6664:
10440:
1219:
8289:
6632:
6702:
6693:
6250:
1178:
1553:
6708:
1525:
2095:
2064:
2033:
1984:
1953:
1922:
1891:
1860:
1829:
1782:
8683:
7273:
1658:
1633:
7287:
6539:
However, not all compilers use the same order; for instance, an ordering in which disjunction is lower precedence than implication or bi-implication has also been used. Sometimes precedence between conjunction and disjunction is unspecified requiring to provide it explicitly in given formula with
6238:
Both conjunction and disjunction are associative, commutative and idempotent in classical logic, most varieties of many-valued logic and intuitionistic logic. The same is true about distributivity of conjunction over disjunction and disjunction over conjunction, as well as for the absorption law.
6230:
For classical and intuitionistic logic, the "=" symbol means that corresponding implications "...→..." and "...←..." for logical compounds can be both proved as theorems, and the "≤" symbol means that "...→..." for logical compounds is a consequence of corresponding "...→..." connectives for
1397:"not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classical
7169:
5257:
5143:
1198:
6389:
6330:
5295:
5030:
5219:
5181:
5062:
6961:
5105:
7100:
7036:
7250:
5820:
Within an expression containing two or more of the same associative connectives in a row, the order of the operations does not matter as long as the sequence of the operands is not changed.
4742:
4710:
4838:
4966:
4902:
4870:
541:
4998:
4934:
4774:
2656:
2550:
968:
483:
396:
8474:
6242:
In classical logic and some varieties of many-valued logic, conjunction and disjunction are dual, and negation is self-dual, the latter is also self-dual in intuitionistic logic.
4806:
608:
269:
4006:
3981:
927:
567:
5937:
2986:
243:
6194:
6099:
4550:
2008:
669:
8503:
6529:
5686:
4678:
4614:
3830:
3786:
3762:
3742:
2696:
2630:
2570:
2524:
5811:
Some logical connectives possess properties that may be expressed in the theorems containing the connective. Some of those properties that a logical connective may have are:
4518:
4481:
3363:
750:
4646:
4582:
2951:
2911:
515:
355:
303:
183:
8579:
4455:
1080:
1028:
634:
8604:
8379:
4240:
3952:
3887:
3691:
3179:
3091:
2438:
885:
8550:
8350:
6113:
is the same as taking the complement of reading the table of the same or another connective from bottom to top. Without resorting to truth tables it may be formulated as
5758:
5617:
4195:
422:
1054:
329:
8325:
5794:
5722:
2836:
994:
217:
3930:
3671:
2676:
2498:
2418:
154:
105:
79:
6580:
5650:
5509:
3718:
3415:
3392:
2871:
2590:
2306:
2246:
1352:
859:
807:
448:
8633:
6451:
4266:
3486:
3462:
2801:
2266:
773:
700:
8670:
8445:
8408:
8279:
6477:
6425:
5545:
5473:
5366:
The meanings of natural language connectives are not precisely identical to their nearest equivalents in classical logic. In particular, disjunction can receive an
4326:
4306:
3810:
3548:
3517:
3442:
3332:
3300:
3117:
3029:
2372:
2332:
2220:
2200:
2160:
2140:
1283:
6707:
6503:
5581:
4346:
4286:
3647:
2716:
2478:
2398:
4159:
4133:
4107:
4081:
4055:
833:
6623:
4029:
723:
128:
6600:
4400:
4380:
3910:
3853:
3620:
3588:
3568:
3157:
3137:
3069:
3049:
2768:
2744:
2610:
2458:
2352:
2286:
2180:
1809:
1762:
1723:
1687:
1619:
1584:
1326:
1306:
1205:
1424:, truth functions are represented by unambiguous symbols. This allows logical statements to not be understood in an ambiguous way. These symbols are called
8819:
6701:
5413:. These phenomena have been taken as motivation for identifying the denotations of natural language conditionals with logical operators including the
1447:. For the rules which allow new well-formed formulas to be constructed by joining other well-formed formulas using truth-functional connectives, see
7627:
Die
Aristotelische Theorie der Möglichkeitsschlösse: Eine logisch-philologische Untersuchung der Kapitel 13-22 von Aristoteles' Analytica priora I
5324:
for more). Neither conjunction, disjunction, nor material conditional has an equivalent form constructed from the other four logical connectives.
7403:
9494:
8233:
7520:
4422:
7118:
9577:
8718:
10476:
6692:
10950:
4421:
set, and define other connectives by some logical form, as in the example with the material conditional above. The following are the
5224:
6540:
parentheses. The order of precedence determines which connective is the "main connective" when interpreting a non-atomic formula.
5110:
9891:
6081:
Each variable always makes a difference in the truth-value of the operation or it never makes a difference. E.g., ¬, ↔,
5382:
accounts of exclusivity which create the illusion of nonclassicality. In such accounts, exclusivity is typically treated as a
10049:
8151:
8132:
8076:
7799:
7747:
6335:
8837:
9904:
9227:
1191:
6846: P is false (although a compound as a whole is successful ≈ "true" in such case). This is closer to intuitionist and
10818:
10485:
8205:
8190:
6292:
5360:
1398:
5262:
5003:
9909:
9899:
9636:
9489:
8842:
6680:
6679:
5186:
5148:
5035:
8833:
6904:
5072:
10045:
8226:
7774:
7722:
7054:
6979:
6675:
6642:
6640:
6289:: ¬ has higher precedence than ∧, ∧ higher than ∨, and ∨ higher than →. So for example,
5402:
4201:
with swapped arguments; thus, the symbol for converse implication is redundant. In some logical calculi (notably, in
17:
9387:
7187:
6637:
5332:
The standard logical connectives of classical logic have rough equivalents in the grammars of natural languages. In
1408:
A logical connective is similar to, but not equivalent to, a syntax commonly used in programming languages called a
10142:
9886:
8711:
8116:
6647:
6670:
6669:
4715:
10905:
9447:
9140:
6681:
8881:
6651:
6649:
6162:
The compound all those arguments are tautologies is a tautology itself. E.g., ∨, ∧, ⊤, →, ↔, ⊂ (see
5301:
Another approach is to use with equal rights connectives of a certain convenient and functionally complete, but
4683:
11026:
10900:
10559:
10469:
10403:
10105:
9868:
9863:
9688:
9109:
8793:
7818:
7336:
6827:
6671:
6639:
5321:
2102:
8168:
4811:
10678:
10499:
10398:
10181:
10098:
9811:
9742:
9619:
8861:
8178:
6682:
6667:
6653:
6645:
4939:
4875:
4843:
520:
6668:
6652:
4971:
4907:
4747:
2635:
2529:
940:
453:
368:
11167:
10323:
10149:
9835:
9469:
9068:
8459:
8219:
7971:
7851:
6678:
6646:
5371:
4779:
1181:
580:
248:
7682:
Verhandlungen des
Dritten Internationalen Mathematiker Kongresses in Heidelberg vom 8. bis 13. August 1904
6674:
6638:
10564:
10201:
10196:
9806:
9545:
9474:
8803:
8704:
8173:
6780:
6261:
5887:
Whenever the operands of the operation are the same, the compound is logically equivalent to the operand.
5828:
The operands of the connective may be swapped, preserving logical equivalence to the original expression.
5428:
The following table shows the standard classically definable approximations for the
English connectives.
5418:
5410:
3986:
3961:
3864:
898:
546:
6644:
5898:
2965:
222:
11046:
10708:
10529:
10130:
9720:
9114:
9082:
8773:
8040:
7694:
6636:
6179:
6084:
5320:. Of its five connectives, {∧, ∨, →, ¬, ⊥}, only negation "¬" can be reduced to other connectives (see
4523:
1993:
639:
8488:
7899:
6635:
6514:
5671:
4651:
4587:
3815:
3771:
3747:
3727:
2681:
2615:
2555:
2509:
1393:. Their classical interpretations are similar to the meanings of natural language expressions such as
11051:
11001:
10763:
10652:
10462:
10420:
10369:
10266:
9764:
9725:
9202:
8847:
7875:
7506:(American Journal of Mathematics 30, p222–262, also in From Frege to Gödel edited by van Heijenoort).
