7257:
6939:
4788:
3855:
3656:
1496:
69:
1537:
3687:
149:
7246:
5182:
3615:
3534:
3412:
3794:
In a parallel (concurrent) language, it is possible to short-circuit both sides: they are evaluated in parallel, and if one terminates with value true, the other is interrupted. This operator is thus called the
3145:
3238:
3963:
3325:
3009:
2361:
4109:-like interpretation of disjunction. As with exclusivity, these inferences have been analyzed both as implicatures and as entailments arising from a nonclassical interpretation of disjunction.
3818:), the logical disjunction operator returns one of its operands: the first operand if it evaluates to a true value, and the second operand otherwise. This allows it to fulfill the role of the
2832:
1575:
4345:, and practically all mathematical logicians after him, advocated, on various grounds, the definition of "logical addition" in a form which does not necessitate mutual exclusiveness.
2058:
859:
2439:
1286:
801:
714:
4973:
3054:
2716:
926:
587:
2543:
1523:
1245:
885:
561:
266:
4137:
987:
342:
5002:
5318:
3455:
1733:
1068:
2793:
1960:
833:
673:
621:
501:
5078:
2104:
2081:
1398:
1346:
952:
5103:
4878:
1203:
5049:
4849:
740:
1372:
647:
4824:
1312:
535:
6975:
5993:
4495:
472:
423:
397:
2859:
2570:
2187:
1656:
1177:
1125:
766:
5132:
2513:
2293:
2269:
1936:
1091:
1018:
136:
5169:
4944:
4907:
4778:
4030:
1879:
1773:
1753:
1626:
2663:
2389:
1151:
223:
189:
102:
1041:
446:
4732:
2766:
2745:
2489:
2468:
2160:
2139:
1992:
1912:
1696:
1676:
4341:, closely following analogy with ordinary mathematics, premised, as a necessary condition to the definition of "x + y", that x and y were mutually exclusive.
7988:
6076:
5217:
7292:
7766:
4325:
4098:
335:
3546:
3465:
6390:
6548:
4644:
4551:
4439:
5336:
6968:
6403:
5726:
3331:
1509:
3064:
3157:
7634:
7301:
4695:
4165:
asking which of the two professions is hers. The role of disjunction in these cases has been analyzed using nonclassical logics such as
4069:
328:
5988:
3900:
3244:
6408:
6398:
6135:
5341:
4526:
1800:
5886:
5332:
6544:
4725:
1834:
Because the logical "or" means a disjunction formula is true when either one or both of its parts are true, it is referred to as an
6641:
6385:
5210:
5946:
5639:
5380:
3831:
7721:
6961:
4295:
3760:
Many languages distinguish between bitwise and logical disjunction by providing two distinct operators; in languages following
1516:
7375:
7842:
7716:
7285:
6902:
6604:
6367:
6362:
6187:
5608:
5292:
1849:
When it is necessary to clarify whether inclusive or exclusive "or" is intended, English speakers sometimes uses the phrase "
2952:
2301:
7494:
7315:
6897:
6680:
6597:
6310:
6241:
6118:
5360:
4674:
4588:
4180:. Other languages express disjunctive meanings in a variety of ways, though it is unknown whether disjunction itself is a
5968:
7978:
6822:
6648:
6334:
5567:
4718:
3835:
1775:
are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an
1499:
50:
5973:
4032:
in classical logic. Notably, classical disjunction is inclusive while natural language disjunction is often understood
7380:
6305:
6044:
5302:
5203:
4669:
3811:
6700:
6695:
4454:
3802:
Although the type of a logical disjunction expression is
Boolean in most languages (and thus can only have the value
7468:
7862:
7524:
7345:
7226:
7221:
6629:
6219:
5613:
5581:
5272:
4065:
2799:
5346:
7867:
7817:
7579:
7278:
6919:
6868:
6765:
6263:
6224:
5701:
6760:
5375:
3787:, then the second (right) operand is not evaluated. The logical disjunction operator thus usually constitutes a
1546:
68:
7922:
7786:
7365:
7210:
6690:
6229:
6081:
6064:
5787:
5267:
4177:
3780:
3761:
1788:
4470:
For the sake of generality across classical systems, this entry suppresses the parameters of evaluation. The "
4610:
Marcus Vinícius Midena Ramos; de
Queiroz, Ruy J. G. B. (2015). "Context-Free Language Theory Formalization".
3965:. Because of this, logical disjunction satisfies many of the same identities as set-theoretic union, such as
2034:
1853:". In terms of logic, this phrase is identical to "or", but makes the inclusion of both being true explicit.
838:
7917:
7463:
6592:
6569:
6530:
6416:
6357:
6003:
5923:
5767:
5711:
5324:
5082:
5053:
4461:, translated by Otto Bird from the French and German editions, Dordrecht, North Holland: D. Reidel, passim.
4305:
4290:
4270:
2397:
1792:
1446:
1258:
771:
686:
195:
161:
4958:
4161:
asking whether it's true that Mary is either a philosopher or a linguist, it can also be interpreted as an
3021:
2671:
898:
566:
7947:
7619:
7589:
7564:
7504:
7403:
7335:
6882:
6609:
6587:
6554:
6447:
6293:
6278:
6251:
6202:
6086:
6021:
5846:
5812:
5807:
5681:
5512:
5489:
4567:
4342:
4275:
3697:
1416:
2519:
1216:
864:
7847:
7741:
7706:
7594:
7569:
7413:
7330:
6985:
6812:
6665:
6457:
6175:
5911:
5817:
5676:
5661:
5542:
5517:
4977:
4923:
4475:
4310:
4300:
4170:
4166:
4094:
3886:
1808:
1632:
language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula
540:
507:
307:
236:
39:
7256:
6938:
4122:
957:
4987:
4787:
7832:
7639:
7418:
7158:
7146:
6785:
6747:
6624:
6428:
6268:
6192:
6170:
5998:
5956:
5855:
5822:
5686:
5474:
5385:
4853:
4265:
4181:
4162:
3701:
3428:
2368:
1963:
1712:
1474:
1046:
593:
229:
2772:
2026:"true" unless both of its arguments are "false". Its semantic entry is standardly given as follows:
1941:
812:
652:
600:
477:
7912:
7827:
7771:
7674:
7659:
7629:
7609:
7584:
7453:
7438:
7088:
7014:
6914:
6805:
6790:
6770:
6727:
6614:
6564:
6490:
6435:
6372:
6165:
6108:
5876:
5865:
5537:
5437:
5365:
5356:
5352:
5287:
5282:
5107:
5063:
4382:
4315:
4106:
4102:
3982:
3978:
3765:
2248:
2247:
systems where logical disjunction is not a primitive, it can be defined in terms of the primitive "
2086:
2063:
1484:
1377:
1325:
931:
369:
5088:
4863:
1811:, as well as the numerous mismatches between classical disjunction and its nearest equivalents in
1182:
7983:
7957:
7882:
7857:
7822:
7802:
7731:
7711:
7649:
7644:
7554:
7544:
7529:
7473:
7261:
7154:
7060:
7056:
6943:
6712:
6675:
6660:
6653:
6636:
6422:
6288:
6214:
6197:
6150:
5963:
5872:
5706:
5691:
5651:
5603:
5588:
5576:
5532:
5507:
5277:
5226:
5034:
4834:
4742:
4664:
4615:
4073:
3890:
2012:
1796:
1605:
1479:
719:
358:
297:
6440:
5896:
1967:
1351:
626:
4809:
1842:, which is true when one or the other of the arguments are true, but not both (referred to as "
1291:
514:
7937:
7892:
7877:
7837:
7776:
7746:
7726:
7519:
7448:
7250:
7031:
6878:
6685:
6495:
6485:
6377:
6258:
6093:
6069:
5850:
5834:
5739:
5716:
5593:
5562:
5527:
5422:
5257:
5186:
5006:
4753:
4640:
4547:
4522:
4480:
4435:
4189:
4057:
3713:
2019:
1421:
451:
402:
376:
272:
2838:
2549:
2166:
1635:
1156:
1104:
745:
7942:
7872:
7761:
7539:
7074:
7070:
6892:
6887:
6780:
6737:
6559:
6520:
6515:
6500:
6326:
6283:
6180:
5978:
5928:
5502:
5464:
5117:
4828:
4514:
4471:
4285:
4185:
4009:
3990:
3986:
2495:
2278:
2272:
2254:
1921:
1812:
1629:
1441:
1318:
1073:
1000:
115:
5154:
4929:
4892:
4763:
4015:
1864:
1758:
1738:
1611:
7751:
7654:
7549:
7514:
6873:
6863:
6817:
6800:
6755:
6717:
6619:
6539:
6346:
6273:
6246:
6234:
6140:
6054:
6028:
5983:
5951:
5752:
5554:
5497:
5447:
5412:
5370:
4690:
4080:
2648:
2374:
2244:
1971:
1702:
1426:
4173:, which have also been adopted to explain the free choice and simplification inferences.
1130:
202:
168:
81:
1023:
428:
7932:
7927:
7852:
7736:
7614:
7509:
7350:
7197:
7193:
7185:
7171:
7142:
7100:
7096:
7084:
7000:
6858:
6837:
6795:
6775:
6670:
6525:
6123:
6113:
6103:
6098:
6032:
5906:
5782:
5671:
5666:
5644:
5245:
5010:
4799:
4568:"Python 3.12.1 Documentation - The Python Language Reference - 6.11 Boolean operations"
4508:
4280:
4158:
4087:
3994:
3974:
3819:
3788:
3058:
2751:
2730:
2474:
2453:
2145:
2124:
2016:
1977:
1897:
1861:
In logic and related fields, disjunction is customarily notated with an infix operator
1706:
1681:
1661:
1436:
679:
7270:
3854:
3655:
7972:
7624:
7599:
7433:
7048:
7043:
6832:
6510:
6017:
5802:
5792:
5762:
5747:
5417:
5148:
5144:
4757:
4406:
4320:
4053:
3970:
3966:
3015:
2946:
1451:
7887:
7812:
7679:
7559:
7443:
7423:
7108:
7026:
7022:
6732:
6579:
6480:
6472:
6352:
6300:
6209:
6145:
6128:
6059:
5918:
5777:
5479:
5262:
4948:
4338:
4196:. For instance, in the Maricopa example below, disjunction is marked by the suffix
4072:
denotation which behaves classically. However, disjunctive constructions including
4033:
3839:
3748:-ing the field with a constant field with the relevant bits set to 1. For example,
3459:
1839:
1784:
1780:
1540:
1251:
4686:
7807:
7781:
7664:
7428:
7355:
6842:
6722:
5901:
5891:
5838:
5522:
5442:
5427:
5307:
5252:
5057:
5024:
4704:
4682:
4589:"JavaScript References - Expressions & Operators - Logical AND (&&)"
4378:
3639:
3629:
3422:
2113:
2023:
1966:. The English word "or" is sometimes used as well, often in capital letters. In
1915:
1431:
891:
108:
7952:
7604:
7370:
7325:
7320:
7181:
5772:
5627:
5598:
5404:
4857:
4145:
In many languages, disjunctive expressions play a role in question formation.
