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Semantics of logic

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will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. The semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested;
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outfitted with such a semantics. The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever (and hence its name
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and has been shown equivalent to and a natural generalization of truth-value semantics. Like truth-value semantics, it is also non-referential in nature.
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in the spirit of Aristotle's syllogisms, but with the generality of modern logics based on the quantifier.
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associates the meaning of propositions with the roles that they can play in inferences.
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the logician traditionally is not interested in the sentence as uttered but in the
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are generally seen as the founders of this approach; it is heavily influenced by
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The main modern approaches to semantics for formal languages are the following:
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Study of the semantics, or interpretations, of formal and natural languages
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Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning
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An Essay Towards a Real Character, and a Philosophical Language
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introduces innovations, but is broadly in the Tarskian mold.
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usually trying to capture the pre-theoretic notion of
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has given some results in the areas of adequacy for
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There might be a discussion about this on 636:in the early 1960s and later championed by 61:Learn how and when to remove these messages 3268:Wittgenstein on Rules and Private Language 2558: 2551: 2537: 978: 793: 779: 445: 431: 564:, and is one of the founding concepts of 497:of various sentences we may encounter in 235:Learn how and when to remove this message 217:Learn how and when to remove this message 158:Learn how and when to remove this message 748:, Cambridge: Cambridge University Press. 676:, which were originally investigated by 14: 3386: 800: 2532: 774: 169: 96:adding citations to reliable sources 67: 26: 3419:Formal semantics (natural language) 728:Formal semantics (natural language) 24: 758:, Oxford: Oxford University Press. 509:Until the advent of modern logic, 469:is the study of the semantics, or 25: 3430: 312:Semantics (programming languages) 42:This article has multiple issues. 