 931: 927: 925: 919: 905: 904: 899: 895: 888: 883: 876: 871: 867: 860: 859: 858: 857: 854: 850: 846: 842: 838: 837:Hasse diagram 829: 824: 820: 813: 812: 811: 810: 807: 804: 799: 798: 797: 796: 793: 789: 785: 777: 773: 764: 761: 756: 755: 754: 753: 750: 747: 743: 739: 738: 737: 736: 733: 726: 722: 718: 715: 711: 707: 703: 699: 695: 691: 688: 684: 680: 677: 676: 675: 672: 671: 661: 660: 657: 651: 649: 643: 641: 637: 630: 626: 622: 619: 618: 617: 612: 608: 605: 603: 599: 596: 595: 594: 586: 585: 581: 577: 571: 565: 563: 559: 555: 551: 547: 540: 538: 533: 529: 515: 511: 507: 503: 499: 492: 491: 472: 464: 460: 459: 456: 454: 449: 448: 443: 439: 435: 431: 425: 422: 421: 418: 401: 400: 395: 391: 390: 382: 371: 369: 366: 362: 361: 357: 350: 345: 342: 339: 335: 334: 322: 318: 312: 309: 308: 305: 288: 284: 280: 279: 271: 265: 260: 258: 255: 251: 250: 246: 240: 237: 234: 230: 229: 225: 221: 215: 207: 206: 196: 192: 187: 186: 177: 173: 170: 167: 163: 159: 155: 152: 149: 146: 143: 140: 137: 134: 131: 127: 124: 123:Find sources: 120: 119: 111: 110:Verifiability 108: 106: 103: 101: 98: 97: 96: 87: 83: 81: 78: 76: 72: 69: 67: 64: 63: 57: 53: 52:Learn to edit 49: 46: 41: 40: 37: 36: 32: 26: 22: 18: 17: 8715: 8685: 8682: 8679: 8676: 8643: 8639: 8635: 8631: 8625:0 AND y: --> 8620: 8617: 8598: 8578: 8556: 8552: 8548: 8544: 8526: 8457: 8428: 8422: 8415: 8395: 8340: 8327: 8308: 8182: 8163: 8158: 8152: 8129: 8113:86.0.254.239 8109: 8064: 8041: 8029:Arthur Rubin 8005: 7945:Arthur Rubin 7904: 7900: 7882: 7770:linear logic 7766: 7726: 7637: 7611: 7605: 7564: 7548: 7525: 7488: 7448: 7296: 7210: 7106: 7008:Tautology ( 7002: 6946: 6936: 6931: 6911: 6888: 6875: 6868:model theory 6859: 6846: 6841:does define 6839:model theory 6785:linear logic 6772: 6768: 6764: 6749:Arthur Rubin 6744: 6741: 6713: 6706: 6703:Boolean bias 6585: 6542: 6519:interpretive 6518: 6514: 6510: 6479: 6456: 6419:Karnaugh Map 6363: 6359: 6327: 6324: 6246: 6198: 6128: 6121: 6092: 6082:Q) = (not P 6065: 6053: 6048: 6047: 6004: 5998: 5967: 5966: 5963: 5868: 5827: 5806: 5782: 5778: 5770: 5767:and, or, not 5766: 5756: 5753:George Boole 5734:Arthur Rubin 5729: 5711: 5698: 5694: 5690: 5683: 5679: 5675: 5637: 5621:Rick Norwood 5617: 5608: 5602: 5598: 5594: 5590: 5586: 5582: 5578: 5572: 5563: 5553: 5540:is called a 5537: 5534: 5518:Rick Norwood 5513: 5512:rather than 5509: 5507: 5478: 5451:Arthur Rubin 5443: 5416: 5389: 5372: 5368: 5364: 5360: 5356: 5322:Arthur Rubin 5316: 5299: 5291: 5280:Rick Norwood 5277: 5256: 5252: 5248: 5244: 5240: 5236: 5232: 5228: 5224: 5219: 5215: 5179:Rick Norwood 5156: 5154: 5140:Rick Norwood 5131: 5127: 5123: 5119: 5115: 5111: 5106: 5089:Rick Norwood 5087: 5084: 5071: 5058: 5045: 5032: 5020: 5007: 4994: 4982: 4973: 4970: 4962: 4954: 4916: 4901: 4890: 4867: 4862: 4840: 4835: 4812: 4807: 4803: 4795:Truth table 4781:Joint denial 4773: 4735: 4720: 4709: 4705: 4700: 4696: 4691: 4668: 4663: 4641: 4633:Truth table 4609: 4571: 4556: 4545: 4522: 4517: 4495: 