6892:
6831:
4491:
4460:
3422:
3341:
728:
8876:
4619:
4555:
2930:
2890:
494:
334:
282:
159:
11111:
10970:
10549:
10261:
10191:
9730:
9582:
9565:
9288:
8768:
8564:
8194:
8047:, translated from the French and German editions by Otto Bird, D. Reidel, Dordrecht, South Holland.
6847:
6203:
4434:
4210:
1059:
1007:
613:
8589:
8364:
4216:
3935:
3870:
3676:
3162:
3074:
2423:
864:
11106:
10647:
10093:
10070:
10031:
9917:
9858:
9504:
9424:
9268:
9212:
8825:
8583:
8554:
8535:
8335:
7316:
7258:
7042:
5772:
5743:
5602:
5337:
4411:
4180:
1128:
401:
7466:
7452:
Sitzungsberichte der
Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse
6772:
1033:
308:
11172:
11136:
10803:
10773:
10748:
10688:
10587:
10519:
10383:
10110:
10088:
10055:
9948:
9794:
9779:
9752:
9703:
9587:
9522:
9347:
9313:
9308:
9182:
9013:
8990:
8310:
8017:
7996:
7948:
7556:
7356:
7175:
5779:
5707:
3623:
2815:
1098:
973:
196:
7764:
7712:
7680:
Hilbert, D. (1905) . "Über die
Grundlagen der Logik und der Arithmetik". In Krazer, K. (ed.).
3915:
3656:
2661:
2483:
2403:
133:
84:
58:
11031:
10925:
10890:
10778:
10753:
10597:
10514:
10313:
10166:
9958:
9676:
9412:
9318:
9177:
9162:
9043:
9018:
8478:
8424:
7923:
7180:
6677:
6676:
6559:
6104:
6076:
5664:
5635:
5494:
5477:
5387:
5367:
4403:
3703:
3400:
2850:
2575:
2503:
2291:
2231:
2043:
1374:
1331:
838:
786:
427:
189:
31:
8618:
6436:
4245:
3471:
3447:
2783:
2251:
755:
682:
11016:
10823:
10602:
10286:
10248:
10125:
9929:
9769:
9693:
9671:
9499:
9457:
9356:
9323:
9187:
8975:
8886:
8655:
8430:
8393:
8354:
8264:
7111:
6863:
6835:
6791:
6673:
6643:
6641:
6462:
6410:
5595:
5559:
5530:
5458:
5395:
5370:
in many languages. Some researchers have taken this fact as evidence that natural language
5352:
5317:
4311:
4291:
4198:
4174:
3795:
3533:
3502:
3427:
3317:
3285:
3102:
3014:
2377:
2357:
2317:
2205:
2185:
2145:
2125:
2074:
1963:
1409:
1370:
1268:
1156:
275:
7536:
6650:
6648:
6488:
5566:
4331:
4271:
3632:
3465:
3338:
in 1908; an alternative notation is to add a horizontal line on top of the formula, as in
2701:
2463:
2383:
8:
11101:
11066:
11011:
10955:
10858:
10843:
10813:
10793:
10768:
10637:
10622:
10415:
10306:
10291:
10271:
10228:
10115:
10065:
9991:
9936:
9873:
9666:
9661:
9609:
9377:
9366:
9038:
8938:
8866:
8857:
8853:
8788:
8783:
8608:
8383:
8104:
7341:
6972:
6897:
6672:
5523:
5487:
5391:
4206:
4138:
4112:
4086:
4060:
4034:
2311:
2225:
1901:
1839:
1448:
1366:
1258:
1166:
812:
779:
51:
8201:
8186:
6605:
4011:
3372:
1454:
Logical connectives can be used to link zero or more statements, so one can speak about
705:
110:
11146:
11071:
11041:
11006:
10986:
10915:
10895:
10833:
10828:
10738:
10728:
10713:
10657:
10444:
10213:
10176:
10161:
10154:
10137:
9941:
9923:
9789:
9715:
9698:
9464:
9373:
9207:
9192:
9152:
9104:
9089:
9077:
9033:
8778:
8727:
7612:
Begriffsschrift, eine der arithmetischen nachgebildete
Formelsprache des reinen Denkens
7482:
Begriffsschrift, eine der arithmetischen nachgebildete
Formelsprache des reinen Denkens
6967:
6843:
6585:
5414:
5383:
5375:
4385:
4365:
3895:
3860:
3838:
3605:
3591:
3573:
3553:
3528:
3493:
3142:
3122:
3054:
3034:
2753:
2729:
2595:
2443:
2337:
2271:
2165:
1794:
1747:
1708:
1672:
1604:
1569:
1390:
1382:
1311:
1291:
1230:
1161:
10454:
9397:
5401:
Other apparent discrepancies between natural language and classical logic include the
4268:. Therefore, a classical-based logical system does not need the conditional operator "
4162:
11126:
11081:
11061:
11021:
10960:
10930:
10910:
10703:
10632:
10439:
10379:
10186:
9996:
9986:
9878:
9759:
9594:
9570:
9351:
9335:
9240:
9217:
9094:
9063:
9028:
8923:
8758:
8687:
8507:
8254:
8147:
8128:
8093:
8072:
7795:
7770:
7743:
7718:
7331:
7321:
7292:
7278:
6784:
6232:
5422:
1511:
1103:
8288:
1476:
can be thought of as zero-ary operators. Negation is a 1-ary connective, and so on.
1218:
11131:
11056:
10945:
10723:
10393:
10388:
10281:
10238:
10060:
10021:
10016:
10001:
9827:
9784:
9681:
9479:
9429:
9003:
8965:
8329:
8120:
8064:
7499:
7346:
7306:
6722:
6197:
6163:
5333:
4356:
3912:
comes also from Boole's interpretation of logic as a ring; other notations include
3765:
3694:
3520:
3335:
1394:
1250:
1123:
1000:
10935:
10838:
10733:
10698:
10374:
10364:
10318:
10301:
10256:
10218:
10120:
10040:
9847:
9774:
9747:
9735:
9641:
9555:
9529:
9484:
9452:
9253:
9055:
8998:
8948:
8913:
8871:
7654:
6795:
6748:
6286:
5406:
4407:
4349:
4202:
3789:
3311:
1465:
1437:
1421:
1378:
1262:
1108:
7580:
Hilbert, D. (2013). "Prinzipien der
Mathematik". In Ewald, W.; Sieg, W. (eds.).
6818:, so these connectives are not commutative if either or both of the expressions
6109:
To read the truth-value assignments for the operation from top to bottom on its
4406:
outputs. These correspond to possible choices of binary logical connectives for
11121:
11116:
11036:
10920:
10798:
10693:
10534:
10359:
10338:
10296:
10276:
10171:
10026:
9624:
9614:
9604:
9599:
9533:
9407:
9283:
9172:
9167:
9145:
8746:
8511:
8300:
8085:
7515:
7371:
7351:
7301:
5890:
5836:
A connective denoted by · distributes over another connective denoted by +, if
5831:
5700:
5341:
3524:
3418:
3366:
1870:
1442:
1386:
1286:
1254:
1118:
361:
8124:
11161:
10808:
10783:
10617:
10333:
10011:
9518:
9303:
9293:
9263:
9248:
8918:
8649:
8645:
8258:
8211:
8112:
7582:
David
Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917–1933
7311:
6553:
6549:
6173:
5823:
5815:
4008:
for disjunction (German's "oder" for "or") in early works by
Hilbert (1904);
3721:
3650:
3307:
3303:
3096:
1539:
1535:
1222:
1133:
8097:
6394:
Here is a table that shows a commonly used precedence of logical operators.
6285:
As a way of reducing the number of necessary parentheses, one may introduce
11076:
10996:
10863:
10743:
10627:
10607:
10233:
10080:
9981:
9973:
9853:
9801:
9710:
9646:
9629:
9560:
9419:
9278:
8980:
8763:
8449:
6850:
views on the material conditional— rather than to classical logic's views.