2512: 707: 674:partially ordered quantification 668:made a resurgence mainly due to 250:For the linguistics branch, see 174: 72: 31: 83:needs additional citations for 50:or discuss these issues on the 3208:Tractatus Logico-Philosophicus 624:(also commonly referred to as 531:problem of multiple generality 13: 1: 3089:Principle of compositionality 2473:History of mathematical logic 733: 626:substitutional quantification 3238:Philosophical Investigations 2398:Primitive recursive function 7: 3079:Modality (natural language) 756:Critical Scientific Realism 700: 582:truth-conditional semantics 574:first-order predicate logic 488: 397:Programming language theory 392:Natural language processing 10: 3435: 3218:Language, Truth, and Logic 2958:Theological noncognitivism 2843:Contrast theory of meaning 2838:Causal theory of reference 2569:Index of language articles 1462:Schröder–Bernstein theorem 1189:Monadic predicate calculus 848:Foundations of mathematics 666:game-theoretical semantics 256:Semantics (disambiguation) 249: 3358: 3303:Philosophy of information 3290: 3139: 2991: 2903:Mediated reference theory 2828: 2575: 2566: 2508: 2495:Philosophy of mathematics 2444:Automated theorem proving 2426: 2321: 2153: 2046: 1898: 1615: 1591: 1569:Von Neumann–Bernays–Gödel 1514: 1408: 1312: 1210: 1201: 1128: 1063: 969: 891: 808: 597:Proof-theoretic semantics 584:, which was pioneered by 550:model-theoretic semantics 417:Automated theorem proving 402:Computational linguistics 3228:Two Dogmas of Empiricism 558:semantic theory of truth 18:Formal semantics (logic) 3029:Use–mention distinction 2873:Direct reference theory 2145:Self-verifying theories 1966:Tarski's axiomatization 917:Tarski's undefinability 912:incompleteness theorems 761:John N. Martin (2019), 689:Probabilistic semantics 672:for logics of (finite) 477:and (idealizations of) 3404:Philosophy of language 2963:Theory of descriptions 2898:Linguistic determinism 2560:Philosophy of language 2519:Mathematics portal 2130:Proof of impossibility 1778:propositional variable 1088:Propositional calculus 529:, needed to solve the 377:Propositional calculus 254:. For other uses, see 3414:Theories of deduction 3074:Mental representation 3009:Linguistic relativity 2893:Inquisitive semantics 2388:Kolmogorov complexity 2341:Computably enumerable 2241:Model complete theory 2033:Principia Mathematica 1093:Propositional formula 922:Banach–Tarski paradox 654:truth-value semantics 621:Truth-value semantics 537:, attempting to find 387:Mathematical notation 3258:Naming and Necessity 3168:De Arte Combinatoria 2967:Definite description 2928:Semantic externalism 2336:Church–Turing thesis 2323:Computability theory 1532:continuum hypothesis 1050:Square of opposition 908:Gödel's completeness 187:confusing or unclear 107:"Semantics of logic" 92:improve this article 3308:Philosophical logic 3298:Analytic philosophy 3104:Sense and reference 2983:Verification theory 2938:Situation semantics 2490:Mathematical object 2381:P versus NP problem 2346:Computable function 2140:Reverse mathematics 2066:Logical consequence 1943:primitive recursive 1938:elementary function 1711:Free/bound variable 1564:Tarski–Grothendieck 1083:Logical connectives 1013:Logical equivalence 863:Logical