4061:
4049:
3894:
3815:
3691:
1804:
1469:
142:
4710:
7756:
7574:
7499:
7478:
7408:
7360:
7340:
7010:
6924:
6827:
5880:
5797:
5757:
5721:
5657:
5469:
5459:
5432:
4981:
4803:
3741:
3610:{\displaystyle (a\rightarrow b)\rightarrow ((a\lor c)\rightarrow (b\lor c))}
3529:{\displaystyle (a\rightarrow b)\rightarrow ((c\lor a)\rightarrow (c\lor b))}
1536:
1209:
17:
4060:
between a classical and a nonclassical interpretation. More recent work in
7669:
7458:
7205:
7134:
7120:
6953:
6909:
6707:
6155:
5860:
5454:
5111:
5028:
4952:
4919:
4093:
Similar deviations from classical logic have been noted in cases such as
3642:
of 'false', produces a truth value of 'false' as a result of disjunction.
993:
7039:
6505:
5297:
4886:
4139:
You can have an apple and you can have a pear (but you can't have both)
3686:
3632:
of 'true', produces a truth value of 'true' as a result of disjunction.
1819:
35:
31:
4176:
In
English, as in many other languages, disjunction is expressed by a
4157:
For instance, while the above
English example can be interpreted as a
7163:
5195:
4389:(Winter 2016 ed.), Metaphysics Research Lab, Stanford University
4193:
3407:{\displaystyle (a\lor (b\equiv c))\equiv ((a\lor b)\equiv (a\lor c))}
1850:
3140:{\displaystyle (a\land (b\lor c))\equiv ((a\land b)\lor (a\land c))}
4620:
3752:
will force the final bit to 1, while leaving other bits unchanged.
3233:{\displaystyle (a\lor (b\land c))\equiv ((a\lor b)\land (a\lor c))}
148:
7534:
7130:
6049:
5395:
5240:
4090:
in contexts where an inclusive reading would otherwise be forced.
1581:
4518:
4220:
4209:
3958:{\displaystyle x\in A\cup B\Leftrightarrow (x\in A)\vee (x\in B)}
3320:{\displaystyle (a\lor (b\lor c))\equiv ((a\lor b)\lor (a\lor c))}
4434:. The basics (1. publ ed.). London: Routledge. p. 57.
7274:
6957:
5199:
4714:
4234:
4238:
4230:
3849:
3650:
3638:: The interpretation under which all variables are assigned a
3628:: The interpretation under which all variables are assigned a
4242:
4086:
have been argued to be inherently exclusive, rendering un
2445:
The latter can be checked by the following truth table:
4036:, as the following English example typically would be.
3866:
3667:
1550:
30:"Disjunction" redirects here. For the logic gate, see
5157:
5120:
5091:
5066:
5037:
4990:
4961:
4932:
4895:
4866:
4837:
4812:
4766:
4483:
4125:
4056:, who suggested that natural language disjunction is
4018:
3903:
3549:
3468:
3431:
3334:
3247:
3160:
3067:
3024:
3004:{\displaystyle a\lor (b\lor c)\equiv (a\lor b)\lor c}
2955:
2841:
2802:
2775:
2754:
2733:
2674:
2651:
2552:
2522:
2498:
2477:
2456:
2400:
2377:
2356:{\displaystyle A\lor B=\neg ((\neg A)\land (\neg B))}
2304:
2281:
2257:
2169:
2148:
2127:
2089:
2066:
2037:
1980:
1944:
1924:
1900:
1867:
1787:
treatments are often given in terms of rules such as
1761:
1741:
1715:
1684:
1664:
1638:
1614:
1549:
1380:
1354:
1328:
1294:
1261:
1219:
1185:
1159:
1133:
1107:
1076:
1049:
1026:
1003:
960:
934:
901:
867:
841:
815:
774:
748:
722:
689:
655:
629:
603:
569:
543:
517:
480:
454:
431:
405:
379:
239:
205:
171:
118:
84:
3783:; that is, if the first (left) operand evaluates to
7905:
7795:
7699:
7692:
7487:
7396:
7389:
7308:
6851:
6746:
6578:
6471:
6323:
6016:
5939:
5833:
5737:
5626:
5553:
5488:
5403:
5394:
5316:
5233:
4544:
Logic with trees: an introduction to symbolic logic
4048:This inference has sometimes been understood as an
3700:corresponding to logical disjunction exist in most
316:
306:
296:
288:
280:
271:
228:
194:
160:
155:
141:
107:
75:
61:
5163:
5126:
5097:
5072:
5043:
4996:
4967:
4938:
4901:
4872:
4843:
4818:
4772:
4489:
4131:
4064:has shown that this inference can be derived as a
4024:
3957:
3609:
3528:
3449:
3406:
3319:
3232:
3139:
3048:
3003:
2853:
2826:
2787:
2760:
2739:
2710:
2657:
2564:
2537:
2507:
2483:
2462:
2433:
2383:
2355:
2287:
2263:
2181:
2154:
2133:
2098:
2075:
2052:
1986:
1954:
1930:
1906:
1873:
1767:
1747:
1727:
1690:
1670:
1650:
1620:
1569:
1392:
1366:
1340:
1306:
1280:
1239:
1197:
1171:
1145:
1119:
1085:
1062:
1035:
1012:
981:
946:
920:
879:
853:
827:
795:
760:
734:
708:
667:
641:
615:
581:
555:
529:
495:
466:
440:
417:
391:
260:
217:
183:
130:
96:
4546:. London ; New York: Routledge. p. 38.
3772:), and logical disjunction with the double pipe (
1948:
7767:Segmented discourse representation theory (SDRT)
4639:(in German) (5 ed.). Springer. p. 32.
4497:here is intended to mean "semantically entails".
2722:It can be checked by the following truth table:
1779:interpretation of disjunction, in contrast with
4012:does not precisely match the interpretation of
2942:The following properties apply to disjunction:
49:as used in engineering and network theory, see
3897:is defined in terms of a logical disjunction:
2367:Alternatively, it may be defined in terms of "
45:"Logical OR" redirects here. For the operator
7286:
6969:
5211:
4726:
2827:{\displaystyle (A\rightarrow B)\rightarrow B}
1517:
336:
8:
3768:is performed with the single pipe operator (
2112:This semantics corresponds to the following
1949:
1945:
1925:
1799:treatments, motivated by problems including
56:
1795:. Disjunction has also been given numerous
7696:
7393:
7293:
7279:
7271:
6994:
6976:
6962:
6954:
6037:
5632:
5400:
5218:
5204:
5196:
4733:
4719:
4711:
2724:
2645:It may also be defined solely in terms of
2447:
2118:
1838:disjunction. This is in contrast with an
1628:and read aloud as "or". For instance, the
1570:{\displaystyle \scriptstyle A\lor B\lor C}
1524:
1510:
354:
343:
329:
5156:
5119:
5090:
5065:
5036:
4989:
4960:
4931:
4894:
4865:
4836:
4811:
4765:
4619:
4482:
4326:Simplification of disjunctive antecedents
4124:
4099:simplification of disjunctive antecedents
4017:
3902:
3548:
3467:
3430:
3333:
3246:
3159:
3066:
3023:
2954:
2840:
2801:
2774:
2753:
2732:
2673:
2650:
2551:
2521:
2497:
2476:
2455:
2399:
2376:
2303:
2280:
2256:
2168:
2147:
2126:
2088:
2065:
2036:
1979:
1943:
1923:
1899:
1866:
1760:
1740:
1714:
1683:
1663:
1637:
1613:
1548:
1379:
1353:
1327:
1293:
1265:
1260:
1226:
1218:
1184:
1158:
1132:
1106:
1075:
1050:
1048:
1025:
1002:
961:
959:
933:
905:
900:
866:
840:
814:
775:
773:
747:
721:
693:
688:
654:
628:
602:
568:
542:
516:
479:
453:
430:
404:
378:
238:
204:
170:
117:
83:
3685:
1535:
38:. For disjunctions in distribution, see
4387:The Stanford Encyclopedia of Philosophy
4355:
2835:
2796:
2769:
2546:
2516:
2492:
2163:
2053:{\displaystyle \models \phi \lor \psi }
1709:semantics according to which a formula
1460:
1407:
854:{\displaystyle A\not \Leftrightarrow B}
357:
3740:operator can be used to set bits in a
2434:{\displaystyle A\lor B=(\lnot A)\to B}
1281:{\displaystyle A{\underline {\lor }}B}
796:{\displaystyle {\overline {A\cdot B}}}
709:{\displaystyle A{\overline {\land }}B}
55:
7722:Discourse representation theory (DRT)
4968:{\displaystyle \not \leftrightarrow }
4707:From MathWorld—A Wolfram Web Resource
4251:John-NOM Bill-NOM 3-come-PL-FUT-INFER
4192:, disjunction is marked using a verb
3049:{\displaystyle a\lor b\equiv b\lor a}
2711:{\displaystyle A\lor B=(A\to B)\to B}
921:{\displaystyle A{\overline {\lor }}B}
582:{\displaystyle A\leftrightharpoons B}
34:. For separation of chromosomes, see
7:
4373:
4371:
4369:
4367:
4365:
4363:
4361:
4359:
4151:Is Mary a philosopher or a linguist?
7989:Formal semantics (natural language)
7635:Quantificational variability effect
7302:Formal semantics (natural language)
4696:Stanford Encyclopedia of Philosophy
2538:{\displaystyle \neg A\rightarrow B}
2106: or both
1830:Inclusive and exclusive disjunction
1240:{\displaystyle A\ {\text{XNOR}}\ B}
880:{\displaystyle A\nleftrightarrow B}
5158:
4933:
4767:
4612:Universidade Federal de Pernambuco
4510:Introduction to Mathematical Logic
4042:Mary is eating an apple or a pear.
2523:
2499:
2416:
2341:
2326:
2317:
2282:
1004:
556:{\displaystyle A\Leftrightarrow B}
487:
484:
458:
261:{\displaystyle x\oplus y\oplus xy}
25:
4635:Ebbinghaus, Heinz-Dieter (2021).
4513:. WORLD SCIENTIFIC. p. 150.
4132:{\displaystyle \rightsquigarrow }
1894:). Alternative notations include
982:{\displaystyle {\overline {A+B}}}
7255:
7244:
6937:
5180:
4997:{\displaystyle \leftrightarrow }
4786:
4115:You can have an apple or a pear.
3853:
3654:
3647:Applications in computer science
1495:
1494:
147:
67:
4296:Conjunction/disjunction duality
3779:Logical disjunction is usually
3450:{\displaystyle a\lor a\equiv a}
2083: or
2060: if
1801:Aristotle's sea battle argument
1728:{\displaystyle \phi \lor \psi }
1063:{\displaystyle {\overline {A}}}
7717:Combinatory categorial grammar
5038:
4991:
4867:
4838:
4813:
4459:A Précis of Mathematical Logic
4126:
3952:
3940:
3934:
3922:
3919:
3810:), in some languages (such as
3712:Disjunction is often used for
3604:
3601:
3589:
3586:
3583:
3571:
3568:
3565:
3562:
3556:
3550:
3523:
3520:
3508:
3505:
3502:
3490:
3487:
3484:
3481:
3475:
3469:
3401:
3398:
3386:
3380:
3368:
3365:
3359:
3356:
3344:
3335:
3314:
3311:
3299:
3293:
3281:
3278:
3272:
3269:
3257:
3248:
3227:
3224:
3212:
3206:
3194:
3191:
3185:
3182:
3170:
3161:
3134:
3131:
3119:
3113:
3101:
3098:
3092:
3089:
3077:
3068:
2992:
2980:
2974:
2962:
2818:
2815:
2809:
2803:
2788:{\displaystyle A\rightarrow B}
2779:
2702:
2699:
2693:
2687:
2652:
2529:
2425:
2422:
2413:
2378:
2350:
2347:
2338:
2332:
2323:
2320:
1955:{\displaystyle \vert \!\vert }
1678:abbreviates "it is sunny" and
1384:
1332:
938:
828:{\displaystyle A\not \equiv B}
726:
668:{\displaystyle A\rightarrow B}
659:
616:{\displaystyle A\Rightarrow B}
607:
573:
547:
496:{\displaystyle A\&\&B}
125:
119:
1:
7495:Antecedent-contained deletion
6898:History of mathematical logic
5073:{\displaystyle \nrightarrow }
4637:Einführung in die Mengenlehre
4385:, in Zalta, Edward N. (ed.),
2099:{\displaystyle \models \psi }
2076:{\displaystyle \models \phi }
2015:, classical disjunction is a
1393:{\displaystyle A\leftarrow B}
1341:{\displaystyle A\Leftarrow B}
947:{\displaystyle A\downarrow B}
6823:Primitive recursive function
5098:{\displaystyle \nleftarrow }
4873:{\displaystyle \rightarrow }
4184:. In many languages such as
1198:{\displaystyle A\parallel B}
1055:
974:
910:
788:
698:
51:Parallel addition (operator)
5044:{\displaystyle \downarrow }
4844:{\displaystyle \leftarrow }
4670:Encyclopedia of Mathematics
3832:Curry–Howard correspondence
735:{\displaystyle A\uparrow B}
8005:
7376:Syntax–semantics interface
5887:Schröder–Bernstein theorem
5614:Monadic predicate calculus
5273:Foundations of mathematics
4430:Beall, Jeffrey C. (2010).