4490: 4467: 4462: 4458: 4454: 4432: 4424:Truth table 4402: 4364: 4349: 4338: 4315: 4310: 4288: 4283: 4260: 4255: 4233: 4229: 4207: 4203: 4181: 4173:Truth table 4149: 4111: 4096: 4082: 4073:Truth table 4057: 4056:Negation of 4048: 4010: 3995: 3981: 3973:Truth table 3957: 3956:Proposition 3946: 3908: 3893: 3882: 3878: 3873: 3869: 3864: 3841: 3836: 3814: 3810: 3788: 3780:Truth table 3758: 3720: 3705: 3694: 3671: 3666: 3662: 3657: 3653: 3648: 3626: 3622: 3600: 3592:Truth table 3568: 3530: 3515: 3501: 3492:Truth table 3476: 3475:Negation of 3467: 3429: 3414: 3400: 3392:Truth table 3376: 3375:Proposition 3365: 3327: 3312: 3301: 3297: 3292: 3270: 3265: 3261: 3256: 3234: 3230: 3226: 3218:Truth table 3196: 3158: 3143: 3132: 3109: 3104: 3100: 3095: 3091: 3086: 3064: 3060: 3038: 3030:Truth table 3006: 2968: 2953: 2942: 2919: 2914: 2910: 2905: 2901: 2896: 2892: 2888: 2884: 2880: 2876: 2868:Truth table 2846: 2808: 2793: 2782: 2759: 2754: 2732: 2727: 2704: 2699: 2677: 2673: 2669: 2661:Truth table 2637: 2599: 2584: 2546:Truth table 2524: 2486: 2471: 2433:Truth table 2356: 2321: 2083: 2068: 2057: 2053: 2048: 2044: 2039: 2035: 2030: 2026: 2022: 2018: 2010:Truth table 1906: 1891: 1880: 1876: 1871: 1867: 1862: 1858: 1853: 1849: 1845: 1841: 1833:Truth table 1747: 1732: 1707:Truth table 1643: 1624: 1608: 1555: 1537: 1522: 1505: 1503: 1492:75.15.135.58 1489: 1453: 1449: 1445: 1441: 1424: 1405: 1397: 1366: 1360: 1330: 1304: 1294: 1288: 1278: 1272: 1262: 1256: 1253: 1250: 1247: 1243: 1240: 1230: 1224: 1194: 1188: 1185: 1182: 1152: 1126: 1113: 1102: 1100: 1081: 936: 928: 914: 886: 879: 834: 788:Arthur Rubin 783: 781: 775: 771: 742:Arthur Rubin 730: 719:D) unifying 687:venn diagram 673: 667: 653: 644: 642:at present. 635: 633: 615: 592: 566: 541: 534: 530: 526: 513: 429: 397: 387: 317:Mid-priority 316: 276: 242:Mid‑priority 220:WikiProjects 203: 171: 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NOR (↓) 1107:empty set 924:tesseract 882:this link 721:main page 656:Dysprosia 208:is rated 88:if needed 71:Be polite 21:talk page 8708:WP:LOGIC 8460:this one 8433:this one 8425:This map 8259:symbolic 8256:negative 8085:operator 7969:Tijfo098 7905:informal 7887:Tijfo098 7822:Tijfo098 7731:Tijfo098 7701:Tijfo098 7682:Tijfo098 7643:Tijfo098 7616:unsigned 7528:validity 7493:validity 7371:ontology 6258:unsigned 6074:Q) = (P 5531:New lede 5479:in logic 5373:kangaroo 4967:The lede 1467:Grammar 853:Gregbard 803:Gregbard 778:sections 760:Gregbard 732:Gregbard 716:; others 714:NOR gate 640:Negation 558:contribs 546:unsigned 56:get help 29:This is 27:article. 8547:, then 8523:only if 8502:Lipedia 8468:Lipedia 8210:Lipedia 8126:Writing 7589:Lipedia 6765:meaning 6745:meaning 6690:Philogo 6523:Philogo 6459:Philogo 6435:Philogo 6423:Philogo 6181:— Carl 6056:wapedia 5976:nibbles 5828:— Carl 5785:etc. -- 5611:Lambiam 5500:Lambiam 5216:nullary 3094:& ¬ 2259:Lambiam 1948:Lambiam 1721:¬P ← Q 1719:P → ¬Q 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