consequence 723:Algebraic semantics 628:) was advocated by 614:Ludwig Wittgenstein 483:logical consequence 412:Formal verification 327:Well-formed formula 195:clarify the article 3394:Mathematical logic 3158:Port-Royal Grammar 3054:Family resemblance 2973:Theory of language 2948:Supposition theory 2288:Transfer principle 2251:Semantics of logic 2236:Categorical theory 2212:Non-standard model 1726:Logical connective 853:Information theory 802:Mathematical logic 682:Henkin quantifiers 650:intensional logics 630:Ruth Barcan Marcus 522:De Interpretatione 463:semantics of logic 337:Regular expression 3381: 3380: 2883:Dynamic semantics 2526: 2525: 2458:Abstract category 2261:Theories of truth 2071:Rule of inference 2061:Natural deduction 2042: 2041: 1587: 1586: 1292:Cartesian product 1197: 1196: 1103:Many-valued logic 1078:Boolean functions 961:Russell's paradox 936:diagonal argument 833:First-order logic 715:Philosophy portal 548:The archetype of 479:natural languages 455: 454: 347:Ground expression 307:Semantics (logic) 245: 244: 237: 227: 226: 219: 168: 167: 160: 142: 65: 16:(Redirected from 3426: 3343:Formal semantics 3291:Related articles 3283: 3273: 3263: 3253: 3243: 3233: 3223: 3213: 3203: 3193: 3183: 3173: 3163: 3153: 2923:Relevance theory 2918:Phallogocentrism 2553: 2546: 2539: 2530: 2529: 2517: 2516: 2468:History of logic 2463:Category of sets 2356:Decision problem 2135:Ordinal analysis 2076:Sequent calculus 1974:Boolean algebras 1914: 1913: 1888: 1859:logical/constant 1613: 1612: 1599: 1522:Zermelo–Fraenkel 1273:Set operations: 1208: 1207: 1145: 976: 975: 956:Löwenheim–Skolem 843:Formal semantics 795: 788: 781: 772: 771: 752:Ilkka Niiniluoto 717: 712: 711: 710: 692:originated from 590:Kripke semantics 495:truth conditions 475:formal languages 467:formal semantics 447: 440: 433: 276:Formal languages 261: 260: 240: 233: 222: 215: 211: 208: 202: 178: 177: 170: 163: 156: 152: 149: 143: 141: 100: 76: 68: 57: 35: 34: 27: 21: 3434: 3433: 3429: 3428: 3427: 3425: 3424: 3423: 3384: 3383: 3382: 3377: 3354: 3333:School of Names 3286: 3281: 3271: 3261: 3251: 3248:Of Grammatology 3241: 3231: 3221: 3211: 3201: 3191: 3181: 3171: 3161: 3151: 3135: 2987: 2933:Semantic holism 2913:Non-cognitivism 2853:Conventionalism 2824: 2571: 2562: 2557: 2527: 2522: 2511: 2504: 2449:Category theory 2439:Algebraic logic 2422: 2393:Lambda calculus 2331:Church encoding 2317: 2293:Truth predicate 2149: 2115:Complete theory 2038: 1907: 1903: 1899: 1894: 1886: 1606: and  1602: 1597: 1583: 1559:New Foundations 1527:axiom of choice 1510: 1472:Gödel numbering 1412: and  1404: 1308: 1193: 1143: 1124: 1073:Boolean algebra 1059: 1023:Equiconsistency 988:Classical logic 965: 946:Halting problem 934: and  910: and  898: and  897: 892:Theorems ( 887: 804: 799: 740:Jaakko Hintikka 736: 713: 708: 706: 703: 670:Jaakko Hintikka 638:J. Michael Dunn 610:Michael Dummett 602:Gerhard Gentzen 586:Donald Davidson 560:, based on his 491: 471:interpretations 451: 422: 421: 407:Syntax analysis 382:Predicate logic 367: 366: 357: 356: 332:Automata theory 287: 286: 259: 248: 241: 230: 229: 228: 223: 212: 206: 