4066:conversational implicature
2239:Defined by other operators
1698:abbreviates "it is warm".
1367:{\displaystyle A\subset B}
642:{\displaystyle A\supset B}
44:
29:
7868:Question under discussion
7818:Conversational scoreboard
7595:Intersective modification
7580:Homogeneity (linguistics)
7241:
6992:
6933:
6920:Philosophy of mathematics
6869:Automated theorem proving
6040:
5994:Von Neumann–Bernays–Gödel
5635:
5177:
5140:
5020:
4915:
4819:{\displaystyle \uparrow }
4795:
4784:
4749:
4254:'John or Bill will come.'
1972:prefix notation for logic
1705:, disjunction is given a
1307:{\displaystyle A\oplus B}
530:{\displaystyle A\equiv B}
324:
66:
7923:Distributional semantics
4507:Walicki, Michał (2016).
4490:{\displaystyle \models }
4178:coordinating conjunction
3826:Constructive disjunction
1998:(English: alternative).
1789:disjunction introduction
467:{\displaystyle A\&B}
418:{\displaystyle A\cdot B}
392:{\displaystyle A\land B}
7918:Computational semantics
7660:Subsective modification
7464:Propositional attitudes
6570:Self-verifying theories
6391:Tarski's axiomatization
5342:Tarski's undefinability
5337:incompleteness theorems
5083:Converse nonimplication
4411:Encyclopedia Britannica
4291:Boolean-valued function
4271:Boolean algebra (logic)
4248:Johnš Billš vʔaawuumšaa
4226:
4215:
4204:
4095:free choice disjunction
3838:form of disjunction to
2854:{\displaystyle A\lor B}
2565:{\displaystyle A\lor B}
2182:{\displaystyle A\lor B}
1793:disjunction elimination
1651:{\displaystyle S\lor W}
1447:Functional completeness
1172:{\displaystyle A\mid B}
1120:{\displaystyle A\lor B}
761:{\displaystyle A\mid B}
7948:Philosophy of language
7590:Inalienable possession
7570:Free choice inferences
7565:Faultless disagreement
7336:Generalized quantifier
7262:Mathematics portal
6944:Mathematics portal
6555:Proof of impossibility
6203:propositional variable
5513:Propositional calculus
5165:
5128:
5127:{\displaystyle \land }
5099:
5074:
5045:
4998:
4969:
4940:
4903:
4874:
4845:
4820:
4774:
4542:Howson, Colin (1997).
4491:
4276:Boolean algebra topics
4133:
4026:
3959:
3694:
3611:
3530:
3451:
3408:
3321:
3234:
3141:
3050:
3005:
2855:
2828:
2789:
2762:
2741:
2712:
2659:
2566:
2539:
2509:
2508:{\displaystyle \neg A}
2485:
2464:
2435:
2385:
2357:
2289:
2288:{\displaystyle \lnot }
2265:
2264:{\displaystyle \land }
2183:
2156:
2135:
2100:
2077:
2054:
1988:
1956:
1932:
1931:{\displaystyle \vert }
1908:
1875:
1822:of a disjunction is a
1769:
1749:
1729:
1692:
1672:
1652:
1622:
1577:
1571:
1417:Propositional calculus
1394:
1368:
1342:
1308:
1282:
1241:
1199:
1173:
1147:
1121:
1087:
1086:{\displaystyle \sim A}
1064:
1037:
1014:
1013:{\displaystyle \neg A}
983:
948:
922:
881:
855:
829:
797:
762:
736:
710:
669:
643:
617:
583:
557:
531:
497:
468:
442:
419:
393:
262:
219:
185:
132:
131:{\displaystyle (1110)}
98:
7848:Plural quantification
7742:Inquisitive semantics
7707:Alternative semantics
7251:Philosophy portal
6813:Kolmogorov complexity
6766:Computably enumerable
6666:Model complete theory
6458:Principia Mathematica
5518:Propositional formula
5347:Banach–Tarski paradox
5187:Philosophy portal
5166:
5164:{\displaystyle \bot }
5129:
5100:
5075:
5046:
4999:
4970:
4941:
4939:{\displaystyle \neg }
4904:
4902:{\displaystyle \lor }
4875:
4846:
4821:
4775:
4773:{\displaystyle \top }
4492:
4455:Józef Maria Bocheński
4407:"Disjunction | logic"
4311:Free choice inference
4301:Disjunctive syllogism
4171:inquisitive semantics
4167:alternative semantics
4134:
4027:
4025:{\displaystyle \lor }
3960:
3702:programming languages
3689:
3612:
3531:
3452:
3409:
3322:
3235:
3142:
3051:
3006:
2856:
2829:
2790:
2763:
2742:
2713:
2660:
2567:
2540:
2510:
2486:
2465:
2436:
2386:
2358:
2290:
2266:
2184:
2157:
2136:
2101:
2078:
2055:
2002:Classical disjunction
1989:
1964:programming languages
1957:
1933:
1909:
1876:
1874:{\displaystyle \lor }
1840:exclusive disjunction
1809:uncertainty principle
1781:exclusive disjunction
1770:
1768:{\displaystyle \psi }
1750:
1748:{\displaystyle \phi }
1730:
1693:
1673:
1653:
1623:
1621:{\displaystyle \lor }
1608:typically notated as
1602:inclusive disjunction
1572:
1539:
1475:Programming languages
1395:
1369:
1343:
1309:
1283:
1242:
1200:
1174:
1148:
1122:
1088:
1065:
1038:
1015:
984:
949:
923:
882:
856:
830:
798:
763:
737:
711:
670:
644:
618:
584:
558:
532:
498:
469:
443:
420:
394:
263:
220:
186:
133:
99:
40:Disjunct distribution
27:Logical connective OR
7833:Function application
7640:Responsive predicate
7630:Privative adjectives
6761:Church–Turing thesis
6748:Computability theory
5957:continuum hypothesis
5475:Square of opposition
5333:Gödel's completeness
5155:
5118:
5089:
5064:
5035:
4988:
4959:
4930:
4893:
4864:
4835:
4829:Converse implication
4810:
4764:
4481:
4306:Fréchet inequalities
4266:Affirming a disjunct
4182:linguistic universal
4163:alternative question
4123:
4016:
3901:
3636:Falsehood-preserving
3547:
3466:
3429:
3332:
3245:
3158:
3065:
3022:
2953:
2839:
2800:
2773:
2752:
2731:
2672:
2658:{\displaystyle \to }
2649:
2550:
2520:
2496:
2475:
2454:
2398:
2384:{\displaystyle \to }
2375:
2302:
2279:
2255:
2167:
2146:
2125:
2087:
2064:
2035:
1978:
1942:
1922:
1898:
1865:
1759:
1739:
1735:is true unless both
1713:
1682:
1662:
1636:
1612:
1547:
1378:
1352:
1326:
1292:
1259:
1217:
1183:
1157:
1131:
1105:
1074:
1047:
1024:
1001:
958:
932:
899:
865:
839:
813:
772:
746:
720:
687:
653:
627:
601:
567:
541:
515:
478:
452:
429:
403:
377:
237:
230:Zhegalkin polynomial
203:
169:
116:
82:
7979:Logical connectives
7913:Cognitive semantics
7828:Existential closure
7772:Situation semantics
7675:Temperature paradox
7645:Rising declaratives
7610:Modal subordination
7585:Hurford disjunction
7545:Discourse relations
6915:Mathematical object
6806:P versus NP problem
6771:Computable function
6565:Reverse mathematics
6491:Logical consequence
6368:primitive recursive
6363:elementary function
6136:Free/bound variable
5989:Tarski–Grothendieck
5508:Logical connectives
5438:Logical equivalence
5288:Logical consequence
4743:logical connectives
4703:Eric W. Weisstein.