6756:
5950:
5628:
3856:
3599:
3595:
3489:
2012:
1253:. Connectives can be used to connect logical formulas. For instance in the
933:
10991:
10965:
10848:
10612:
10539:
10343:
10223:
9402:
9392:
9339:
9023:
8943:
8928:
8808:
8753:
8558:
8525:
7381:
7376:
7326:
6760:
6235:
may have incompatible definitions of equivalence and order (entailment).
6110:
5882:
5798:
5736:
4360:
1932:
1362:
1113:
573:
7584:. Heidelberg, New York, Dordrecht and London: Springer. pp. 59–221.
7450:
Heyting, A. (1930). "Die formalen Regeln der intuitionistischen Logik".
6249:
11141:
10788:
10554:
10509:
10504:
9273:
9128:
9099:
8905:
8358:
7366:
7361:
6869:
6859:
6768:
6744:
6738:
6726:
5895:
A pair of connectives ∧, ∨ satisfies the absorption law if
5585:
5379:
5356:
3889:(abbreviation for the Latin word "verum") to be found in Peano in 1889.
3744:
in Becker in 1933 (not the first time and for this see the following);
1402:
1151:
7164:{\displaystyle A\subseteq B\leftrightarrow (x\in A\rightarrow x\in B)}
3570:
is also used, in spite of the ambiguity coming from the fact that the
2770:) is transformed, when the two are combined with logical connectives:
10940:
10758:
10683:
10662:
10592:
10544:
10524:
10425:
10328:
9381:
9298:
9258:
9222:
9158:
8970:
8960:
8933:
8696:
8482:
8304:
6868:
Logical connectives are used to define the fundamental operations of
6776:
5726:
5690:
891:
7576:. Lecture notes at Universität Göttingen, Winter Semester, 1917-1918
4410:. Different implementations of classical logic can choose different
10853:
10642:
10410:
10208:
9656:
9361:
8955:
8612:
8529:
8453:
8420:
7404:"What is the difference between logical and conditional /operator/"
7047:
6764:
6743:
A truth-functional approach to logical operators is implemented as
5762:
5654:
5513:
5451:
5363:, a field that studies the logical structure of natural languages.
3768:
in 1954; other symbols appeared punctually in the history, such as
3673:
was used by Russell in 1908 (compare to Peano's Ɔ the inverted C);
2119:
1643:
1358:
675:
1389:, though they receive a variety of alternative interpretations in
10006:
8798:
8387:
5549:
3001:
5359:
of natural language connectives is a major topic of research in
7106:
5348:
5309:, and each equivalence between logical forms must be either an
3622:
together with a dot in the lower right corner has been used by
2115:
Commonly used logical connectives include the following ones.
1552:
7794:. Mineola, New York: Dover Publications, Inc. pp. 26–29.
10718:
9550:
8896:
8741:
7614:(in German). Halle a/S.: Verlag von Louis Nebert. p. 15.
5310:
5306:
5252:{\displaystyle \{\land ,\leftrightarrow ,\nleftrightarrow \}}
4213:
example of a redundancy is the classical equivalence between
3008:
1524:
1507:
1456:
8092:, vol. 1, University of Chicago Press, pp. 54–64,
8057:
Mathematical Logic: Applications of the Formalization Method
7644:(in French). Paris: Hermann & Cie, Éditeurs. p. 32.
7629:(in German). Berlin: Junker und Dünnhaupt Verlag. p. 4.
7434:
Mathematical Logic: Applications of the Formalization Method
5138:{\displaystyle \{\lor ,\leftrightarrow ,\nleftrightarrow \}}
6752:
6751:. Practically all digital circuits (the major exception is
5378:. However, others maintain classical semantics by positing
5345:
2094:
2063:
2032:
1983:
1952:
1921:
1890:
1859:
1828:
1781:
8018:"Set Operations and Subsets – Foundations of Mathematics"
7997:"Set Operations and Subsets – Foundations of Mathematics"
7949:"Set Operations and Subsets – Foundations of Mathematics"
7742:(3rd ed.). Cambridge, Massachusetts: The MIT Press.
4205:), certain essentially different compound statements are
1657:
1632:
4352:
for a compound having one negation and one disjunction.
10484:
6384:{\displaystyle (P\vee (Q\wedge (\neg R)))\rightarrow S}
5336:, as in many languages, such expressions are typically
8059:] (in Chinese). Beijing: Preprint. pp. 15–28.
7436:] (in Chinese). Beijing: Preprint. pp. 15–28.
5322:
False (logic) § False, negation and contradiction
8658:
8621:
8592:
8567:
8538:
8491:
8462:
8433:
8396:
8367:
8338:
8313:
8267:
7710:
7257:
This definition of set equality is equivalent to the
7190:
7121:
7057:
6982:
6907:
6608:
6588:
6562:
6517:
6491:
6465:
6439:
6413:
6338:
6295:
6182:
6087:
5901:
5782:
5746:
5710:
5674:
5638:
5605:
5569:
5533:
5497:
5461:
5265:
5227:
5189:
5151:
5113:
5075:
5038:
5006:
4974:
4942:
4910:
4878:
4846:
4814:
4782:
4750:
4718:
4686:
4654:
4622:
4590:
4558:
4526:
4494:
4463:
4437:
4388:
4368:
4334:
4314:
4294:
4274:
4248:
4219:
4183:
4141:
4115:
4089:
4063:
4037:
4014:
3989:
3964:
3938:
3918:
3898:
3873:
3841:
3818:
3798:
3774:
3750:
3730:
3706:
3679:
3659:
3635:
3608:
3576:
3556:
3536:
3505:
3474:
3450:
3430:
3403:
3375:
3344:
3320:
3288:
3165:
3145:
3125:
3105:
3077:
3057:
3037:
3017:
2968:
2933:
2893:
2853:
2818:
2786:
2756:
2732:
2704:
2684:
2664:
2638:
2618:
2598:
2578:
2558:
2532:
2512:
2486:
2466:
2446:
2426:
2406:
2386:
2360:
2340:
2320:
2294:
2274:
2254:
2234:
2208:
2188:
2168:
2148:
2128:
2110:
1996:
1797:
1750:
1711:
1675:
1607:
1572:
1334:
1314:
1294:
1271:
1062:
1036:
1010:
976:
943:
901:
867:
841:
815:
789:
758:
731:
708:
685:
642:
616:
583:
549:
523:
497:
456:
430:
404:
371:
337:
311:
285:
251:
225:
199:
162:
136:
113:
87:
61:
7766:
Software Abstractions: Logic, Language, and Analysis
7268:
7711:O'Donnell, John; Hall, Cordelia; Page, Rex (2007),
7532:
7530:
6838:connective, is essentially non-Boolean because for
6325:{\displaystyle P\vee Q\wedge {\neg R}\rightarrow S}
6176:is a contradiction itself. E.g., ∨, ∧,
8664:
8627:
8598:
8573:
8544:
8497:
8468:
8439:
8402:
8373:
8344:
8319:
8273:
7670:Chazal (1996) : Éléments de logique formelle.
7504:Mathematical logic as based on the theory of types
7495:
7493:
7491:
7484:. Halle a/S.: Verlag von Louis Nebert. p. 10.