203: 192: 179: 175: 164: 153: 147: 144: 101: 99: 89: 77: 36: 32: 23: 22: 15: 12: 11: 5: 3432: 3422: 3421: 3416: 3411: 3406: 3401: 3396: 3379: 3378: 3376: 3375: 3370: 3365: 3359: 3356: 3355: 3353: 3352: 3347: 3346: 3345: 3335: 3330: 3325: 3320: 3315: 3310: 3305: 3300: 3294: 3292: 3288: 3287: 3285: 3284: 3274: 3264: 3254: 3244: 3234: 3224: 3214: 3204: 3194: 3184: 3174: 3164: 3154: 3143: 3141: 3137: 3136: 3134: 3133: 3126: 3121: 3116: 3111: 3106: 3101: 3096: 3091: 3086: 3084:Presupposition 3081: 3076: 3071: 3066: 3061: 3056: 3051: 3046: 3041: 3036: 3031: 3026: 3021: 3016: 3011: 3006: 3001: 2995: 2993: 2989: 2988: 2986: 2985: 2980: 2975: 2970: 2960: 2955: 2950: 2945: 2940: 2935: 2930: 2925: 2920: 2915: 2910: 2905: 2900: 2895: 2890: 2885: 2880: 2875: 2870: 2865: 2863:Deconstruction 2860: 2855: 2850: 2845: 2840: 2834: 2832: 2826: 2825: 2823: 2822: 2817: 2812: 2807: 2802: 2797: 2792: 2787: 2782: 2777: 2772: 2767: 2762: 2757: 2752: 2747: 2742: 2737: 2732: 2727: 2722: 2717: 2712: 2707: 2702: 2697: 2692: 2687: 2682: 2677: 2672: 2667: 2662: 2657: 2652: 2647: 2642: 2637: 2632: 2627: 2622: 2617: 2612: 2607: 2602: 2597: 2592: 2587: 2581: 2579: 2573: 2572: 2567: 2564: 2563: 2556: 2555: 2548: 2541: 2533: 2524: 2523: 2509: 2506: 2505: 2503: 2502: 2497: 2492: 2487: 2482: 2481: 2480: 2470: 2465: 2460: 2451: 2446: 2441: 2436: 2434:Abstract logic 2430: 2428: 2424: 2423: 2421: 2420: 2415: 2413:Turing machine 2410: 2405: 2400: 2395: 2390: 2385: 2384: 2383: 2378: 2373: 2368: 2363: 2353: 2351:Computable set 2348: 2343: 2338: 2333: 2327: 2325: 2319: 2318: 2316: 2315: 2310: 2305: 2300: 2295: 2290: 2285: 2280: 2279: 2278: 2273: 2268: 2258: 2253: 2248: 2246:Satisfiability 2243: 2238: 2233: 2232: 2231: 2221: 2220: 2219: 2209: 2208: 2207: 2202: 2197: 2192: 2187: 2177: 2176: 2175: 2170: 2163:Interpretation 2159: 2157: 2151: 2150: 2148: 2147: 2142: 2137: 2132: 2127: 2117: 2112: 2111: 2110: 2109: 2108: 2098: 2093: 2083: 2078: 2073: 2068: 2063: 2058: 2052: 2050: 2044: 2043: 2040: 2039: 2037: 2036: 2028: 2027: 2026: 2025: 2020: 2019: 2018: 2013: 2008: 1988: 1987: 1986: 1984:minimal axioms 1981: 1970: 1969: 1968: 1957: 1956: 1955: 1950: 1945: 1940: 1935: 1930: 1917: 1915: 1896: 1895: 1893: 1892: 1891: 1890: 1878: 1873: 1872: 1871: 1866: 1861: 1856: 1846: 1841: 1836: 1831: 1830: 1829: 1824: 1814: 1813: 1812: 1807: 1802: 1797: 1787: 1782: 1781: 1780: 1775: 1770: 1760: 1759: 1758: 1753: 1748: 1743: 1738: 1733: 1723: 1718: 1713: 1708: 1707: 1706: 1701: 1696: 1691: 1681: 1676: 1674:Formation rule 1671: 1666: 1665: 1664: 1659: 1649: 1648: 1647: 1637: 1632: 1627: 1622: 1616: 1610: 1593:Formal systems 1589: 1588: 1585: 1584: 1582: 1581: 1576: 1571: 1566: 1561: 1556: 1551: 1546: 1541: 1536: 1535: 1534: 1529: 1518: 1516: 1512: 1511: 1509: 1508: 1507: 1506: 1496: 1491: 1490: 1489: 1482:Large cardinal 1479: 1474: 1469: 1464: 1459: 1445: 1444: 1443: 1438: 1433: 1418: 1416: 1406: 1405: 1403: 1402: 1401: 1400: 1395: 1390: 1380: 1375: 1370: 1365: 1360: 1355: 1350: 1345: 1340: 1335: 1330: 1325: 1319: 1317: 1310: 1309: 1307: 1306: 1305: 1304: 1299: 1294: 1289: 1284: 1279: 1271: 1270: 1269: 1264: 1254: 