4591:. 25 September 2023
4316:Hurford disjunction
3983:logical conjunction
3889:of an element of a
3766:bitwise disjunction
3732:1010 or 1100 = 1110
1994:, short for Polish
1590:logical disjunction
1485:Philosophy of logic
1146:{\displaystyle A+B}
359:Logical connectives
218:{\displaystyle x+y}
184:{\displaystyle x+y}
97:{\displaystyle x+y}
58:
57:Logical disjunction
7958:Semantics of logic
7883:Strict conditional
7858:Quantifier raising
7823:Downward entailing
7803:Autonomy of syntax
7732:Generative grammar
7712:Categorial grammar
7650:Scalar implicature
7555:Epistemic modality
7530:De dicto and de re
6713:Transfer principle
6676:Semantics of logic
6661:Categorical theory
6637:Non-standard model
6151:Logical connective
5278:Information theory
5227:Mathematical logic
5161:
5124:
5095:
5070:
5041:
4994:
4965:
4936:
4899:
4870:
4841:
4816:
4800:Alternative denial
4770:
4487:
4129:
4068:on the basis of a
4052:, for instance by
4022:
3955:
3865:. You can help by
3750:x = x | 0b00000001
3714:bitwise operations
3695:
3666:. You can help by
3607:
3526:
3447:
3404:
3317:
3230:
3137:
3046:
3001:
2851:
2824:
2785:
2758:
2737:
2708:
2655:
2562:
2535:
2505:
2481:
2460:
2431:
2381:
2353:
2285:
2261:
2179:
2152:
2131:
2096:
2073:
2050:
2022:which returns the
2013:semantics of logic
1984:
1974:, the operator is
1952:
1928:
1904:
1871:
1765:
1745:
1725:
1688:
1668:
1648:
1618:
1606:logical connective
1578:
1567:
1566:
1480:Mathematical logic
1390:
1364:
1338:
1304:
1278:
1273:
1237:
1195:
1169:
1143:
1117:
1083:
1060:
1036:{\displaystyle -A}
1033:
1010:
979:
944:
918:
877:
851:
825:
793:
758:
732:
706:
665:
639:
613:
579:
553:
527:
493:
464:
441:{\displaystyle AB}
438:
415:
389:
258:
215:
181:
128:
94:
7966:
7965:
7938:Logic translation
7901:
7900:
7893:Universal grinder
7878:Squiggle operator
7838:Meaning postulate
7777:Supervaluationism
7747:Intensional logic
7727:Dynamic semantics
7688:
7687:
7520:Crossover effects
7469:Tense–aspect–mood
7449:Lexical semantics
7268:
7267:
7236:
7235:
6951:
6950:
6883:Abstract category
6686:Theories of truth
6496:Rule of inference
6486:Natural deduction
6467:
6466:
6012:
6011:
5717:Cartesian product
5622:
5621:
5528:Many-valued logic
5503:Boolean functions
5386:Russell's paradox
5361:diagonal argument
5258:First-order logic
5193:
5192:
4646:978-3-662-63865-1
4553:978-0-415-13342-5
4441:978-0-203-85155-5
4432:Logic: the basics
4010:natural languages
3883:
3882:
3756:Logical operation
3708:Bitwise operation
3684:
3683:
2932:
2931:
2761:{\displaystyle B}
2740:{\displaystyle A}
2643:
2642:
2484:{\displaystyle B}
2463:{\displaystyle A}
2236:
2235:
2155:{\displaystyle B}
2134:{\displaystyle A}
1987:{\displaystyle A}
1914:, used mainly in
1907:{\displaystyle +}
1813:natural languages
1785:proof theoretical
1691:{\displaystyle W}
1671:{\displaystyle S}
1534:
1533:
1403:
1402:
1266:
1233:
1229:
1225:
1058:
977:
913:
791:
701:
353:
352:
16:(Redirected from
7996:
7943:Linguistics wars
7873:Semantic parsing
7762:Montague grammar
7697:
7540:Deontic modality
7394:
7381:Truth conditions
7316:Compositionality
7309:Central concepts
7295:
7288:
7281:
7272:
7260:
7259:
7249:
7248:
7247:
7179:
7128:
7008:
6995:
6978:
6971:
6964:
6955:
6942:
6941:
6893:History of logic
6888:Category of sets
6781:Decision problem
6560:Ordinal analysis
6501:Sequent calculus
6399:Boolean algebras
6339:
6338:
6313:
6284:logical/constant
6038:
6024:
5947:Zermelo–Fraenkel
5698:Set operations:
5633:
5570:
5401:
5381:Löwenheim–Skolem
5268:Formal semantics
5220:
5213:
5206:
5197:
5185:
5184:
5183:
5170:
5168:
5167:
5162:
5133:
5131:
5130:
5125:
5104:
5102:
5101:
5096:
5079:
5077:
5076:
5071:
5050:
5048:
5047:
5042:
5003:
5001:
5000:
4995:
4974:
4972:
4971:
4966:
4945:
4943:
4942:
4937:
4908:
4906:
4905:
4900:
4879:
4877:
4876:
4871:
4850:
4848:
4847:
4842:
4825:
4823:
4822:
4817:
4790:
4779:
4777:
4776:
4771:
4735:
4728:
4721:
4712:
4700:
4691:Zalta, Edward N.
4678:
4651:
4650:
4632:
4626:
4625:
4623:
4607:
4601:
4600:
4598:
4596:
4585:
4579:
4578:
4576:
4574:
4564:
4558:
4557:
4539:
4533:
4532:
4504:
4498:
4496:
4494:
4493:
4488:
4472:double turnstile
4468:
4462:
4452:
4446:
4445:
4427:
4421:
4420:
4418:
4417:
4403:
4397:
4396:
4395:
4394:
4375:
4286:Boolean function
4244:
4240:
4236:
4232:
4222:
4211:
4138:
4136:
4135:
4130:
4101:, where certain
4031:
4029:
4028:
4023:
4004:Natural language
3991:logical negation
3987:set intersection
3979:de Morgan's laws
3964:
3962:
3961:
3956:
3878:
3875:
3857:
3850:
3809:
3805:
3786:
3775:
3771:
3751:
3747:
3739:
3679:
3676:
3658:
3651:
3626:Truth-preserving
3616:
3614:
3613:
3608:
3535:
3533:
3532:
3527:
3456:
3454:
3453:
3448:
3413:
3411:
3410:
3405:
3326:
3324:
3323:
3318:
3239:
3237:
3236:
3231:
3146:
3144:
3143:
3138:
3055:
3053:
3052:
3047:
3010:
3008:
3007:
3002:
2860:
2858:
2857:
2852:
2833:
2831:
2830:
2825:
2794:
2792:
2791:
2786:
2767:
2765:
2764:
2759:
2746:
2744:
2743:
2738:
2725:
2717:
2715:
2714:
2709:
2664:
2662:
2661:
2656:
2571:
2569:
2568:
2563:
2544:
2542:
2541:
2536:
2514:
2512:
2511:
2506:
2490:
2488:
2487:
2482:
2469:
2467:
2466:
2461:
2448:
2440:
2438:
2437:
2432:
2391:) and "not" as:
2390:
2388:
2387:
2382:
2362:
2360:
2359:
2354:
2294:
2292:
2291:
2286:
2270:
2268:
2267:
2262:
2188:
2186:
2185:
2180:
2161:
2159:
2158:
2153:
2140:
2138:
2137:
2132:
2119:
2105:
2103:
2102:
2097:
2082:
2080:
2079:
2074:
2059:
2057:
2056:
2051:
2017:truth functional
1993:
1991:
1990:
1985:
1961:
1959:
1958:
1953:
1937:
1935:
1934:
1929:
1913:
1911:
1910:
1905:
1893:
1890:
1887:
1885:
1880:
1878:
1877:
1872:
1774:
1772:
1771:
1766:
1754:
1752:
1751:
1746:
1734:
1732:
1731:
1726:
1707:truth functional
1697:
1695:
1694:
1689:
1677:
1675:
1674:
1669:
1658:, assuming that
1657:
1655:
1654:
1649:
1627:
1625:
1624:
1619:
1598:logical addition
1588:, also known as
1576:
1574:
1573:
1568:
1526:
1519:
1512:
1498:
1497:
1442:Boolean function
1408:Related concepts
1399:
1397:
1396:
1391:
1373:
1371:
1370:
1365:
1347:
1345:
1344:
1339:
1313:
1311:
1310:
1305:
1287:
1285:
1284:
1279:
1274:
1246:
1244:
1243:
1238:
1231:
1230:
1227:
1223:
1204:
1202:
1201:
1196:
1178:
1176:
1175:
1170:
1152:
1150:
1149:
1144:
1126:
1124:
1123:
1118:
1092:
1090:
1089:
1084:
1069:
1067:
1066:
1061:
1059:
1051:
1042:
1040:
1039:
1034:
1019:
1017:
1016:
1011:
988:
986:
985:
980:
978:
973:
962:
953:
951:
950:
945:
927:
925:
924:
919:
914:
906:
886:
884:
883:
878:
860:
858:
857:
852:
834:
832:
831:
826:
802:
800:
799:
794:
792:
787:
776:
767:
765:
764:
759:
741:
739:
738:
733:
715:
713:
712:
707:
702:
694:
674:
672:
671:
666:
648:
646:
645:
640:
622:
620:
619:
614:
588:
586:
585:
580:
562:
560:
559:
554:
536:
534:
533:
528:
502:
500:
499:
494:
473:
471:
470:
465:
447:
445:
444:
439:
424:
422:
421:
416:
398:
396:
395:
390:
366:
365:
355:
345:
338:
331:
275:
267:
265:
264:
259:
224:
222:
221:
216:
190:
188:
187:
182:
151:
137:
135:
134:
129:
103:
101:
100:
95:
71:
59:
21:
8004:
8003:
7999:
7998:
7997:
7995:
7994:
7993:
7969:
7968:
7967:
7962:
7897:
7791:
7752:Lambda calculus
7684:
7655:Sloppy identity
7615:Opaque contexts
7550:Donkey anaphora
7515:Counterfactuals
7483:
7385:
7304:
7299:
7269:
7264:
7254:
7253:
7245:
7243:
7237:
7232:
7231:
7228:
7224:
7216:
7215:
7212:
7208:
7200:
7196:
7188:
7184:
7175:
7166:
7162:
7157:
7149:
7145:
7137:
7133:
7124:
7115:
7111:
7103:
7099:
7091:
7087:
7079:
7076:
7073:
7065:
7062:
7059:
7051:
7047:
7042:
7034:
7030:
7025:
7017:
7013:
7004:
6988:
6986:logical symbols
6982:
6952:
6947:
6936:
6929:
6874:Category theory
6864:Algebraic logic
6847:
6818:Lambda calculus
6756:Church encoding
6742:
6718:Truth predicate
6574:
6540:Complete theory
6463:
6332:
6328:
6324:
6319:
6311:
6031: and
6027:
6022:
6008:
5984:New Foundations
5952:axiom of choice
5935:
5897:Gödel numbering
5837: and
5829:
5733:
5618:
5568:
5549:
5498:Boolean algebra
5484:
5448:Equiconsistency
5413:Classical logic
5390:
5371:Halting problem
5359: and
5335: and
5323: and
5322:
5317:Theorems (
5312:
5229:
5224:
5194:
5189:
5181:
5179:
5173:
5153:
5152:
5136:
5116:
5115:
5087:
5086:
5062:
5061:
5033:
5032:
5016:
4986:
4985:
4957:
4956:
4928:
4927:
4911:
4891:
4890:
4862:
4861:
4833:
4832:
4808:
4807:
4791:
4782:
4762:
4761:
4745:
4739:
4681:
4663:
4660:
4655:
4654:
4647:
4634:
4633:
4629:
4609:
4608:
4604:
4594:
4592:
4587:
4586:
4582:
4572:
4570:
4566:
4565:
4561:
4554:
4541:
4540:
4536:
4529:
4506:
4505:
4501:
4479:
4478:
4469:
4465:
4453:
4449:
4442:
4429:
4428:
4424:
4415:
4413:
4405:
4404:
4400:
4392:
4390:
4377:
4376:
4357:
4352:
4335:
4330:
4261:
4256:
4246:
4224:
4213:
4121:
4120:
4103:modal operators
4014:
4013:
4008:Disjunction in
4006:
4000:
3899:
3898:
3879:
3873:
3870:
3863:needs expansion
3848:
3828:
3807:
3803:
3784:
3781:short-circuited
3773:
3769:
3758:
3749:
3745:
3737:
3710:
3680:
3674:
3671:
3664:needs expansion
3649:
3545:
3544:
3464:
3463:
3427:
3426:
3330:
3329:
3243:
3242:
3156:
3155:
3063:
3062:
3020:
3019:
2951:
2950:
2940:
2934:
2837:
2836:
2798:
2797:
2771:
2770:
2750:
2749:
2729:
2728:
2670:
2669:
2647:
2646:
2548:
2547:
2518:
2517:
2494:
2493:
2473:
2472:
2452:
2451:
2396:
2395:
2373:
2372:
2300:
2299:
2277:
2276:
2253:
2252:
2245:classical logic
2241:
2165:
2164:
2144:
2143:
2123:
2122:
2085:
2084:
2062:
2061:
2033:
2032:
2009:
2004:
1976:
1975:
1968:Jan Łukasiewicz
1940:
1939:
1920:
1919:
1896:
1895:
1891:
1888:
1883:
1882:
1863:
1862:
1859:
1832:
1757:
1756:
1737:
1736:
1711:
1710:
1703:classical logic
1680:
1679:
1660:
1659:
1634:
1633:
1610:
1609:
1545:
1544:
1530:
1489:
1456:
1427:Boolean algebra
1422:Predicate logic
1376:
1375:
1350:
1349:
1324:
1323:
1290:
1289:
1257:
1256:
1215:
1214:
1181:
1180:
1155:
1154:
1129:
1128:
1103:
1102:
1072:
1071:
1045:
1044:
1022:
1021:
999:
998:
963:
956:
955:
930:
929:
897:
896:
863:
862:
837:
836:
811:
810:
777:
770:
769:
744:
743:
718:
717:
685:
684:
651:
650:
625:
624:
599:
598:
565:
564:
539:
538:
513:
512:
476:
475:
450:
449:
427:
426:
401:
400:
375:
374:
349:
274:Post's lattices
273:
235:
234:
201:
200:
167:
166:
114:
113:
80:
79:
54:
43:
28:
23:
22:
15:
12:
11:
5:
8002:
8000:
7992:
7991:
7986:
7981:
7971:
7970:
7964:
7963:
7961:
7960:
7955:
7950:
7945:
7940:
7935:
7933:Inferentialism
7930:
7928:Formal grammar
7925:
7920:
7915:
7909:
7907:
7903:
7902:
7899:
7898:
7896:
7895:
7890:
7885:
7880:
7875:
7870:
7865:
7860:
7855:
7853:Possible world
7850:
7845:
7840:
7835:
7830:
7825:
7820:
7815:
7810:
7805:
7799:
7797:
7793:
7792:
7790:
7789:
7784:
7779:
7774:
7769:
7764:
7759:
7754:
7749:
7744:
7739:
7737:Glue semantics
7734:
7729:
7724:
7719:
7714:
7709:
7703:
7701:
7700:Formal systems
7694:
7690:
7689:
7686:
7685:
7683:
7682:
7677:
7672:
7667:
7662:
7657:
7652:
7647:
7642:
7637:
7632:
7627:
7625:Polarity items
7622:
7617:
7612:
7607:
7602:
7597:
7592:
7587:
7582:
7577:
7572:
7567:
7562:
7557:
7552:
7547:
7542:
7537:
7532:
7527:
7522:
7517:
7512:
7510:Conservativity
7507:
7502:
7497:
7491:
7489:
7485:
7484:
7482:
7481:
7476:
7474:Quantification
7471:
7466:
7461:
7456:
7451:
7446:
7441:
7436:
7431:
7426:
7421:
7416:
7411:
7406:
7400:
7398:
7391:
7387:
7386:
7384:
7383:
7378:
7373:
7368:
7363:
7358:
7353:
7351:Presupposition
7348:
7343:
7338:
7333:
7328:
7323:
7318:
7312:
7310:
7306:
7305:
7300:
7298:
7297:
7290:
7283:
7275:
7266:
7265:
7242:
7239:
7238:
7234:
7233:
7229:quantification
7225:
7220:
7219:
7217:
7213:quantification
7209:
7204:
7203:
7201:
7192:
7191:
7189:
7170:
7169:
7167:
7153:
7152:
7150:
7141:
7140:
7138:
7119:
7118:
7116:
7107:
7106:
7104:
7095:
7094:
7092:
7083:
7082:
7080:
7069:
7068:
7066:
7055:
7054:
7052:
7038:
7037:
7035:
7021:
7020:
7018:
6999:
6998:
6993:
6990:
6989:
6983:
6981:
6980:
6973:
6966:
6958:
6949:
6948:
6934:
6931:
6930:
6928:
6927:
6922:
6917:
6912:
6907:
6906:
6905:
6895:
6890:
6885:
6876:
6871:
6866:
6861:
6859:Abstract logic
6855:
6853:
6849:
6848:
6846:
6845:
6840:
6838:Turing machine
6835:
6830:
6825:
6820:
6815:
6810:
6809:
6808:
6803:
6798:
6793:
6788:
6778:
6776:Computable set
6773:
6768:
6763:
6758:
6752:
6750:
6744:
6743:
6741:
6740:
6735:
6730:
6725:
6720:
6715:
6710:
6705:
6704:
6703:
6698:
6693:
6683:
6678:
6673:
6671:Satisfiability
6668:
6663:
6658:
6657:
6656:
6646:
6645:
6644:
6634:
6633:
6632:
6627:
6622:
6617:
6612:
6602:
6601:
6600:
6595:
6588:Interpretation
6584:
6582:
6576:
6575:
6573:
6572:
6567:
6562:
6557:
6552:
6542:
6537:
6536:
6535:
6534:
6533:
6523:
6518:
6508:
6503:
6498:
6493:
6488:
6483:
6477:
6475:
6469:
6468:
6465:
6464:
6462:
6461:
6453:
6452:
6451:
6450:
6445:
6444:
6443:
6438:
6433:
6413:
6412:
6411:
6409:minimal axioms
6406:
6395:
6394:
6393:
6382:
6381:
6380:
6375:
6370:
6365:
6360:
6355:
6342:
6340:
6321:
6320:
6318:
6317:
6316:
6315:
6303:
6298:
6297:
6296:
6291:
6286:
6281:
6271:
6266:
6261:
6256:
6255:
6254:
6249:
6239:
6238:
6237:
6232:
6227:
6222:
6212:
6207:
6206:
6205:
6200:
6195:
6185:
6184:
6183:
6178:
6173:
6168:
6163:
6158:
6148:
6143:
6138:
6133:
6132:
6131:
6126:
6121:
6116:
6106:
6101:
6099:Formation rule
6096:
6091:
6090:
6089:
6084:
6074:
6073:
6072:
6062:
6057:
6052:
6047:
6041:
6035:
6018:Formal systems
6014:
6013:
6010:
6009:
6007:
6006:
6001:
5996:
5991:
5986:
5981:
5976:
5971:
5966:
5961:
5960:
5959:
5954:
5943:
5941:
5937:
5936:
5934:
5933:
5932:
5931:
5921:
5916:
5915:
5914:
5907:Large cardinal
5904:
5899:
5894:
5889:
5884:
5870:
5869:
5868:
5863:
5858:
5843:
5841:
5831:
5830:
5828:
5827:
5826:
5825:
5820:
5815:
5805:
5800:
5795:
5790:
5785:
5780:
5775:
5770:
5765:
5760:
5755:
5750:
5744:
5742:
5735:
5734:
5732:
5731:
5730:
5729:
5724:
5719:
5714:
5709:
5704:
5696:
5695:
5694:
5689:
5679:
5674:
5672:Extensionality
5669:
5667:Ordinal number
5664:
5654:
5649:
5648:
5647:
5636:
5630:
5624:
5623:
5620:
5619:
5617:
5616:
5611:
5606:
5601:
5596:
5591:
5586:
5585:
5584:
5574:
5573:
5572:
5559:
5557:
5551:
5550:
5548:
5547:
5546:
5545:
5540:
5535:
5525:
5520:
5515:
5510:
5505:
5500:
5494:
5492:
5486:
5485:
5483:
5482:
5477:
5472:
5467:
5462:
5457:
5452:
5451:
5450:
5440:
5435:
5430:
5425:
5420:
5415:
5409:
5407:
5398:
5392:
5391:
5389:
5388:
5383:
5378:
5373:
5368:
5363:
5351:Cantor's
5349:
5344:
5339:
5329:
5327:
5314:
5313:
5311:
5310:
5305:
5300:
5295:
5290:
5285:
5280:
5275:
5270:
5265:
5260:
5255:
5250:
5249:
5248:
5237:
5235:
5231:
5230:
5225:
5223:
5222:
5215:
5208:
5200:
5191:
5190:
5178:
5175:
5174:
5172:
5171:
5160:
5141:
5138:
5137:
5135:
5134:
5123:
5105:
5094:
5080:
5069:
5054:Nonimplication
5051:
5040:
5021:
5018:
5017:
5015:
5014:
5011:Digital buffer
5004:
4993:
4975:
4964:
4946:
4935:
4916:
4913:
4912:
4910:
4909:
4898:
4880:
4869:
4851:
4840:
4826:
4815:
4796:
4793:
4792:
4785:
4783:
4781:
4780:
4769:
4750:
4747:
4746:
4740:
4738:
4737:
4730:
4723:
4715:
4709:
4708:
4705:"Disjunction."
4701:
4679:
4659:
4658:External links
4656:
4653:
4652:
4645:
4627:
4602:
4580:
4559:
4552:
4534:
4528:978-9814343879
4527:
4499:
4486:
4463:
4447:
4440:
4422:
4398:
4354:
4353:
4351:
4348:
4347:
4346:
4334:
4331:
4329:
4328:
4323:
4318:
4313:
4308:
4303:
4298:
4293:
4288:
4283:
4281:Boolean domain
4278:
4273:
4268:
4262:
4260:
4257:
4225:
4214:
4203:
4202:
4159:polar question
4155:
4154:
4153:
4152:
4143:
4142:
4141:
4140:
4128:
4117:
4116:
4088:grammaticality
4046:
4045:
4044:
4043:
4021:
4005:
4002:
3995:set complement
3981:, identifying
3975:distributivity
3954:
3951:
3948:
3945:
3942:
3939:
3936:
3933:
3930:
3927:
3924:
3921:
3918:
3915:
3912:
3909:
3906:
3881:
3880:
3860:
3858:
3847:
3844:
3836:constructivist
3827:
3824:
3820:Elvis operator
3789:sequence point
3757:
3754:
3734:
3733:
3730:
3727:
3724:
3721:
3709:
3706:
3682:
3681:
3661:
3659:
3648:
3645:
3644:
3643:
3633:
3622:
3621:
3620:
3619:
3618:
3617:
3606:
3603:
3600:
3597:
3594:
3591:
3588:
3585:
3582:
3579:
3576:
3573:
3570:
3567:
3564:
3561:
3558:
3555:
3552:
3537:
3536:
3525:
3522:
3519:
3516:
3513:
3510:
3507:
3504:
3501:
3498:
3495:
3492:
3489:
3486:
3483:
3480:
3477:
3474:
3471:
3457:
3446:
3443:
3440:
3437:
3434:
3419:
3418:
3417:
3416:
3415:
3414:
3403:
3400:
3397:
3394:
3391:
3388:
3385:
3382:
3379:
3376:
3373:
3370:
3367:
3364:
3361:
3358:
3355:
3352:
3349:
3346:
3343:
3340:
3337:
3327:
3316:
3313:
3310:
3307:
3304:
3301:
3298:
3295:
3292:
3289:
3286:
3283:
3280:
3277:
3274:
3271:
3268:
3265:
3262:
3259:
3256:
3253:
3250:
3240:
3229:
3226:
3223:
3220:
3217:
3214:
3211:
3208:
3205:
3202:
3199:
3196:
3193:
3190:
3187:
3184:
3181:
3178:
3175:
3172:
3169:
3166:
3163:
3148:
3147:
3136:
3133:
3130:
3127:
3124:
3121:
3118:
3115:
3112:
3109:
3106:
3103:
3100:
3097:
3094:
3091:
3088:
3085:
3082:
3079:
3076:
3073:
3070:
3059:Distributivity
3056:
3045:
3042:
3039:
3036:
3033:
3030:
3027:
3013:
3000:
2997:
2994:
2991:
2988:
2985:
2982:
2979:
2976:
2973:
2970:
2967:
2964:
2961:
2958:
2939:
2936:
2930:
2929:
2926:
2923:
2920:
2917:
2913:
2912:
2909:
2906:
2903:
2900:
2896:
2895:
2892:
2889:
2886:
2883:
2879:
2878:
2875:
2872:
2869:
2866:
2862:
2861:
2850:
2847:
2844:
2834:
2823:
2820:
2817:
2814:
2811:
2808:
2805:
2795:
2784:
2781:
2778:
2768:
2757:
2747:
2736:
2720:
2719:
2707:
2704:
2701:
2698:
2695:
2692:
2689:
2686:
2683:
2680:
2677:
2654:
2641:
2640:
2637:
2634:
2631:
2628:
2624:
2623:
2620:
2617:
2614:
2611:
2607:
2606:
2603:
2600:
2597:
2594:
2590:
2589:
2586:
2583:
2580:
2577:
2573:
2572:
2561:
2558:
2555:
2545:
2534:
2531:
2528:
2525:
2515:
2504:
2501:
2491:
2480:
2470:
2459:
2443:
2442:
2430:
2427:
2424:
2421:
2418:
2415:
2412:
2409:
2406:
2403:
2380:
2365:
2364:
2352:
2349:
2346:
2343:
2340:
2337:
2334:
2331:
2328:
2325:
2322:
2319:
2316:
2313:
2310:
2307:
2284:
2260:
2240:
2237:
2234:
2233:
2230:
2227:
2223:
2222:
2219:
2216:
2212:
2211:
2208:
2205:
2201:
2200:
2197:
2194:
2190:
2189:
2178:
2175:
2172:
2162:
2151:
2141:
2130:
2110:
2109:
2108:
2107:
2095:
2092:
2072:
2069:
2049:
2046:
2043:
2040:
2008:
2005:
2003:
2000:
1983:
1951:
1947:
1927:
1903:
1870:
1858:
1855:
1846:", or "XOR").