7244:
7163:
7094:
7030:
6955:
6617:
6594:
6574:
6556:. The partial order is defined by declaring that
6523:
6497:
6471:
6445:
6419:
6383:
6324:
6188:
6093:
5931:
5788:
5752:
5716:
5680:
5644:
5611:
5575:
5539:
5503:
5467:
5290:{\displaystyle \{\land ,\nleftrightarrow ,\top \}}
5289:
5251:
5213:
5175:
5137:
5099:
5056:
5025:{\displaystyle \{\nrightarrow ,\leftrightarrow \}}
5024:
4992:
4960:
4928:
4896:
4864:
4832:
4800:
4768:
4736:
4704:
4672:
4640:
4608:
4576:
4544:
4512:
4475:
4449:
4425:in classical logic whose arities do not exceed 2:
4394:
4374:
4340:
4320:
4300:
4280:
4260:
4234:
4189:
4153:
4127:
4101:
4075:
4049:
4023:
4000:
3975:
3946:
3924:
3904:
3881:
3847:
3824:
3804:
3780:
3756:
3736:
3712:
3685:
3665:
3641:
3614:
3582:
3562:
3542:
3511:
3480:
3456:
3436:
3409:
3386:
3357:
3326:
3294:
3173:
3151:
3131:
3111:
3085:
3063:
3043:
3023:
2980:
2945:
2905:
2865:
2830:
2795:
2762:
2738:
2710:
2690:
2670:
2650:
2624:
2604:
2584:
2564:
2544:
2518:
2492:
2472:
2452:
2432:
2412:
2392:
2366:
2346:
2326:
2300:
2280:
2260:
2240:
2214:
2194:
2174:
2154:
2134:
2002:
1803:
1756:
1717:
1681:
1613:
1578:
1346:
1320:
1300:
1277:
1074:
1048:
1022:
988:
962:
921:
879:
853:
827:
801:
767:
744:
717:
694:
663:
628:
602:
561:
535:
509:
477:
442:
416:
390:
349:
323:
297:
263:
237:
211:
177:
148:
122:
99:
73:
7599:. Paris: Hermann & Cie, Éditeurs. p. 14.
5214:{\displaystyle \{\land ,\leftrightarrow ,\bot \}}
5176:{\displaystyle \{\lor ,\nleftrightarrow ,\top \}}
5057:{\displaystyle \{\nleftarrow ,\leftrightarrow \}}
3000:formula to be connective (in which case they are
2644:
2643:
2642:
2538:
2537:
2536:
11159:
10951:Segmented discourse representation theory (SDRT)
7547:in From Frege to Gödel edited by van Heijenoort.
7527:
7467:A brief survey of 20th century logical notations
6956:{\displaystyle A\cap B=\{x:x\in A\land x\in B\}}
5386:. Related puzzles involving disjunction include
5100:{\displaystyle \{\lor ,\leftrightarrow ,\bot \}}
7561:On an improvement in Boole's calculus of logic.
7488:
7095:{\displaystyle {\overline {A}}=\{x:x\notin A\}}
7031:{\displaystyle A\cup B=\{x:x\in A\lor x\in B\}}
6842:, the consequent Q is not executed if the
6790:But not every usage of a logical connective in
6666:
6634:
5316:The situation, however, is more complicated in
5305:set. This approach requires more propositional
4423:minimal functionally complete sets of operators
3983:for conjunction (German's "und" for "and") and
8241:
8103:
7245:{\displaystyle A=B\leftrightarrow (\forall X)}
27:Symbol connecting sentential formulas in logic
10470:
8712:
8227:
7633:
7588:
7521:Arithmetices principia, nova methodo exposita
7445:
7443:
1199:
8109:A Concise Introduction to Mathematical Logic
8071:(2nd ed.), Boston, MA: Academic Press,
7545:On the building blocks of mathematical logic
7089:
7071:
7025:
6995:
6950:
6920:
5284:
5266:
5246:
5228:
5208:
5190:
5170:
5152:
5132:
5114:
5094:
5076:
5051:
5039:
5019:
5007:
4987:
4975:
4955:
4943:
4923:
4911:
4891:
4879:
4859:
4847:
4827:
4815:
4795:
4783:
4763:
4751:
4737:{\displaystyle \{\gets ,\nleftrightarrow \}}
4731:
4719:
4699:
4687:
4667:
4655:
4635:
4623:
4603:
4591:
4571:
4559:
4539:
4527:
4507:
4495:
4470:
4464:
4444:
4438:
3598:when interpreted logically in a two-element
8141:
7673:
7565:
7541:Über die Bausteine der mathematischen Logik
4328:" (or) are already in use, or may use the "
3958:Some authors used letters for connectives:
3365:; another alternative notation is to use a
2722:For example, the meaning of the statements
10477:
10463:
8904:
8719:
8705:
8234:
8220:
7659:Untersuchungen über das logische Schließen
7618:
7603:
7440:
6543:
5340:. However, they can also take the form of
4705:{\displaystyle \{\to ,\nleftrightarrow \}}
1206:
1192:
7737:
7473:
6834:, which in some sense corresponds to the
5394:, and the contribution of disjunction in
8063:
7639:
7594:
4833:{\displaystyle \{\gets ,\nrightarrow \}}
3527:'s use of the set-theoretic notation of
3421:'s use of the set-theoretic notation of
3417:appeared in Heyting in 1930 (compare to
2632:is the most modern and widely used, and
2480:is the most modern and widely used, and
2202:is the most modern and widely used, and
1217:
7762:
7679:
7579:
7572:Hilbert, D. (1918). Bernays, P. (ed.).
7571:
7449:
7421:
4961:{\displaystyle \{\nrightarrow ,\top \}}
4897:{\displaystyle \{\nrightarrow ,\neg \}}
4865:{\displaystyle \{\gets ,\nleftarrow \}}
3276:
3185:This table summarizes the terminology:
536:{\displaystyle A\not \Leftrightarrow B}
14:
11160:
8726:
7789:
7624:
6876:Set theory operations and connectives
6280:
4993:{\displaystyle \{\nleftarrow ,\top \}}
4929:{\displaystyle \{\nleftarrow ,\neg \}}
4769:{\displaystyle \{\to ,\nrightarrow \}}
2658:may be also a good choice compared to
2651:{\displaystyle \subset \!\!\!\supset }
2545:{\displaystyle \subset \!\!\!\supset }
963:{\displaystyle A{\underline {\lor }}B}
478:{\displaystyle {\overline {A\cdot B}}}
391:{\displaystyle A{\overline {\land }}B}
10906:Discourse representation theory (DRT)
10458:
8700:
8469:{\displaystyle \not \leftrightarrow }
8215:
8084:
7966:
7964:
7846:
7844:
7842:
7840:
7838:
7813:
7811:
7714:Discrete Mathematics Using a Computer
7609:
7479:
6794:has a Boolean semantic. For example,
4801:{\displaystyle \{\to ,\nleftarrow \}}
603:{\displaystyle A{\overline {\lor }}B}
264:{\displaystyle A\leftrightharpoons B}
8187:Sentence Connectives in Formal Logic
8069:A Mathematical Introduction to Logic
8050:
7738:Allen, Colin; Hand, Michael (2022).
7427:
7401:
6244:
6172:The compound all those argument are
10819:Quantificational variability effect
10486:Formal semantics (natural language)
8206:Stanford Encyclopedia of Philosophy
8191:Stanford Encyclopedia of Philosophy
7731:
6732:
6226:. E.g. negation in classical logic.
5327:
4001:{\displaystyle \operatorname {o.} }
3976:{\displaystyle \operatorname {u.} }
2374:is the most modern and widely used;
2308:is the most modern and widely used;
922:{\displaystyle A\ {\text{XNOR}}\ B}
562:{\displaystyle A\nleftrightarrow B}
24:
8659:
8434:
8268:
8015:
7994:
7961:
7946:
7835:
7808:
7206:
6773:Truth function in computer science
6662:
6630:
6548:The 16 logical connectives can be
6414:
6360:
6309:
5932:{\displaystyle a\land (a\lor b)=a}
5462:
5281:
5205:
5167:
5091:
4984:
4952:
4920:
4888:
4664:
4632:
4600:
4568:
4536:
4504:
4295:
4220:
3991:
3966:
3940:
3919:
3875:
3451:
3289:
3167:
3106:
3079:
3018:
2992:It is also common to consider the
2981:{\displaystyle p\leftrightarrow q}
2787:
2255:
2189:
2129:
2111:List of common logical connectives
686:
238:{\displaystyle A\Leftrightarrow B}
169:
166:
140:
25:
11184:
8161:
6189:{\displaystyle \nleftrightarrow }
6094:{\displaystyle \nleftrightarrow }
5403:paradoxes of material implication
4545:{\displaystyle \{\wedge ,\neg \}}
3859:'s interpretation of logic as an
3492:'s interpretation of logic as an
2003:{\displaystyle \nleftrightarrow }
664:{\displaystyle {\overline {A+B}}}
10438:
8681:
8498:{\displaystyle \leftrightarrow }
8287:
7285:
7271:
6721:Logical connectives are used in
6706:
6700:
6691:
6524:{\displaystyle \leftrightarrow }
6248:
5681:{\displaystyle \leftrightarrow }
4673:{\displaystyle \{\gets ,\bot \}}
4609:{\displaystyle \{\gets ,\neg \}}
3825:{\displaystyle \subset \supset }
3781:{\displaystyle \supset \subset }
3757:{\displaystyle \Leftrightarrow }
3737:{\displaystyle \leftrightarrow }
2691:{\displaystyle \leftrightarrow }
2625:{\displaystyle \leftrightarrow }
2565:{\displaystyle \Leftrightarrow }
2519:{\displaystyle \leftrightarrow }
2093:
2062:
2031:
1982:
1951:
1920:
1889:
1858:
1827:
1780:
1656:
1631:
1551:
1523:
1499:Zeroary connectives (constants)
1328:, rendering the complex formula
1177:
1176:
8117:Springer Science+Business Media
8009:
7988:
7940:
7924:"Complement and Set Difference"
7916:
7892:
7868:
7783:
7756:
7704:
7688:
7664:
7648:
6716:
6073:. E.g., ∨, ∧, ⊤, ⊥.