1249: 1247:Extensionality 1244: 1242:Ordinal number 1239: 1229: 1224: 1223: 1222: 1211: 1205: 1199: 1198: 1195: 1194: 1192: 1191: 1186: 1181: 1176: 1171: 1166: 1161: 1160: 1159: 1149: 1148: 1147: 1134: 1132: 1126: 1125: 1123: 1122: 1121: 1120: 1115: 1110: 1100: 1095: 1090: 1085: 1080: 1075: 1069: 1067: 1061: 1060: 1058: 1057: 1052: 1047: 1042: 1037: 1032: 1027: 1026: 1025: 1015: 1010: 1005: 1000: 995: 990: 984: 982: 973: 967: 966: 964: 963: 958: 953: 948: 943: 938: 926:Cantor's  924: 919: 914: 904: 902: 889: 888: 886: 885: 880: 875: 870: 865: 860: 855: 850: 845: 840: 835: 830: 825: 824: 823: 812: 810: 806: 805: 798: 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2811: 2808: 2806: 2803: 2801: 2798: 2796: 2793: 2791: 2788: 2786: 2783: 2781: 2778: 2776: 2773: 2771: 2768: 2766: 2763: 2761: 2758: 2756: 2753: 2751: 2748: 2746: 2743: 2741: 2738: 2736: 2733: 2731: 2728: 2726: 2723: 2721: 2718: 2716: 2713: 2711: 2708: 2706: 2703: 2701: 2698: 2696: 2693: 2691: 2688: 2686: 2683: 2681: 2678: 2676: 2673: 2671: 2668: 2666: 2663: 2661: 2658: 2656: 2653: 2651: 2648: 2646: 2643: 2641: 2638: 2636: 2633: 2631: 2628: 2626: 2623: 2621: 2618: 2616: 2613: 2611: 2608: 2606: 2603: 2601: 2598: 2596: 2593: 2591: 2588: 2586: 2583: 2582: 2580: 2578: 2574: 2570: 2565: 2561: 2554: 2549: 2547: 2542: 2540: 2535: 2534: 2531: 2521: 2520: 2515: 2507: 2501: 2498: 2496: 2493: 2491: 2488: 2486: 2483: 2479: 2476: 2475: 2474: 2471: 2469: 2466: 2464: 2461: 2459: 2455: 2452: 2450: 2447: 2445: 2442: 2440: 2437: 2435: 2432: 2431: 2429: 2425: 2419: 2416: 2414: 2411: 2409: 2408:Recursive set 2406: 2404: 2401: 2399: 2396: 2394: 2391: 2389: 2386: 2382: 2379: 2377: 2374: 2372: 2369: 2367: 2364: 2362: 2359: 2358: 2357: 2354: 2352: 2349: 2347: 2344: 2342: 2339: 2337: 2334: 2332: 2329: 2328: 2326: 2324: 2320: 2314: 2311: 2309: 2306: 2304: 2301: 2299: 2296: 2294: 2291: 2289: 2286: 2284: 2281: 2277: 2274: 2272: 2269: 2267: 2264: 2263: 2262: 2259: 2257: 2254: 2252: 2249: 2247: 2244: 2242: 2239: 2237: 2234: 2230: 2227: 2226: 2225: 2222: 2218: 2217:of arithmetic 2215: 2214: 2213: 2210: 2206: 2203: 2201: 2198: 2196: 2193: 2191: 2188: 2186: 2183: 2182: 2181: 2178: 2174: 2171: 2169: 2166: 2165: 2164: 2161: 2160: 2158: 2156: 2152: 2146: 2143: 2141: 2138: 2136: 2133: 2131: 2128: 2125: 2124:from ZFC 2121: 2118: 2116: 2113: 2107: 2104: 2103: 2102: 2099: 2097: 2094: 2092: 2089: 2088: 2087: 2084: 2082: 2079: 2077: 2074: 2072: 2069: 2067: 2064: 2062: 2059: 2057: 2054: 2053: 2051: 2049: 2045: 2035: 2034: 2030: 2029: 2024: 2023:non-Euclidean 2021: 2017: 2014: 2012: 2009: 2007: 2006: 2002: 2001: 1999: 1996: 1995: 1993: 1989: 1985: 1982: 1980: 1977: 1976: 1975: 1971: 1967: 1964: 1963: 1962: 1958: 1954: 1951: 1949: 1946: 1944: 1941: 1939: 1936: 1934: 1931: 1929: 1926: 1925: 1923: 1919: 1918: 1916: 1911: 1905: 1900:Example  1897: 1889: 1884: 1883: 1882: 1879: 1877: 1874: 1870: 1867: 1865: 1862: 1860: 1857: 1855: 1852: 1851: 1850: 1847: 1845: 1842: 1840: 1837: 1835: 1832: 1828: 1825: 1823: 1820: 1819: 1818: 1815: 1811: 1808: 1806: 1803: 1801: 1798: 1796: 1793: 1792: 1791: 1788: 1786: 1783: 1779: 1776: 1774: 1771: 1769: 