1831:
1828:
1764:
1744:
1724:
1721:
1718:
1687:
1667:
1647:
1644:
1641:
1617:
1565:
1562:
1559:
1556:
1553:
1532:
1531:
1529:
1528:
1521:
1514:
1506:
1503:
1502:
1491:
1490:
1488:
1487:
1482:
1477:
1472:
1466:
1463:
1462:
1458:
1457:
1455:
1454:
1449:
1444:
1439:
1437:Truth function
1434:
1429:
1424:
1419:
1413:
1410:
1409:
1405:
1404:
1401:
1400:
1389:
1386:
1383:
1363:
1360:
1357:
1337:
1334:
1331:
1321:
1315:
1314:
1303:
1300:
1297:
1277:
1272:
1269:
1264:
1254:
1248:
1247:
1236:
1222:
1212:
1206:
1205:
1194:
1191:
1188:
1168:
1165:
1162:
1142:
1139:
1136:
1116:
1113:
1110:
1100:
1094:
1093:
1082:
1079:
1057:
1054:
1032:
1029:
1009:
1006:
996:
990:
989:
976:
972:
969:
966:
943:
940:
937:
917:
912:
909:
904:
894:
888:
887:
876:
873:
870:
850:
847:
844:
824:
821:
818:
808:
804:
803:
790:
786:
783:
780:
757:
754:
751:
731:
728:
725:
705:
700:
697:
692:
682:
676:
675:
664:
661:
658:
638:
635:
632:
612:
609:
606:
596:
590:
589:
578:
575:
572:
552:
549:
546:
526:
523:
520:
510:
504:
503:
492:
489:
486:
483:
463:
460:
457:
437:
434:
414:
411:
408:
388:
385:
382:
372:
362:
361:
351:
350:
348:
347:
340:
333:
325:
322:
321:
318:
314:
313:
310:
304:
303:
300:
294:
293:
290:
286:
285:
282:
278:
277:
269:
268:
257:
254:
251:
248:
245:
242:
232:
226:
225:
214:
211:
208:
198:
192:
191:
180:
177:
174:
164:
158:
157:
153:
152:
145:
139:
138:
127:
124:
121:
111:
105:
104:
93:
90:
87:
77:
73:
72:
64:
63:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
8001:
7990:
7987:
7985:
7982:
7980:
7977:
7976:
7974:
7959:
7956:
7954:
7951:
7949:
7946:
7944:
7941:
7939:
7936:
7934:
7931:
7929:
7926:
7924:
7921:
7919:
7916:
7914:
7911:
7910:
7908:
7904:
7894:
7891:
7889:
7886:
7884:
7881:
7879:
7876:
7874:
7871:
7869:
7866:
7864:
7861:
7859:
7856:
7854:
7851:
7849:
7846:
7844:
7841:
7839:
7836:
7834:
7831:
7829:
7826:
7824:
7821:
7819:
7816:
7814:
7811:
7809:
7806:
7804:
7801:
7800:
7798:
7794:
7788:
7785:
7783:
7780:
7778:
7775:
7773:
7770:
7768:
7765:
7763:
7760:
7758:
7755:
7753:
7750:
7748:
7745:
7743:
7740:
7738:
7735:
7733:
7730:
7728:
7725:
7723:
7720:
7718:
7715:
7713:
7710:
7708:
7705:
7704:
7702:
7698:
7695:
7691:
7681:
7678:
7676:
7673:
7671:
7668:
7666:
7663:
7661:
7658:
7656:
7653:
7651:
7648:
7646:
7643:
7641:
7638:
7636:
7633:
7631:
7628:
7626:
7623:
7621:
7620:Performatives
7618:
7616:
7613:
7611:
7608:
7606:
7603:
7601:
7600:Logophoricity
7598:
7596:
7593:
7591:
7588:
7586:
7583:
7581:
7578:
7576:
7573:
7571:
7568:
7566:
7563:
7561:
7558:
7556:
7553:
7551:
7548:
7546:
7543:
7541:
7538:
7536:
7533:
7531:
7528:
7526:
7523:
7521:
7518:
7516:
7513:
7511:
7508:
7506:
7503:
7501:
7498:
7496:
7493:
7492:
7490:
7486:
7480:
7477:
7475:
7472:
7470:
7467:
7465:
7462:
7460:
7457:
7455:
7452:
7450:
7447:
7445:
7442:
7440:
7437:
7435:
7434:Evidentiality
7432:
7430:
7427:
7425:
7422:
7420:
7417:
7415:
7412:
7410:
7407:
7405:
7402:
7401:
7399:
7395:
7392:
7388:
7382:
7379:
7377:
7374:
7372:
7369:
7367:
7364:
7362:
7359:
7357:
7354:
7352:
7349:
7347:
7344:
7342:
7339:
7337:
7334:
7332:
7329:
7327:
7324:
7322:
7319:
7317:
7314:
7313:
7311:
7307:
7303:
7296:
7291:
7289:
7284:
7282:
7277:
7276:
7273:
7263:
7258:
7252:
7240:
7230:
7223:
7218:
7214:
7207:
7202:
7199:
7195:
7190:
7187:
7183:
7178:
7173:
7168:
7165:
7160:
7156:
7151:
7148:
7144:
7139:
7136:
7132:
7127:
7122:
7117:
7114:
7110:
7105:
7102:
7098:
7093:
7090:
7086:
7081:
7078:
7072:
7067:
7064:
7058:
7053:
7050:
7049:contradiction
7045:
7041:
7036:
7033:
7028:
7024:
7019:
7016:
7012:
7007:
7002:
6997:
6996:
6991:
6987:
6979:
6974:
6972:
6967:
6965:
6960:
6959:
6956:
6946:
6945:
6940:
6932:
6926:
6923:
6921:
6918:
6916:
6913:
6911:
6908:
6904:
6901:
6900:
6899:
6896:
6894:
6891:
6889:
6886:
6884:
6880:
6877:
6875:
6872:
6870:
6867:
6865:
6862:
6860:
6857:
6856:
6854:
6850:
6844:
6841:
6839:
6836:
6834:
6833:Recursive set
6831:
6829:
6826:
6824:
6821:
6819:
6816:
6814:
6811:
6807:
6804:
6802:
6799:
6797:
6794:
6792:
6789:
6787:
6784:
6783:
6782:
6779:
6777:
6774:
6772:
6769:
6767:
6764:
6762:
6759:
6757:
6754:
6753:
6751:
6749:
6745:
6739:
6736:
6734:
6731:
6729:
6726:
6724:
6721:
6719:
6716:
6714:
6711:
6709:
6706:
6702:
6699:
6697:
6694:
6692:
6689:
6688:
6687:
6684:
6682:
6679:
6677:
6674:
6672:
6669:
6667:
6664:
6662:
6659:
6655:
6652:
6651:
6650:
6647:
6643:
6642:of arithmetic
6640:
6639:
6638:
6635:
6631:
6628:
6626:
6623:
6621:
6618:
6616:
6613:
6611:
6608:
6607:
6606:
6603:
6599:
6596:
6594:
6591:
6590:
6589:
6586:
6585:
6583:
6581:
6577:
6571:
6568:
6566:
6563:
6561:
6558:
6556:
6553:
6550:
6549:from ZFC
6546:
6543:
6541:
6538:
6532:
6529:
6528:
6527:
6524:
6522:
6519:
6517:
6514:
6513:
6512:
6509:
6507:
6504:
6502:
6499:
6497:
6494:
6492:
6489:
6487:
6484:
6482:
6479:
6478:
6476:
6474:
6470:
6460:
6459:
6455:
6454:
6449:
6448:non-Euclidean
6446:
6442:
6439:
6437:
6434:
6432:
6431:
6427:
6426:
6424:
6421:
6420:
6418:
6414:
6410:
6407:
6405:
6402:
6401:
6400:
6396:
6392:
6389:
6388:
6387:
6383:
6379:
6376:
6374:
6371:
6369:
6366:
6364:
6361:
6359:
6356:
6354:
6351:
6350:
6348:
6344:
6343:
6341:
6336:
6330:
6325:Example
6322:
6314:
6309:
6308:
6307:
6304:
6302:
6299:
6295:
6292:
6290:
6287:
6285:
6282:
6280:
6277:
6276:
6275:
6272:
6270:
6267:
6265:
6262:
6260:
6257:
6253:
6250:
6248:
6245:
6244:
6243:
6240:
6236:
6233:
6231:
6228:
6226:
6223:
6221:
6218:
6217:
6216:
6213:
6211:
6208:
6204:
6201:
6199:
6196:
6194:
6191:
6190:
6189:
6186:
6182:
6179:
6177:
6174:
6172:
6169:
6167:
6164:
6162:
6159:
6157:
6154:
6153:
6152:
6149:
6147:
6144:
6142:
6139:
6137:
6134:
6130:
6127:
6125:
6122:
6120:
6117:
6115:
6112:
6111:
6110:
6107:
6105:
6102:
6100:
6097:
6095:
6092:
6088:
6085:
6083:
6082:by definition
6080:
6079:
6078:
6075:
6071:
6068:
6067:
6066:
6063:
6061:
6058:
6056:
6053:
6051:
6048:
6046:
6043:
6042:
6039:
6036:
6034:
6030:
6025:
6019:
6015:
6005:
6002:
6000:
5997:
5995:
5992:
5990:
5987:
5985:
5982:
5980:
5977:
5975:
5972:
5970:
5969:Kripke–Platek
5967:
5965:
5962:
5958:
5955:
5953:
5950:
5949:
5948:
5945:
5944:
5942:
5938:
5930:
5927:
5926:
5925:
5922:
5920:
5917:
5913:
5910:
5909:
5908:
5905:
5903:
5900:
5898:
5895:
5893:
5890:
5888:
5885:
5882:
5878:
5874:
5871:
5867:
5864:
5862:
5859:
5857:
5854:
5853:
5852:
5848:
5845:
5844:
5842:
5840:
5836:
5832:
5824:
5821:
5819:
5816:
5814:
5813:constructible
5811:
5810:
5809:
5806:
5804:
5801:
5799:
5796:
5794:
5791:
5789:
5786:
5784:
5781:
5779:
5776:
5774:
5771:
5769:
5766:
5764:
5761:
5759:
5756:
5754:
5751:
5749:
5746:
5745:
5743:
5741:
5736:
5728:
5725:
5723:
5720:
5718:
5715:
5713:
5710:
5708:
5705:
5703:
5700:
5699:
5697:
5693:
5690:
5688:
5685:
5684:
5683:
5680:
5678:
5675:
5673:
5670:
5668:
5665:
5663:
5659:
5655:
5653:
5650:
5646:
5643:
5642:
5641:
5638:
5637:
5634:
5631:
5629:
5625:
5615:
5612:
5610:
5607:
5605:
5602:
5600:
5597:
5595:
5592:
5590:
5587:
5583:
5580:
5579:
5578:
5575:
5571:
5566:
5565:
5564:
5561:
5560:
5558:
5556:
5552:
5544:
5541:
5539:
5536:
5534:
5531:
5530:
5529:
5526:
5524:
5521:
5519:
5516:
5514:
5511:
5509:
5506:
5504:
5501:
5499:
5496:
5495:
5493:
5491:
5490:Propositional
5487:
5481:
5478:
5476:
5473:
5471:
5468:
5466:
5463:
5461:
5458:
5456:
5453:
5449:
5446:
5445:
5444:
5441:
5439:
5436:
5434:
5431:
5429:
5426:
5424:
5421:
5419:
5418:Logical truth
5416:
5414:
5411:
5410:
5408:
5406:
5402:
5399:
5397:
5393:
5387:
5384:
5382:
5379:
5377:
5374:
5372:
5369:
5367:
5364:
5362:
5358:
5354:
5350:
5348:
5345:
5343:
5340:
5338:
5334:
5331:
5330:
5328:
5326:
5320:
5315:
5309:
5306:
5304:
5301:
5299:
5296:
5294:
5291:
5289:
5286:
5284:
5281:
5279:
5276:
5274:
5271:
5269:
5266:
5264:
5261:
5259:
5256:
5254:
5251:
5247:
5244:
5243:
5242:
5239:
5238:
5236:
5232:
5228:
5221:
5216:
5214:
5209:
5207:
5202:
5201:
5198:
5188:
5176:
5150:
5146:
5145:Contradiction
5143:
5142:
5139:
5121:
5113:
5109:
5106:
5092:
5084:
5081:
5067:
5059:
5055:
5052:
5030:
5026:
5023:
5022:
5019:
5012:
5008:
5005:
4983:
4979:
4978:Biconditional
4976:
4962:
4954:
4950:
4947:
4925:
4921:
4918:
4917:
4914:
4896:
4888:
4884:
4881:
4859:
4855:
4852:
4830:
4827:
4805:
4801:
4798:
4797:
4794:
4789:
4759:
4755:
4752:
4751:
4748:
4744:
4736:
4731:
4729:
4724:
4722:
4717:
4716:
4713:
4706:
4702:
4698:
4697:
4692:
4688:
4687:"Disjunction"
4684:
4680:
4676:
4672:
4671:
4666:
4665:"Disjunction"
4662:
4661:
4657:
4648:
4642:
4638:
4631:
4628:
4622:
4617:
4613:
4606:
4603:
4590:
4584:
4581:
4569:
4563:
4560:
4555:
4549:
4545:
4538:
4535:
4530:
4524:
4520:
4516:
4512:
4511:
4503:
4500:
4484:
4477:
4473:
4467:
4464:
4460:
4456:
4451:
4448:
4443:
4437:
4433:
4426:
4423:
4412:
4408:
4402:
4399:
4388:
4384:
4383:"Disjunction"
4380:
4374:
4372:
4370:
4368:
4366:
4364:
4362:
4360:
4356:
4349:
4344:
4340:
4337:
4336:
4332:
4327:
4324:
4322:
4321:Logical graph
4319:
4317:
4314:
4312:
4309:
4307:
4304:
4302:
4299:
4297:
4294:
4292:
4289:
4287:
4284:
4282:
4279:
4277:
4274:
4272:
4269:
4267:
4264:
4263:
4258:
4255:
4252:
4249:
4245:
4228:
4223:
4217:
4212:
4206:
4201:
4199:
4195:
4191:
4187:
4183:
4179:
4174:
4172:
4168:
4164:
4160:
4150:
4149:
4148:
4147:
4146:
4119:
4118:
4114:
4113:
4112:
4111:
4110:
4108:
4104:
4100:
4096:
4091:
4089:
4085:
4082:
4078:
4075:
4071:
4067:
4063:
4059:
4055:
4054:Alfred Tarski
4051:
4041:
4040:
4039:
4038:
4037:
4035:
4019:
4011:
4003:
4001:
3998:
3996:
3992:
3988:
3984:
3980:
3976:
3972:
3971:commutativity
3968:
3967:associativity
3949:
3946:
3943:
3937:
3931:
3928:
3925:
3916:
3913:
3910:
3907:
3904:
3896:
3892:
3888:
3877:
3874:February 2021
3868:
3864:
3861:This section
3859:
3856:
3852:
3851:
3845:
3843:
3841:
3837:
3833:
3825:
3823:
3821:
3817:
3813:
3800:
3798:
3792:
3790:
3782:
3777:
3767:
3763:
3755:
3753:
3743:
3731:
3728:
3725:
3722:
3719:
3718:
3717:
3715:
3707:
3705:
3703:
3699:
3693:
3688:
3678:
3675:February 2021
3669:
3665:
3662:This section
3660:
3657:
3653:
3652:
3646:
3641:
3637:
3634:
3631:
3627:
3624:
3623:
3598:
3595:
3592:
3580:
3577:
3574:
3559:
3553:
3543:
3542:
3541:
3540:
3539:
3538:
3517:
3514:
3511:
3499:
3496:
3493:
3478:
3472:
3461:
3458:
3444:
3441:
3438:
3435:
3432:
3424:
3421:
3420:
3395:
3392:
3389:
3383:
3377:
3374:
3371:
3362:
3353:
3350:
3347:
3341:
3338:
3328:
3308:
3305:
3302:
3296:
3290:
3287:
3284:
3275:
3266:
3263:
3260:
3254:
3251:
3241:
3221:
3218:
3215:
3209:
3203:
3200:
3197:
3188:
3179:
3176:
3173:
3167:
3164:
3154:
3153:
3152:
3151:
3150:
3149:
3128:
3125:
3122:
3116:
3110:
3107:
3104:
3095:
3086:
3083:
3080:
3074:
3071:
3060:
3057:
3043:
3040:
3037:
3034:
3031:
3028:
3025:
3017:
3016:Commutativity
3014:
3012:
2998:
2995:
2989:
2986:
2983:
2977:
2971:
2968:
2965:
2959:
2956:
2948:
2947:Associativity
2945:
2944:
2943:
2937:
2935:
2927:
2924:
2921:
2918:
2915:
2914:
2910:
2907:
2904:
2901:
2898:
2897:
2893:
2890:
2887:
2884:
2881:
2880:
2876:
2873:
2870:
2867:
2864:
2863:
2848:
2845:
2842:
2821:
2812:
2806:
2782:
2776:
2755:
2748:
2734:
2727:
2726:
2723:
2705:
2696:
2690:
2684:
2681:
2678:
2675:
2668:
2667:
2666:
2638:
2635:
2632:
2629:
2626:
2625:
2621:
2618:
2615:
2612:
2609:
2608:
2604:
2601:
2598:
2595:
2592:
2591:
2587:
2584:
2581:
2578:
2575:
2574:
2559:
2556:
2553:
2532:
2526:
2502:
2478:
2471:
2457:
2450:
2449:
2446:
2428:
2419:
2410:
2407:
2404:
2401:
2394:
2393:
2392:
2370:
2344:
2335:
2329:
2314:
2311:
2308:
2305:
2298:
2297:
2296:
2274:
2258:
2250:
2246:
2238:
2231:
2228:
2225:
2224:
2220:
2217:
2214:
2213:
2209:
2206:
2203:
2202:
2198:
2195:
2192:
2191:
2176:
2173:
2170:
2149:
2142:
2128:
2121:
2120:
2117:
2115:
2093:
2090:
2070:
2067:
2047:
2044:
2041:
2038:
2031:
2030:
2029:
2028:
2027:
2025:
2021:
2018:
2014:
2006:
2001:
1999:
1997:
1981:
1973:
1969:
1965:
1918:, as well as
1917:
1901:
1868:
1856:
1854:
1852:
1847:
1845:
1841:
1837:
1829:
1827:
1825:
1821:
1816:
1814:
1810:
1806:
1802:
1798:
1797:non-classical
1794:
1790:
1786:
1782:
1778:
1762:
1742:
1722:
1719:
1716:
1708:
1704:
1699:
1685:
1665:
1645:
1642:
1639:
1631:
1615:
1607:
1603:
1599:
1595:
1591:
1587:
1583:
1563:
1560:
1557:
1554:
1551:
1542:
1538:
1527:
1522:
1520:
1515:
1513:
1508:
1507:
1505:
1504:
1501:
1493:
1492:
1486:
1483:
1481:
1478:
1476:
1473:
1471:
1470:Digital logic
1468:
1467:
1465:
1464:
1459:
1453:
1452:Scope (logic)
1450:
1448:
1445:
1443:
1440:
1438:
1435:
1433:
1430:
1428:
1425:
1423:
1420:
1418:
1415:
1414:
1412:
1411:
1406:
1387:
1381:
1361:
1358:
1355:
1335:
1329:
1322:
1320:
1317:
1316:
1301:
1298:
1295:
1275:
1270:
1267:
1262:
1255:
1253:
1250:
1249:
1234:
1220:
1213:
1211:
1208:
1207:
1192:
1189:
1186:
1166:
1163:
1160:
1140:
1137:
1134:
1114:
1111:
1108:
1101:
1099:
1096:
1095:
1080:
1077:
1052:
1030:
1027:
1007:
997:
995:
992:
991:
970:
967:
964:
941:
935:
915:
907:
902:
895:
893:
890:
889:
874:
871:
868:
848:
845:
842:
822:
819:
816:
809:
807:nonequivalent
806:
805:
784:
781:
778:
755:
752:
749:
729:
723:
703:
695:
690:
683:
681:
678:
677:
662:
656:
636:
633:
630:
610:
604:
597:
595:
592:
591:
576:
570:
550:
544:
524:
521:
518:
511:
509:
506:
505:
490:
481:
461:
455:
435:
432:
412:
409:
406:
386:
383:
380:
373:
371:
368:
367:
364:
363:
360:
356:
346:
341:
339:
334:
332:
327:
326:
323:
319:
315:
311:
309:
305:
301:
299:
295:
291:
287:
283:
279:
276:
270:
255:
252:
249:
246:
243:
240:
233:
231:
227:
212:
209:
206:
199:
197:
193:
178:
175:
172:
165:
163:
159:
154:
150:
146:
144:
140:
122:
112:
110:
106:
91:
88:
85:
78:
74:
70:
65:
60:
52:
48:
41:
37:
33:
19:
7888:Type shifter
7863:Quantization
7813:Continuation
7680:Veridicality
7560:Exhaustivity
7525:Cumulativity
7444:Indexicality
7424:Definiteness
7419:Conditionals
7346:Logical form
7176:
7125:
7112:
7005:
6935:
6733:Ultraproduct
6580:Model theory
6545:Independence
6481:Formal proof
6473:Proof theory
6456:
6429:
6386:real numbers
6358:second-order
6269:Substitution
6160:
6146:Metalanguage
6087:conservative
6060:Axiom schema
6004:Constructive
5974:Morse–Kelley
5940:Set theories
5919:Aleph number
5912:inaccessible
5818:Grothendieck
5702:intersection
5589:Higher-order
5577:Second-order
5523:Truth tables
5480:Venn diagram
5263:Formal proof
5025:Joint denial
4949:Exclusive or
4882:
4694:
4683:Aloni, Maria
4668:
4636:
4630:
4611:
4605:
4593:. Retrieved
4583:
4571:. Retrieved
4562:
4543:
4537:
4519:10.1142/9783
4509:
4502:
4466:
4458:
4450:
4431:
4425:
4414:. Retrieved
4410:
4401:
4391:, retrieved
4386:
4379:Aloni, Maria
4339:George Boole
4253:
4250:
4247:
4229:
4218:
4207:
4197:
4175:
4156:
4144:
4092:
4084:soit... soit
4083:
4077:vagy... vagy
4076:
4047:
4007:
3999:
3884:
3871:
3867:adding to it
3862:
3840:tagged union
3829:
3801:
3796:
3793:
3778:
3776:) operator.