4513:{\displaystyle \{\vee ,\neg \}}
4476:{\displaystyle \{\downarrow \}}
3954:) to be found in Peano in 1889.
3358:{\displaystyle {\overline {p}}}
2678:denoting implication just like
745:{\displaystyle {\overline {A}}}
30:For other logical symbols, see
10901:Combinatory categorial grammar
8539:
8492:
8368:
8339:
8314:
8045:A Précis of Mathematical Logic
7699:A Précis of Mathematical Logic
7550:
7509:
7458:
7395:
7337:List of Boolean algebra topics
7239:
7227:
7215:
7212:
7203:
7200:
7158:
7146:
7134:
7131:
6518:
6492:
6375:
6372:
6369:
6366:
6357:
6348:
6339:
6316:
6231:propositional variables. Some
5920:
5908:
5747:
5711:
5675:
5606:
5570:
5237:
5199:
5123:
5085:
5048:
5016:
4850:
4818:
4786:
4754:
4722:
4690:
4658:
4641:{\displaystyle \{\to ,\bot \}}
4626:
4594:
4577:{\displaystyle \{\to ,\neg \}}
4562:
4467:
4441:
4335:
4275:
4252:
4184:
3751:
3731:
3680:
3636:
3602:; punctually in the history a
2972:
2946:{\displaystyle q\rightarrow p}
2937:
2906:{\displaystyle p\rightarrow q}
2897:
2705:
2685:
2619:
2559:
2513:
2467:
2427:
2387:
1066:
1014:
620:
510:{\displaystyle A\not \equiv B}
408:
350:{\displaystyle A\rightarrow B}
341:
298:{\displaystyle A\Rightarrow B}
289:
255:
229:
178:{\displaystyle A\&\&B}
13:
1:
10679:Antecedent-contained deletion
10399:History of mathematical logic
8574:{\displaystyle \nrightarrow }
7900:"Set Inclusion and Relations"
7388:
6853:
6798:is sometimes implemented for
5806:
4450:{\displaystyle \{\uparrow \}}
4173:Such a logical connective as
4168:
1075:{\displaystyle A\leftarrow B}
1023:{\displaystyle A\Leftarrow B}
629:{\displaystyle A\downarrow B}
10324:Primitive recursive function
8599:{\displaystyle \nleftarrow }
8374:{\displaystyle \rightarrow }
7063:
4417:One approach is to choose a
4235:{\displaystyle \neg p\vee q}
3947:{\displaystyle \mathrm {V} }
3882:{\displaystyle \mathrm {V} }
3686:{\displaystyle \Rightarrow }
3350:
3174:{\displaystyle \mathrm {F} }
3086:{\displaystyle \mathrm {T} }
2504:Equivalence (if and only if)
2433:{\displaystyle \Rightarrow }
1285:can be used to join the two
880:{\displaystyle A\parallel B}
737:
656:
592:
470:
380:
7:
8545:{\displaystyle \downarrow }
8345:{\displaystyle \leftarrow }
8185:Lloyd Humberstone (2010), "
8174:Encyclopedia of Mathematics
8142:Humberstone, Lloyd (2011).
8090:Logic, Language and Meaning
7790:Pinter, Charles C. (2014).
7264:
5753:{\displaystyle \downarrow }
5612:{\displaystyle \leftarrow }
5419:variably strict conditional
5411:counterfactual conditionals
4190:{\displaystyle \leftarrow }
3865:two-element Boolean algebra
2500:is used by many people too;
2222:is used by many people too;
1415:
1357:Common connectives include
417:{\displaystyle A\uparrow B}
10:
11189:
10560:Syntax–semantics interface
9388:Schröder–Bernstein theorem
9115:Monadic predicate calculus
8774:Foundations of mathematics
8169:"Propositional connective"
8034:
7769:, MIT Press, p. 263,
6857:
6736:
6659:
5313:or provable as a theorem.
4197:" is actually the same as
3867:; other notations include
3236:It is not the case that A
1049:{\displaystyle A\subset B}
324:{\displaystyle A\supset B}
29:
11094:
11052:Question under discussion
11002:Conversational scoreboard
10979:
10883:
10876:
10779:Intersective modification
10764:Homogeneity (linguistics)
10671:
10580:
10573:
10492:
10434:
10421:Philosophy of mathematics
10370:Automated theorem proving
10352:
10247:
10079:
9972:
9824:
9541:
9517:
9495:Von Neumann–Bernays–Gödel
9440:
9334:
9238:
9136:
9127:
9054:
8989:
8895:
8817:
8734:
8678:
8641:
8521:
8416:
8320:{\displaystyle \uparrow }
8296:
8285:
8250:
8200:John MacFarlane (2005), "
8197:approach to connectives.)
8125:10.1007/978-1-4419-1221-3
7717:, Springer, p. 120,
7574:Prinzipien der Mathematik
6779:(corresponding to finite
6775:. Logical operators over
6552:to produce the following
5789:{\displaystyle \not \to }
5717:{\displaystyle \uparrow }
2831:{\displaystyle p\wedge q}
2101:
1664:
1652:
1649:
1627:
1624:
1591:
1588:
1564:
1559:
1547:
1545:
1519:
1517:
1498:
1484:
1481:
1377:. In standard systems of
989:{\displaystyle A\oplus B}
212:{\displaystyle A\equiv B}
11112:Distributional semantics
8195:abstract algebraic logic
7904:autry.sites.grinnell.edu
7763:Jackson, Daniel (2012),
6582:if and only if whenever
5368:exclusive interpretation
5338:grammatical conjunctions
4414:subsets of connectives.
4083:for alternative denial,
3925:{\displaystyle \Lambda }
3700:Equivalence: the symbol
3666:{\displaystyle \supset }
3629:Implication: the symbol
3499:Disjunction: the symbol
3397:Conjunction: the symbol
2671:{\displaystyle \supset }
2493:{\displaystyle \supset }
2413:{\displaystyle \supset }
1381:, these connectives are
149:{\displaystyle A\&B}
100:{\displaystyle A\cdot B}
74:{\displaystyle A\land B}
11107:Computational semantics
10844:Subsective modification
10648:Propositional attitudes
10071:Self-verifying theories
9892:Tarski's axiomatization
8843:Tarski's undefinability
8838:incompleteness theorems
8584:Converse nonimplication
7317:Boolean-valued function
7259:axiom of extensionality
6575:{\displaystyle x\leq y}
6544:Table and Hasse diagram
6206:(for unary connectives)
5773:material nonimplication
5645:{\displaystyle \oplus }
5504:{\displaystyle \wedge }
3713:{\displaystyle \equiv }
3410:{\displaystyle \wedge }
3270:A and B are equivalent
3253:antecedent, consequent
3222:Either A or B, or both
2866:{\displaystyle p\lor q}
2585:{\displaystyle \equiv }
2378:Implication (if...then)
2301:{\displaystyle \wedge }
2241:{\displaystyle \wedge }
1434:propositional operators
1399:compositional semantics
1347:{\displaystyle P\lor Q}
1225:of logical connectives.