1766: 1765: 1764: 1761: 1757: 1754: 1752: 1749: 1747: 1744: 1742: 1739: 1737: 1734: 1732: 1729: 1728: 1727: 1724: 1722: 1719: 1717: 1714: 1712: 1709: 1705: 1702: 1700: 1697: 1695: 1692: 1690: 1687: 1686: 1685: 1682: 1680: 1677: 1675: 1672: 1670: 1667: 1663: 1660: 1658: 1657:by definition 1655: 1654: 1653: 1650: 1646: 1643: 1642: 1641: 1638: 1636: 1633: 1631: 1628: 1626: 1623: 1621: 1618: 1617: 1614: 1611: 1609: 1605: 1600: 1594: 1590: 1580: 1577: 1575: 1572: 1570: 1567: 1565: 1562: 1560: 1557: 1555: 1552: 1550: 1547: 1545: 1544:Kripke–Platek 1542: 1540: 1537: 1533: 1530: 1528: 1525: 1524: 1523: 1520: 1519: 1517: 1513: 1505: 1502: 1501: 1500: 1497: 1495: 1492: 1488: 1485: 1484: 1483: 1480: 1478: 1475: 1473: 1470: 1468: 1465: 1463: 1460: 1457: 1453: 1449: 1446: 1442: 1439: 1437: 1434: 1432: 1429: 1428: 1427: 1423: 1420: 1419: 1417: 1415: 1411: 1407: 1399: 1396: 1394: 1391: 1389: 1388:constructible 1386: 1385: 1384: 1381: 1379: 1376: 1374: 1371: 1369: 1366: 1364: 1361: 1359: 1356: 1354: 1351: 1349: 1346: 1344: 1341: 1339: 1336: 1334: 1331: 1329: 1326: 1324: 1321: 1320: 1318: 1316: 1311: 1303: 1300: 1298: 1295: 1293: 1290: 1288: 1285: 1283: 1280: 1278: 1275: 1274: 1272: 1268: 1265: 1263: 1260: 1259: 1258: 1255: 1253: 1250: 1248: 1245: 1243: 1240: 1238: 1234: 1230: 1228: 1225: 1221: 1218: 1217: 1216: 1213: 1212: 1209: 1206: 1204: 1200: 1190: 1187: 1185: 1182: 1180: 1177: 1175: 1172: 1170: 1167: 1165: 1162: 1158: 1155: 1154: 1153: 1150: 1146: 1141: 1140: 1139: 1136: 1135: 1133: 1131: 1127: 1119: 1116: 1114: 1111: 1109: 1106: 1105: 1104: 1101: 1099: 1096: 1094: 1091: 1089: 1086: 1084: 1081: 1079: 1076: 1074: 1071: 1070: 1068: 1066: 1065:Propositional 1062: 1056: 1053: 1051: 1048: 1046: 1043: 1041: 1038: 1036: 1033: 1031: 1028: 1024: 1021: 1020: 1019: 1016: 1014: 1011: 1009: 1006: 1004: 1001: 999: 996: 994: 993:Logical truth 991: 989: 986: 985: 983: 981: 977: 974: 972: 968: 962: 959: 957: 954: 952: 949: 947: 944: 942: 939: 937: 933: 929: 925: 923: 920: 918: 915: 913: 909: 906: 905: 903: 901: 895: 890: 884: 881: 879: 876: 874: 871: 869: 866: 864: 861: 859: 856: 854: 851: 849: 846: 844: 841: 839: 836: 834: 831: 829: 826: 822: 819: 818: 817: 814: 813: 811: 807: 803: 796: 791: 789: 784: 782: 777: 776: 773: 766: 765: 760: 757: 753: 750: 747: 746: 741: 738: 737: 729: 726: 724: 721: 720: 716: 705: 695: 691: 690: 686: 683: 679: 675: 671: 667: 663: 662: 658: 655: 651: 647: 643: 639: 635: 631: 627: 623: 622: 618: 615: 611: 607: 603: 599: 598: 594: 591: 587: 583: 579: 575: 571: 567: 563: 559: 555: 554:Alfred Tarski 551: 547: 546: 545: 542: 540: 536: 532: 528: 524: 523: 519:, especially 518: 517: 512: 507: 505: 500: 496: 486: 484: 480: 476: 472: 468: 464: 460: 448: 443: 441: 436: 434: 429: 428: 426: 425: 418: 415: 413: 410: 408: 405: 403: 400: 398: 395: 393: 390: 388: 385: 383: 380: 378: 375: 373: 370: 369: 361: 360: 353: 350: 348: 345: 343: 340: 338: 335: 333: 330: 328: 325: 323: 320: 318: 315: 313: 310: 308: 305: 303: 300: 298: 295: 293: 292:Formal system 290: 289: 281: 280: 277: 274: 273: 269: 268: 263: 262: 257: 253: 239: 236: 221: 218: 210: 207:December 2022 200: 