3759:
3735:
3716:. Examples:
3711:
3696:
3672:
3668:adding to it
3663:
3635:
3625:
3460:Monotonicity
3011:
2941:
2933:
2721:
2644:
2444:
2366:
2242:
2111:
2010:
1995:
1860:
1848:
1844:exclusive or
1843:
1835:
1833:
1823:
1817:
1783:. Classical
1776:
1700:
1601:
1597:
1593:
1589:
1585:
1579:
1541:Venn diagram
1461:Applications
1097:
289:1-preserving
281:0-preserving
156:Normal forms
46:
18:Inclusive-or
7808:Context set
7782:Type theory
7665:Subtrigging
7429:Disjunction
7356:Proposition
7227:existential
6843:Type theory
6791:undecidable
6723:Truth value
6610:equivalence
6289:non-logical
5902:Enumeration
5892:Isomorphism
5839:cardinality
5823:Von Neumann
5788:Ultrafilter
5753:Uncountable
5687:equivalence
5604:Quantifiers
5594:Fixed-point
5563:First-order
5443:Consistency
5428:Proposition
5405:Traditional
5376:Lindström's
5366:Compactness
5308:Type theory
5253:Cardinality
5108:Conjunction
5058:NIMPLY gate
4883:Disjunction
4854:Implication
4227:vʔaawuumšaa
4107:conjunction
4034:exclusively
3797:parallel or
3640:truth value
3630:truth value
3423:Idempotency
2114:truth table
2024:truth value
1996:alternatywa
1916:electronics
1586:disjunction
1432:Truth table
196:Conjunctive
162:Disjunctive
109:Truth table
7973:Categories
7953:Pragmatics
7605:Mirativity
7371:Speech act
7326:Entailment
7321:Denotation
6654:elementary
6347:arithmetic
6215:Quantifier
6193:functional
6065:Expression
5783:Transitive
5727:identities
5712:complement
5645:hereditary
5628:Set theory
4858:IMPLY gate
4621:1505.00061
4416:2020-09-03
4393:2020-09-03
4350:References
4105:trigger a
4062:pragmatics
4050:entailment
3895:set theory
3887:membership
3846:Set theory
3834:relates a
3816:JavaScript
3729:1 or 1 = 1
3726:1 or 0 = 1
3723:0 or 1 = 1
3720:0 or 0 = 0
3692:logic gate
2938:Properties
1892:LOGICAL OR
1805:Heisenberg
1594:logical or
508:equivalent
143:Logic gate
76:Definition
7984:Semantics
7757:Mereology
7693:Formalism
7575:Givenness
7500:Cataphora
7488:Phenomena
7479:Vagueness
7409:Ambiguity
7361:Reference
7341:Intension
7331:Extension
7211:universal
7089:therefore
7077:therefore
7032:tautology
6925:Supertask
6828:Recursion
6786:decidable
6620:saturated
6598:of models
6521:deductive
6516:axiomatic
6436:Hilbert's
6423:Euclidean
6404:canonical
6327:axiomatic
6259:Signature
6188:Predicate
6077:Extension
5999:Ackermann
5924:Operation
5803:Universal
5793:Recursive
5768:Singleton
5763:Inhabited
5748:Countable
5738:Types of
5722:power set
5692:partition
5609:Predicate
5555:Predicate
5470:Syllogism
5460:Soundness
5433:Inference
5423:Tautology
5325:paradoxes
5159:⊥
5122:∧
5093:↚
5068:↛
5039:↓
5007:Statement
4992:↔
4982:XNOR gate
4934:¬
4897:∨
4868:→
4839:←
4814:↑
4804:NAND gate
4768:⊤
4754:Tautology
4675:EMS Press
4485:⊨
4127:⇝
4074:Hungarian
4058:ambiguous
4020:∨
3947:∈
3938:∨
3929:∈
3920:⇔
3914:∪
3908:∈
3891:union set
3744:to 1, by
3742:bit field
3698:Operators
3596:∨
3587:→
3578:∨
3566:→
3557:→
3515:∨
3506:→
3497:∨
3485:→
3476:→
3442:≡
3436:∨
3393:∨
3384:≡
3375:∨
3363:≡
3351:≡
3342:∨
3306:∨
3297:∨
3288:∨
3276:≡
3264:∨
3255:∨
3219:∨
3210:∧
3201:∨
3189:≡
3177:∧
3168:∨
3126:∧
3117:∨
3108:∧
3096:≡
3084:∨
3075:∧
3041:∨
3035:≡
3029:∨
2996:∨
2987:∨
2978:≡
2969:∨
2960:∨
2846:∨
2819:→
2810:→
2780:→
2703:→
2694:→
2679:∨
2653:→
2557:∨
2530:→
2524:¬
2500:¬
2426:→
2417:¬
2405:∨
2379:→
2342:¬
2336:∧
2327:¬
2318:¬
2309:∨
2283:¬
2259:∧
2174:∨
2094:ψ
2091:⊨
2071:ϕ
2068:⊨
2048:ψ
2045:∨
2042:ϕ
2039:⊨
2020:operation
2007:Semantics
1881:(Unicode
1869:∨
1836:inclusive
1777:inclusive
1763:ψ
1743:ϕ
1723:ψ
1720:∨
1717:ϕ
1643:∨
1616:∨
1561:∨
1555:∨
1385:←
1359:⊂
1333:⇐
1299:⊕
1271:_
1268:∨
1190:∥
1164:∣
1112:∨
1078:∼
1056:¯
1028:−
1005:¬
975:¯
939:↓
911:¯
908:∨
872:↮
789:¯
782:⋅
753:∣
727:↑
699:¯
696:∧
660:→
634:⊃
608:⇒
574:⇋
548:⇔
522:≡
488:&
485:&
459:&
410:⋅
384:∧
317:Self-dual
250:⊕
244:⊕
7906:See also
7796:Concepts
7670:Telicity
7505:Coercion
7459:Negation
7454:Modality
7404:Anaphora
7164:superset
7075:entails,
7061:entails,
6910:Logicism
6903:timeline
6879:Concrete
6738:Validity
6708:T-schema
6701:Kripke's
6696:Tarski's
6691:semantic
6681:Strength
6630:submodel
6625:spectrum
6593:function
6441:Tarski's
6430:Elements
6417:geometry
6373:Robinson
6294:variable
6279:function
6252:spectrum
6242:Sentence
6198:variable
6141:Language
6094:Relation
6055:Automata
6045:Alphabet
6029:language
5883:-jection
5861:codomain
5847:Function
5808:Universe
5778:Infinite
5682:Relation
5465:Validity
5455:Argument
5353:theorem,
5112:AND gate
5029:NOR gate
4963:↮
4953:XOR gate
4924:NOT gate
4920:Negation
4457:(1959),
4381:(2016),
4259:See also
4190:Maricopa
4070:semantic
1962:in many
1889:∨
1857:Notation
1824:disjunct
1500:Category
1319:converse
846:⇎
820:≢
298:Monotone
7414:Binding
7180:
7159:implies
7147:implies
7129:
7101:because
7009:
6984:Common
6852:Related
6649:Diagram
6547: (
6526:Hilbert
6511:Systems
6506:Theorem
6384:of the
6329:systems
6109:Formula
6104:Grammar
6020: (
5964:General
5677:Forcing
5662:Element
5582:Monadic
5357:paradox
5298:Theorem
5234:General
5114:)
5110: (
5060:)
5056: (
5031:)
5027: (
5009: (
4984:)
4980: (
4955:)
4951: (
4926:)
4922: (
4889:)
4887:OR gate
4885: (
4860:)
4856: (
4806:)
4802: (
4741:Common
4693:(ed.).
4677:, 2001
4186:Dyirbal
3842:types.
2369:implies
2271:) and "
2011:In the
1820:operand
1630:English
1604:, is a
594:implies
36:Meiosis
32:OR gate
7843:Monads
7390:Topics
7174:
7123:
7063:proves
7003:
6615:finite
6378:Skolem
6331:
6306:Theory
6274:Symbol
6264:String
6247:atomic
6124:ground
6119:closed
6114:atomic
6070:ground
6033:syntax
5929:binary
5856:domain
5773:Finite
5538:finite
5396:Logics
5355:
5303:Theory
5151:
5085:
4831:
4760:
4643:
4595:25 Dec
4573:25 Dec
4550:
4525:
4476:symbol
4438:
4343:Jevons
4233:-come-
4194:suffix
4081:French
3977:, and
3812:Python
2295:) as:
1886:
1884:U+2228
1851:and/or
1232:
1224:
308:Affine
7535:De se
7439:Focus
7397:Areas
7366:Scope
7044:false
7011:&
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6210:Proof
6050:Arity
5979:Naive
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5283:Lemma
5241:Axiom
5149:False
4689:. In
4616:arXiv
4614:: 6.
4333:Notes
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4219:Bill-
4216:Billš
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4210:NOM
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3806:or
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292:yes
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7975::
7177:or
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6425::
6419::
6349::
6026:),
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4673:,
4667:,
4521:.
4474:"
4409:.
4358:^
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4756:/
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4624:.
4618::
4599:.
4577:.
4556:.
4531:.
4517::
4444:.
4419:.
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2585:F
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2533:B
2527:A
2503:A
2479:B
2458:A
2441:.
2429:B
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2420:A
2414:(
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2402:A
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2351:)
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2345:B
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2324:(
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2204:F
2199:F
2196:F
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2171:A
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1982:A
1950:|
1946:|
1926:|
1902:+
1686:W
1666:S
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1640:S
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1388:B
1382:A
1362:B
1356:A
1336:B
1330:A
1302:B
1296:A
1276:B
1263:A
1235:B
1221:A
1193:B
1187:A
1167:B
1161:A
1141:B
1138:+
1135:A
1115:B
1109:A
1081:A
1053:A
1031:A
1008:A
971:B
968:+
965:A
942:B
936:A
916:B
903:A
875:B
869:A
849:B
843:A
823:B
817:A
785:B
779:A
756:B
750:A
730:B
724:A
704:B
691:A
663:B
657:A
637:B
631:A
611:B
605:A
577:B
571:A
551:B
545:A
525:B
519:A
491:B
482:A
462:B
456:A
436:B
433:A
413:B
407:A
387:B
381:A
344:e
337:t
330:v
256:y
253:x
247:y
241:x
213:y
210:+
207:x
179:y
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173:x
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89:+
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