1129:Functional completeness
854:{\displaystyle A\mid B}
802:{\displaystyle A\lor B}
443:{\displaystyle A\mid B}
11137:Philosophy of language
10774:Inalienable possession
10754:Free choice inferences
10749:Faultless disagreement
10520:Generalized quantifier
10445:Mathematics portal
10056:Proof of impossibility
9704:propositional variable
9014:Propositional calculus
8666:
8629:
8628:{\displaystyle \land }
8600:
8575:
8546:
8499:
8470:
8441:
8404:
8375:
8346:
8321:
8275:
8041:Bocheński, Józef Maria
7470:(see chart on page 2).
7464:Denis Roegel (2002),
7357:Propositional calculus
7246:
7165:
7096:
7032:
6957:
6771:; see more details in
6685:
6656:
6619:
6596:
6576:
6525:
6499:
6473:
6447:
6446:{\displaystyle \land }
6421:
6385:
6326:
6190:
6095:
5933:
5790:
5754:
5718:
5682:
5646:
5613:
5577:
5541:
5505:
5469:
5388:free choice inferences
5291:
5253:
5215:
5177:
5139:
5101:
5058:
5026:
4994:
4962:
4930:
4898:
4866:
4834:
4802:
4770:
4738:
4706:
4674:
4642:
4610:
4578:
4546:
4514:
4477:
4451:
4396:
4376:
4359:associating the input
4342:
4322:
4302:
4282:
4262:
4261:{\displaystyle p\to q}
4236:
4191:
4155:
4129:
4103:
4077:
4051:
4025:
4002:
3977:
3948:
3926:
3906:
3883:
3849:
3826:
3806:
3782:
3758:
3738:
3714:
3687:
3667:
3643:
3616:
3584:
3564:
3544:
3513:
3482:
3481:{\displaystyle \cdot }
3458:
3457:{\displaystyle \&}
3438:
3411:
3388:
3359:
3328:
3296:
3228:A and B are disjoined
3214:A and B are conjoined
3175:
3153:
3133:
3113:
3087:
3065:
3045:
3025:
2982:
2947:
2907:
2867:
2832:
2797:
2796:{\displaystyle \neg p}
2764:
2740:
2712:
2692:
2672:
2652:
2626:
2606:
2586:
2566:
2546:
2520:
2494:
2474:
2454:
2434:
2414:
2394:
2368:
2348:
2328:
2302:
2282:
2262:
2261:{\displaystyle \&}
2242:
2216:
2196:
2176:
2156:
2136:
2004:
1805:
1758:
1719:
1683:
1615:
1580:
1348:
1322:
1302:
1279:
1226:
1099:Propositional calculus
1076:
1050:
1024:
990:
964:
923:
881:
855:
829:
803:
769:
768:{\displaystyle \sim A}
746:
719:
696:
695:{\displaystyle \neg A}
665:
630:
604:
563:
537:
511:
479:
444:
418:
392:
351:
325:
299:
265:
239:
213:
179:
150:
124:
101:
75:
11032:Plural quantification
10926:Inquisitive semantics
10891:Alternative semantics
10314:Kolmogorov complexity
10267:Computably enumerable
10167:Model complete theory
9959:Principia Mathematica
9019:Propositional formula
8848:Banach–Tarski paradox
8688:Philosophy portal
8667:
8665:{\displaystyle \bot }
8630:
8601:
8576:
8547:
8500:
8471:
8442:
8440:{\displaystyle \neg }
8405:
8403:{\displaystyle \lor }
8376:
8347:
8322:
8276:
8274:{\displaystyle \top }
8088:(1991), "Chapter 2",
7642:Théorie des ensembles
7640:Bourbaki, N. (1954).
7597:Théorie des ensembles
7595:Bourbaki, N. (1954).
7247:
7166:
7097:
7033:
6958:
6684:
6655:
6620:
6597:
6577:
6526:
6500:
6474:
6472:{\displaystyle \lor }
6448:
6422:
6420:{\displaystyle \neg }
6386:
6327:
6191:
6096:
5934:
5791:
5755:
5719:
5683:
5647:
5629:exclusive disjunction
5614:
5578:
5542:
5540:{\displaystyle \vee }
5506:
5470:
5468:{\displaystyle \neg }
5421:, as well as various
5396:alternative questions
5292:
5254:
5216:
5178:
5140:
5102:
5059:
5027:
4995:
4963:
4931:
4899:
4867:
4835:
4803:
4771:
4739:
4707:
4675:
4643:
4611:
4579:
4547:
4515:
4478:
4452:
4412:functionally complete
4397:
4377:
4343:
4323:
4321:{\displaystyle \vee }
4303:
4301:{\displaystyle \neg }
4283:
4263:
4237:
4192:
4161:for biconditional in
4156:
4130:
4104:
4078:
4052:
4026:
4003:
3978:
3949:
3927:
3907:
3884:
3850:
3827:
3807:
3805:{\displaystyle \sim }
3783:
3759:
3739:
3715:
3688:
3668:
3644:
3617:
3585:
3565:
3545:
3543:{\displaystyle \cup }
3514:
3512:{\displaystyle \vee }
3483:
3464:appeared at least in
3459:
3439:
3437:{\displaystyle \cap }
3412:
3389:
3360:
3329:
3327:{\displaystyle \sim }
3297:
3295:{\displaystyle \neg }
3282:Negation: the symbol
3264:A if, and only if, B
3176:
3154:
3134:
3114:
3112:{\displaystyle \bot }
3088:
3066:
3046:
3026:
3024:{\displaystyle \top }
2983:
2948:
2908:
2868:
2833:
2798:
2765:
2741:
2713:
2693:
2673:
2653:
2627:
2607:
2587:
2567:
2547:
2521:
2495:
2475:
2455:
2435:
2415:
2395:
2369:
2367:{\displaystyle \vee }
2349:
2329:
2327:{\displaystyle \vee }
2303:
2283:
2263:
2243:
2217:
2215:{\displaystyle \sim }
2197:
2195:{\displaystyle \neg }
2177:
2157:
2155:{\displaystyle \sim }
2137:
2135:{\displaystyle \neg }
2005:
1806:
1759:
1720:
1684:
1616:
1581:
1349:
1323:
1303:
1280:
1278:{\displaystyle \lor }
1243:sentential connective
1221:
1157:Programming languages
1077:
1051:
1025:
991:
965:
924:
882:
856:
830:
804:
770:
747:
720:
697:
666:
631:
605:
564:
538:
512:
480:
445:
419:
393:
352:
326:
300:
266:
240:
214:
180:
151:
125:
102:
76:
32:List of logic symbols
11017:Function application
10824:Responsive predicate
10814:Privative adjectives
10262:Church–Turing thesis
10249:Computability theory
9458:continuum hypothesis
8976:Square of opposition
8834:Gödel's completeness
8656:
8619:
8590:
8565:
8536:
8489:
8460:
8431:
8394:
8365:
8336:
8330:Converse implication
8311:
8265:
7852:"1.5 Logic and Sets"
7792:A book of set theory
7188:
7119:
7055:
6980:
6905:
6864:Axiomatic set theory
6836:material conditional
6792:computer programming
6755:) are built up from
6606:
6586:
6560:
6515:
6498:{\displaystyle \to }
6489:
6463:
6437:
6411:
6336:
6293:
6180:
6169:Falsehood-preserving
6085:
5899:
5780:
5744:
5708:
5672:
5636:
5603:
5596:converse implication
5576:{\displaystyle \to }
5567:
5560:material implication
5531:
5495:
5459:
5392:Hurford's Constraint
5318:intuitionistic logic
5263:
5225:
5187:
5149:
5111:
5073:
5036:
5004:
4972:
4940:
4908:
4876:
4844:
4812:
4780:
4748:
4716:
4684:
4652:
4620:
4588:
4556:
4524:
4492:
4461:
4435:
4386:
4366:
4341:{\displaystyle \to }
4332:
4312:
4292:
4281:{\displaystyle \to }
4272:
4246:
4217:
4207:logically equivalent
4199:material conditional
4181:
4175:converse implication
4139:
4113:
4087:
4061:
4035:
4012:
3987:
3962:
3936:
3916:
3896:
3871:
3839:
3816:
3796:
3772:
3748:
3728:
3704:
3677:
3657:
3642:{\displaystyle \to }
3633:
3606:
3574:
3554:
3534:
3523:in 1908 (compare to
3503:
3472:
3468:in 1924; the symbol
3448:
3428:
3401:
3373:
3342:
3318:
3306:in 1930 (compare to
3286:
3277:History of notations
3163:
3143:
3123:
3103:
3075:
3055:
3035:
3015:
2966:
2931:
2891:
2851:
2816:
2784:
2754:
2730:
2711:{\displaystyle \to }
2702:
2682:
2662:
2636:
2616:
2596:
2576:
2556:
2530:
2510:
2484:
2473:{\displaystyle \to }
2464:
2444:
2424:
2404:
2393:{\displaystyle \to }
2384:
2358:
2338:
2318:
2292:
2272:
2252:
2232:
2206:
2186:
2166:
2146:
2126:
2075:Converse implication
1994:
1964:Material conditional
1795:
1748:
1709:
1673:
1605:
1570:
1410:conditional operator
1332:
1312:
1292:
1269:
1060:
1034:
1008:
974:
941:
899:
865:
839:
813:
787:
756:
729:
706:
683:
640:
614:
581:
547:
521:
495:
454:
428:
402:
369:
335:
309:
283:
249:
223:
197:
160:
134:
111:
85:
59:
11168:Logical connectives
11102:Cognitive semantics
11067:Strawson entailment
11012:Existential closure
10956:Situation semantics
10859:Temperature paradox
10829:Rising declaratives
10794:Modal subordination
10769:Hurford disjunction
10729:Discourse relations
10416:Mathematical object
10307:P versus NP problem
10272:Computable function
10066:Reverse mathematics
9992:Logical consequence
9869:primitive recursive
9864:elementary function
9637:Free/bound variable
9490:Tarski–Grothendieck
9009:Logical connectives
8939:Logical equivalence
8789:Logical consequence
8244:logical connectives
7880:mirror.clarkson.edu
7684:. pp. 174–185.