199:the talk page 196: 190: 188: 183:This article 181: 172: 171: 162: 159: 151: 140: 137: 133: 130: 126: 123: 119: 116: 112: 109: â€“  108: 104: 103:Find sources: 97: 93: 87: 86: 81:This article 79: 75: 70: 69: 64: 62: 55: 54: 49: 48: 43: 38: 29: 28: 19: 3399:Model theory 3276: 3266: 3256: 3246: 3236: 3226: 3216: 3206: 3186: 3176: 3166: 3156: 3146: 3128: 3069:Metalanguage 3064:Logical form 3019:Truth-bearer 2978:Unilalianism 2888:Expressivism 2715:Wittgenstein 2660:von Humboldt 2577:Philosophers 2510: 2308:Ultraproduct 2250: 2155:Model theory 2120:Independence 2056:Formal proof 2048:Proof theory 2031: 2004: 1961:real numbers 1933:second-order 1844:Substitution 1721:Metalanguage 1662:conservative 1635:Axiom schema 1579:Constructive 1549:Morse–Kelley 1515:Set theories 1494:Aleph number 1487:inaccessible 1393:Grothendieck 1277:intersection 1164:Higher-order 1152:Second-order 1098:Truth tables 1055:Venn diagram 838:Formal proof 767:, Routledge. 762: 755: 743: 694:Hartry Field 687: 665: 659: 653: 646:James Garson 634:modal logics 625: 619: 595: 566:model theory 549: 543: 520: 514: 508: 492: 466: 462: 456: 365:Applications 306: 285:Key concepts 266: 231: 213: 204: 193:Please help 184: 154: 145: 135: 128: 121: 114: 102: 90:Please help 85:verification 82: 58: 51: 45: 44:Please help 41: 3313:Linguistics 3278:Limited Inc 3198:On Denoting 3024:Proposition 2675:de Saussure 2640:Ibn Khaldun 2418:Type theory 2366:undecidable 2298:Truth value 2185:equivalence 1864:non-logical 1477:Enumeration 1467:Isomorphism 1414:cardinality 1398:Von Neumann 1363:Ultrafilter 1328:Uncountable 1262:equivalence 1179:Quantifiers 1169:Fixed-point 1138:First-order 1018:Consistency 1003:Proposition 980:Traditional 951:Lindström's 941:Compactness 883:Type theory 828:Cardinality 678:Leon Henkin 642:Nuel Belnap 606:Dag Prawitz 578:individuals 504:proposition 3388:Categories 3373:Discussion 3368:Task Force 3318:Pragmatics 3109:Speech act 3039:Categories 2953:Symbiosism 2908:Nominalism 2820:Watzlawick 2700:Bloomfield 2620:Chrysippus 2229:elementary 1922:arithmetic 1790:Quantifier 1768:functional 1640:Expression 1358:Transitive 1302:identities 1287:complement 1220:hereditary 1203:Set theory 734:References 535:term logic 342:Production 189:to readers 148:April 2011 118:newspapers 47:improve it 3409:Semantics 3350:Semiotics 3338:Semantics 3188:Alciphron 3124:Statement 3059:Intension 2999:Ambiguity 2878:Dramatism 2858:Cratylism 2610:Eubulides 2605:Aristotle 2585:Confucius 2500:Supertask 2403:Recursion 2361:decidable 2195:saturated 2173:of models 2096:deductive 2091:axiomatic 2011:Hilbert's 1998:Euclidean 1979:canonical 1902:axiomatic 1834:Signature 1763:Predicate 1652:Extension 1574:Ackermann 1499:Operation 1378:Universal 1368:Recursive 1343:Singleton 1338:Inhabited 1323:Countable 1313:Types of 1297:power set 1267:partition 1184:Predicate 1130:Predicate 1045:Syllogism 1035:Soundness 1008:Inference 998:Tautology 900:paradoxes 511:Aristotle 499:arguments 252:Semantics 53:talk page 3363:Category 3323:Rhetoric 3148:Cratylus 3119:Sentence 3094:Property 3014:Language 2992:Concepts 2830:Theories 