Boolean-valued function
Source π
33:
603:, interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final
690:
576:, predicate, or proposition. In all of these uses, it is understood that the various terms refer to a mathematical object and not the corresponding
702:
274:
484:
229:
572:, and their applied disciplines, a Boolean-valued function may also be referred to as a characteristic function,
102:
460:
259:
724:
596:
699:, 1st edition, Kluwer Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003.
54:
214:
294:
672:
382:
45:
17:
761:
711:, 1st edition, McGrawβHill, 1970. 2nd edition, McGrawβHill, 1978. 3rd edition, McGrawβHill, 2010.
627:
477:
244:
169:
50:
642:
510:
77:
440:
425:
387:
199:
110:
8:
359:
349:
344:
731:, 2nd edition, 2 vols., Kiyosi ItΓ΄ (ed.), MIT Press, Cambridge, MA, 1993. Cited as EDM.
714:
657:
652:
573:
565:
470:
354:
329:
738:
662:
622:
518:
502:
430:
334:
324:
309:
304:
734:
677:
420:
397:
154:
707:
695:
600:
415:
392:
339:
632:
557:
526:
435:
755:
637:
538:
534:
139:
748:, MIT Press, Cambridge, MA, 1969. Revised, 1972. Expanded edition, 1988.
32:
743:
667:
647:
604:
561:
550:
542:
506:
569:
319:
314:
584:
364:
577:
445:
184:
114:
450:
588:
231:
617:
546:
160:
696:Boolean Reasoning: The Logic of Boolean Equations
156:
753:
276:
529:, i.e. a generic two-element set, (for example
533:= {0, 1}), whose elements are interpreted as
478:
132:
746:, An Introduction to Computational Geometry
485:
471:
141:
261:
252:
14:
754:
729:Encyclopedic Dictionary of Mathematics
280:
265:
246:
235:
220:
201:
190:
171:
145:
126:
708:Switching and Finite Automata Theory
216:
207:
26:
24:
25:
773:
719:Discrete Computational Structures
186:
177:
31:
721:, Academic Press, New York, NY.
103:History of the function concept
580:sign or syntactic expression.
13:
1:
725:Mathematical Society of Japan
684:
7:
610:
44:to comply with Knowledge's
10:
778:
517:, where X is an arbitrary
461:List of specific functions
673:Finitary boolean function
513:of the type f : X β
57:may contain suggestions.
42:may need to be rewritten
628:Boolean algebra (logic)
499:Boolean-valued function
643:Propositional calculus
595:is a predicate on the
691:Brown, Frank Markham
501:(sometimes called a
739:Papert, Seymour, A.
715:Korfhage, Robert R.
537:, for example, 0 =
658:Indicator function
653:Logic minimization
574:indicator function
566:mathematical logic
295:Classes/properties
735:Minsky, Marvin L.
623:Boolean data type
545:, i.e., a single
495:
494:
407:Generalizations
72:
71:
46:quality standards
16:(Redirected from
769:
678:Boolean function
487:
480:
473:
285:
284:
278:
270:
269:
263:
255:
254:
250:
240:
239:
233:
225:
224:
218:
210:
209:
205:
195:
194:
188:
180:
179:
175:
165:
164:
158:
150:
149:
143:
135:
134:
130:
97:
74:
73:
67:
64:
58:
35:
27:
21:
777:
776:
772:
771:
770:
768:
767:
766:
762:Boolean algebra
752:
751:
687:
682:
613:
601:formal language
593:truth predicate
585:formal semantic
558:formal sciences
491:
455:
416:Binary relation
402:
369:
289:
283:
275:
268:
260:
249:
245:
238:
230:
223:
215:
204:
200:
193:
185:
174:
170:
163:
155:
148:
140:
129:
125:
84:
68:
62:
59:
49:
36:
23:
22:
15:
12:
11:
5:
775:
765:
764:
750:
749:
732:
722:
712:
700:
686:
683:
681:
680:
675:
670:
665:
660:
655:
650:
645:
640:
635:
633:Boolean domain
630:
625:
620:
614:
612:
609:
535:logical values
527:Boolean domain
493:
492:
490:
489:
482:
475:
467:
464:
463:
457:
456:
454:
453:
448:
443:
438:
433:
428:
423:
418:
412:
409:
408:
404:
403:
401:
400:
395:
390:
385:
379:
376:
375:
371:
370:
368:
367:
362:
357:
352:
347:
342:
337:
332:
327:
322:
317:
312:
307:
301:
298:
297:
291:
290:
288:
287:
281:
272:
266:
257:
247:
242:
236:
227:
221:
212:
202:
197:
191:
182:
172:
167:
161:
152:
146:
137:
127:
121:
118:
117:
106:
105:
99:
98:
81:
80:
70:
69:
39:
37:
30:
9:
6:
4:
3:
2:
774:
763:
760:
759:
757:
747:
745:
740:
736:
733:
730:
726:
723:
720:
716:
713:
710:
709:
704:
701:
698:
697:
692:
689:
688:
679:
676:
674:
671:
669:
666:
664:
661:
659:
656:
654:
651:
649:
646:
644:
641:
639:
638:Boolean logic
636:
634:
631:
629:
626:
624:
621:
619:
616:
615:
608:
606:
602:
598:
594:
590:
586:
581:
579:
575:
571:
567:
563:
559:
554:
552:
548:
544:
540:
536:
532:
528:
524:
520:
516:
512:
508:
504:
500:
488:
483:
481:
476:
474:
469:
468:
466:
465:
462:
459:
458:
452:
449:
447:
444:
442:
439:
437:
434:
432:
429:
427:
424:
422:
419:
417:
414:
413:
411:
410:
406:
405:
399:
396:
394:
391:
389:
386:
384:
381:
380:
378:
377:
374:Constructions
373:
372:
366:
363:
361:
358:
356:
353:
351:
348:
346:
343:
341:
338:
336:
333:
331:
328:
326:
323:
321:
318:
316:
313:
311:
308:
306:
303:
302:
300:
299:
296:
293:
292:
286:
273:
271:
258:
256:
243:
241:
228:
226:
213:
211:
198:
196:
183:
181:
168:
166:
153:
151:
138:
136:
123:
122:
120:
119:
116:
112:
108:
107:
104:
101:
100:
95:
91:
87:
83:
82:
79:
76:
75:
66:
56:
52:
47:
43:
40:This article
38:
34:
29:
28:
19:
742:
728:
718:
706:
694:
592:
587:theories of
582:
555:
530:
522:
514:
498:
496:
441:Higher-order
124:
93:
89:
85:
60:
51:You can help
41:
744:Perceptrons
703:Kohavi, Zvi
668:Proposition
648:Truth table
605:truth value
562:mathematics
551:information
507:proposition
426:Multivalued
388:Composition
383:Restriction
685:References
570:statistics
521:and where
360:Surjective
350:Measurable
345:Continuous
320:Polynomial
63:March 2011
663:Predicate
597:sentences
503:predicate
365:Bijective
355:Injective
330:Algebraic
109:Types by
55:talk page
18:Logic one
756:Category
741:(1988),
717:(1974),
705:(1978),
693:(2003),
611:See also
578:semiotic
541:and 1 =
511:function
446:Morphism
431:Implicit
335:Analytic
325:Rational
310:Identity
305:Constant
115:codomain
92: (
78:Function
556:In the
509:) is a
451:Functor
421:Partial
398:Inverse
737:, and
340:Smooth
315:Linear
111:domain
53:. The
599:of a
589:truth
539:false
525:is a
505:or a
436:Space
591:, a
543:true
113:and
618:Bit
583:In
549:of
547:bit
519:set
758::
727:,
607:.
568:,
564:,
560:,
553:.
497:A
279:β
264:β
251:β
234:β
219:β
206:β
189:β
176:β
159:β
157:πΉ
144:β
142:πΉ
133:πΉ
131:β
88:β¦
531:B
523:B
515:B
486:e
479:t
472:v
393:Ξ»
282:X
277:β
267:X
262:β
253:β
248:X
237:X
232:β
222:X
217:β
208:β
203:X
192:X
187:β€
178:β€
173:X
162:X
147:X
128:X
96:)
94:x
90:f
86:x
65:)
61:(
48:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
β