7625:Becker, A. (1933).
7454:(in German): 42–56.
7342:Logical conjunction
6877:
6602:holds then so does
6281:Order of precedence
5409:and the problem of
4154:{\displaystyle Epq}
4128:{\displaystyle Cpq}
4102:{\displaystyle Apq}
4076:{\displaystyle Dpq}
4050:{\displaystyle Kpq}
3310:'s symbol ⫟ in his
2460:(prefix) in which
2354:(prefix) in which
2288:(prefix) in which
1665:Binary connectives
1462:logical connectives
1449:well-formed formula
1426:logical connectives
1391:nonclassical logics
1259:propositional logic
1247:sentential operator
1167:Philosophy of logic
828:{\displaystyle A+B}
41:Logical connectives
11147:Semantics of logic
11072:Strict conditional
11042:Quantifier raising
11007:Downward entailing
10987:Autonomy of syntax
10916:Generative grammar
10896:Categorial grammar
10834:Scalar implicature
10739:Epistemic modality
10714:De dicto and de re
10214:Transfer principle
10177:Semantics of logic
10162:Categorical theory
10138:Non-standard model
9652:Logical connective
8779:Information theory
8728:Mathematical logic
8662:
8625:
8596:
8571:
8542:
8495:
8466:
8437:
8400:
8371:
8342:
8317:
8301:Alternative denial
8271:
7610:Frege, G. (1879).
7480:Frege, G. (1879).
7242:
7161:
7092:
7028:
6953:
6875:
6785:bitwise operations
6769:transmission gates
6686:
6657:
6618:{\displaystyle y.}
6615:
6592:
6572:
6521:
6495:
6469:
6443:
6417:
6381:
6322:
6260:. You can help by
6233:many-valued logics
6186:
6091:
6027:∈ {0,1} such that
5929:
5786:
5750:
5714:
5701:alternative denial
5678:
5642:
5609:
5573:
5537:
5501:
5465:
5415:strict conditional
5384:scalar implicature
5287:
5249:
5211:
5173:
5135:
5097:
5054:
5022:
4990:
4958:
4926:
4894:
4862:
4830:
4798:
4766:
4734:
4702:
4670:
4638:
4606:
4574:
4542:
4510:
4473:
4447:
4392:
4372:
4355:There are sixteen
4338:
4318:
4298:
4278:
4258:
4232:
4187:
4151:
4125:
4099:
4073:
4047:
4024:{\displaystyle Np}
4021:
3998:
3973:
3944:
3922:
3902:
3892:False: the symbol
3879:
3861:elementary algebra
3845:
3822:
3820:⊂ ⊃
3812:in Schönfinkel or
3802:
3778:
3776:⊃ ⊂
3754:
3734:
3710:
3683:
3663:
3639:
3612:
3592:elementary algebra
3580:
3560:
3540:
3509:
3494:elementary algebra
3478:
3454:
3434:
3407:
3387:{\displaystyle p'}
3384:
3355:
3324:
3292:
3256:B is implied by A
3171:
3149:
3129:
3109:
3083:
3061:
3041:
3021:
2978:
2943:
2903:
2863:
2828:
2793:
2760:
2736:
2708:
2688:
2668:
2648:
2622:
2612:(prefix) in which
2602:
2582:
2562:
2542:
2516:
2490:
2470:
2450:
2430:
2410:
2390:
2364:
2344:
2324:
2298:
2278:
2258:
2238:
2212:
2192:
2182:(prefix) in which
2172:
2152:
2132:
2000:
1871:Alternative denial
1801:
1754:
1715:
1679:
1611:
1576:
1560:Unary connectives
1344:
1318:
1298:
1275:
1235:logical connective
1227:
1162:Mathematical logic
1072:
1046:
1020:
986:
960:
955:
919:
877:
851:
825:
799:
765:
742:
718:{\displaystyle -A}
715:
692:
661:
626:
600:
559:
533:
507:
475:
440:
414:
388:
347:
321:
295:
261:
235:
209:
175:
146:
123:{\displaystyle AB}
120:
97:
71:
11155:
11154:
11127:Logic translation
11090:
11089:
11082:Universal grinder
11062:Squiggle operator
11022:Meaning postulate
10961:Supervaluationism
10931:Intensional logic
10911:Dynamic semantics
10872:
10871:
10704:Crossover effects
10653:Tense–aspect–mood
10633:Lexical semantics
10452:
10451:
10384:Abstract category
10187:Theories of truth
9997:Rule of inference
9987:Natural deduction
9968:
9967:
9513:
9512:
9218:Cartesian product
9123:
9122:
9029:Many-valued logic
9004:Boolean functions
8887:Russell's paradox
8862:diagonal argument
8759:First-order logic
8694:
8693:
8202:Logical constants
8153:978-0-262-01654-4
8134:978-1-4419-1220-6
8078:978-0-12-238452-3
8065:Enderton, Herbert
8051:Chao, C. (2023).
7801:978-0-486-49708-2
7749:978-0-262-54364-4
7428:Chao, C. (2023).