2795:Strawson 2780:Davidson 2770:Hintikka 2765:Anscombe 2710:Vygotsky 2665:Mauthner 2635:Averroes 2625:Zhuangzi 2615:Diodorus 2595:Cratylus 2485:Logicism 2478:timeline 2454:Concrete 2313:Validity 2283:T-schema 2276:Kripke's 2271:Tarski's 2266:semantic 2256:Strength 2205:submodel 2200:spectrum 2168:function 2016:Tarski's 2005:Elements 1992:geometry 1948:Robinson 1869:variable 1854:function 1827:spectrum 1817:Sentence 1773:variable 1716:Language 1669:Relation 1630:Automata 1620:Alphabet 1604:language 1458:-jection 1436:codomain 1422:Function 1383:Universe 1353:Infinite 1257:Relation 1040:Validity 1030:Argument 928:theorem, 754:(1999), 742:(2007), 701:See also 562:T-schema 489:Overview 297:Alphabet 267:a series 264:Part of 3130:more... 3034:Concept 2775:Dummett 2750:Gadamer 2745:Chomsky 2730:Derrida 2720:Russell 2705:Bergson 2690:Tillich 2650:Leibniz 2590:Gorgias 2427:Related 2224:Diagram 2122: ( 2101:Hilbert 2086:Systems 2081:Theorem 1959:of the 1904:systems 1684:Formula 1679:Grammar 1595: ( 1539:General 1252:Forcing 1237:Element 1157:Monadic 932:paradox 873:Theorem 809:General 539:calculi 516:Organon 185:may be 132:scholar 3282:(1988) 3272:(1982) 3262:(1980) 3252:(1967) 3242:(1953) 3232:(1951) 3222:(1936) 3212:(1921) 3202:(1905) 3192:(1732) 3182:(1668) 3172:(1666) 3162:(1660) 3152:(n.d.) 3114:Symbol 2815:Searle 2805:Putnam 2755:Kripke 2740:Austin 2725:Carnap 2670:RicƓur 2655:Herder 2645:Hobbes 2190:finite 1953:Skolem 1906:  1881:Theory 1849:Symbol 1839:String 1822:atomic 1699:ground 1694:closed 1689:atomic 1645:ground 1608:syntax 1504:binary 1431:domain 1348:Finite 1113:finite 971:Logics 930:  878:Theory 461:, the 302:Syntax 134:  127:  120:  113:  105:  3140:Works 3049:Class 2810:Lewis 2800:Quine 2785:Grice 2735:Whorf 2695:Sapir 2680:Frege 2630:Xunzi 2600:Plato 2180:Model 1928:Peano 1785:Proof 1625:Arity 1554:Naive 1441:image 1373:Fuzzy 1333:Empty 1282:union 1227:Class 868:Model 858:Lemma 816:Axiom 473:, of 459:logic 139:JSTOR 125:books 3099:Sign 3004:Cant 2790:Ryle 2760:Ayer 2685:Boas 2303:Type 2106:list 1910:list 1887:list 1876:Term 1810:rank 1704:open 1598:list 1410:Maps 1315:sets 1174:Free 1144:list 894:list 821:list 632:for 608:and 493:The 111:news 3044:Set 1990:of 1972:of 1920:of 1452:Sur 1426:Map 1233:Ur- 1215:Set 664:or 572:of 556:'s 552:is 513:'s 465:or 457:In 94:by 3390:: 3200:" 2376:NP 2000:: 1994:: 1924:: 1601:), 1456:Bi 1448:In 656:). 640:, 604:, 588:. 485:. 270:on 56:. 3196:" 2969:) 2965:( 2552:e 2545:t 2538:v 2456:/ 2371:P 2126:) 1912:) 1908:( 1805:∀ 1800:! 1795:∃ 1756:= 1751:↔ 1746:→ 1741:∧ 1736:√ 1731:ÂŹ 1454:/ 1450:/ 1424:/ 1235:) 1231:( 1118:∞ 1108:3 896:) 794:e 787:t 780:v 684:. 446:e 439:t 432:v 258:. 238:) 232:( 220:) 214:( 209:) 205:( 201:. 191:. 161:) 155:( 150:) 146:( 136:· 129:· 122:· 115:· 88:. 63:) 59:( 20:)

Index

Formal semantics (logic)
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"Semantics of logic"
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Semantics
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Semantics (programming languages)
Formal grammar

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