7332:Four-valued logic
7293:Psychology portal
7279:Philosophy portal
7255:
7254:
7066:
6714:
6713:
6595:{\displaystyle x}
6550:partially ordered
6537:
6536:
6278:
6277:
5939:for all operands
5867:for all operands
5804:
5803:
4395:{\displaystyle q}
4375:{\displaystyle p}
4357:Boolean functions
4135:for implication,
4109:for disjunction,
4057:for conjunction,
3905:{\displaystyle 0}
3848:{\displaystyle 1}
3835:True: the symbol
3615:{\displaystyle +}
3583:{\displaystyle +}
3563:{\displaystyle +}
3353:
3274:
3273:
3152:{\displaystyle O}
3132:{\displaystyle 0}
3064:{\displaystyle V}
3044:{\displaystyle 1}
2763:{\displaystyle q}
2739:{\displaystyle p}
2605:{\displaystyle E}
2453:{\displaystyle C}
2347:{\displaystyle A}
2281:{\displaystyle K}
2226:Conjunction (and)
2175:{\displaystyle N}
2108:
2107:
1804:{\displaystyle q}
1757:{\displaystyle p}
1718:{\displaystyle q}
1682:{\displaystyle p}
1614:{\displaystyle p}
1579:{\displaystyle p}
1494:
1430:logical operators
1321:{\displaystyle Q}
1301:{\displaystyle P}
1216:
1215:
1085:
1084:
948:
915:
911:
907:
740:
659:
595:
473:
383:
18:Logical operation
16:(Redirected from
11180:
11132:Linguistics wars
11057:Semantic parsing
10946:Montague grammar
10881:
10880:
10724:Deontic modality
10578:
10577:
10565:Truth conditions
10500:Compositionality
10493:Central concepts
10479:
10472:
10465:
10456:
10455:
10443:
10442:
10394:History of logic
10389:Category of sets
10282:Decision problem
10061:Ordinal analysis
10002:Sequent calculus
9900:Boolean algebras
9840:
9839:
9814:
9785:logical/constant
9539:
9538:
9525:
9448:Zermelo–Fraenkel
9199:Set operations:
9134:
9133:
9071:
8902:
8901:
8882:Löwenheim–Skolem
8769:Formal semantics
8721:
8714:
8707:
8698:
8697:
8686:
8685:
8684:
8671:
8669:
8668:
8663:
8634:
8632:
8631:
8626:
8605:
8603:
8602:
8597:
8580:
8578:
8577:
8572:
8551:
8549:
8548:
8543:
8504:
8502:
8501:
8496:
8475:
8473:
8472:
8467:
8446:
8444:
8443:
8438:
8409:
8407:
8406:
8401:
8380:
8378:
8377:
8372:
8351:
8349:
8348:
8343:
8326:
8324:
8323:
8318:
8291:
8280:
8278:
8277:
8272:
8236:
8229:
8222:
8213:
8212:
8182:
8157:
8137:
8111:(3rd ed.),
8100:
8081:
8060:
8028:
8027:
8025:
8024:
8013:
8007:
8006:
8004:
8003:
7992:
7986:
7985:
7983:
7982:
7972:"Basic concepts"
7968:
7959:
7958:
7956:
7955:
7944:
7938:
7937:
7935:
7934:
7920:
7914:
7913:
7911:
7910:
7896:
7890:
7889:
7887:
7886:
7872:
7866:
7865:
7863:
7862:
7848:
7833:
7832:
7830:
7829:
7819:"Set operations"
7815:
7806:
7805:
7787:
7781:
7779:
7760:
7754:
7753:
7735:
7729:
7727:
7708:
7702:
7692:
7686:
7685:
7677:
7671:
7668:
7662:
7652:
7646:
7645:
7637:
7631:
7630:
7622:
7616:
7615:
7607:
7601:
7600:
7592:
7586:
7585:
7577:
7569:
7563:
7554:
7548:
7543:, translated as
7534:
7525:
7513:
7507:
7497:
7486:
7485:
7477:
7471:
7462:
7456:
7455:
7447:
7438:
7437:
7425:
7419:
7418:
7416:
7414:
7399:
7347:Logical constant
7307:Boolean function
7295:
7290:
7289:
7288:
7281:
7276:
7275:
7274:
7251:
7249:
7248:
7243:
7170:
7168:
7167:
7162:
7101:
7099:
7098:
7093:
7067:
7059:
7037:
7035:
7034:
7029:
6962:
6960:
6959:
6954:
6878:
6874:
6841:
6825:
6821:
6817:
6807:
6781:Boolean algebras
6749:digital circuits
6733:Computer science
6723:computer science
6710:
6704:
6695:
6665:
6633:
6627:
6626:
6624:
6622:
6621:
6616:
6601:
6599:
6598:
6593:
6581:
6579:
6578:
6573:
6530:
6528:
6527:
6522:
6504:
6502:
6501:
6496:
6478:
6476:
6475:
6470:
6452:
6450:
6449:
6444:
6426:
6424:
6423:
6418:
6397:
6396:
6390:
6388:
6387:
6382:
6331:
6329:
6328:
6323:
6315:
6287:precedence rules
6273:
6270:
6252:
6245:
6225:
6195:
6193:
6192:
6187:
6159:Truth-preserving
6155:
6100:
6098:
6097:
6092:
5946:
5942:
5938:
5936:
5935:
5930:
5878:
5874:
5870:
5866:
5795:
5793:
5792:
5787:
5759:
5757:
5756:
5751:
5723:
5721:
5720:
5715:
5687:
5685:
5684:
5679:
5651:
5649:
5648:
5643:
5618:
5616:
5615:
5610:
5582:
5580:
5579:
5574:
5546:
5544:
5543:
5538:
5510:
5508:
5507:
5502:
5474:
5472:
5471:
5466:
5431:
5430:
5361:formal semantics
5328:Natural language
5296:
5294:
5293:
5288:
5258:
5256:
5255:
5250:
5220:
5218:
5217:
5212:
5182:
5180:
5179:
5174:
5144:
5142:
5141:
5136:
5106:
5104:
5103:
5098:
5063:
5061:
5060:
5055:
5031:
5029:
5028:
5023:
4999:
4997:
4996:
4991:
4967:
4965:
4964:
4959:
4935:
4933:
4932:
4927:
4903:
4901:
4900:
4895:
4871:
4869:
4868:
4863:
4839:
4837:
4836:
4831:
4807:
4805:
4804:
4799:
4775:
4773:
4772:
4767:
4743:
4741:
4740:
4735:
4711:
4709:
4708:
4703:
4679:
4677:
4676:
4671:
4647:
4645:
4644:
4639:
4615:
4613:
4612:
4607:
4583:
4581:
4580:
4575:
4551:
4549:
4548:
4543:
4519:
4517:
4516:
4511:
4482:
4480:
4479:
4474:
4456:
4454:
4453:
4448:
4402:with four-digit
4401:
4399:
4398:
4393:
4381:
4379:
4378:
4373:
4347:
4345:
4344:
4339:
4327:
4325:
4324:
4319:
4307:
4305:
4304:
4299:
4287:
4285:
4284:
4279:
4267:
4265:
4264:
4259:
4241:
4239:
4238:
4233:
4196:
4194:
4193:
4188:
4160:
4158:
4157:
4152:
4134:
4132:
4131:
4126:
4108:
4106:
4105:
4100:
4082:
4080:
4079:
4074:
4056:
4054:
4053:
4048:
4030:
4028:
4027:
4022:
4007:
4005:
4004:
3999:
3997:
3982:
3980:
3979:
3974:
3972:
3953:
3951:
3950:
3945:
3943:
3931:
3929:
3928:
3923:
3911:
3909:
3908:
3903:
3888:
3886:
3885:
3880:
3878:
3854:
3852:
3851:
3846:
3831:
3829:
3828:
3823:
3811:
3809:
3808:
3803:
3787:
3785:
3784:
3779:
3763:
3761:
3760:
3755:
3743:
3741:
3740:
3735:
3719:
3717:
3716:
3711:
3692:
3690:
3689:
3684:
3672:
3670:
3669:
3664:
3648:
3646:
3645:
3640:
3621:
3619:
3618:
3613:
3589:
3587:
3586:
3581:
3569:
3567:
3566:
3561:
3549:
3547:
3546:
3541:
3518:
3516:
3515:
3510:
3487:
3485:
3484:
3479:
3463:
3461:
3460:
3455:
3443:
3441:
3440:
3435:
3416:
3414:
3413:
3408:
3393:
3391:
3390:
3385:
3383:
3364:
3362:
3361:
3356:
3354:
3346:
3333:
3331:
3330:
3325:
3301:
3299:
3298:
3293:
3188:
3187:
3180:
3178:
3177:
3172:
3170:
3158:
3156:
3155:
3150:
3138:
3136:
3135:
3130:
3118:
3116:
3115:
3110:
3092:
3090:
3089:
3084:
3082:
3070:
3068:
3067:
3062:
3050:
3048:
3047:
3042:
3030:
3028:
3027:
3022:
2996:formula and the
2987:
2985:
2984:
2979:
2952:
2950:
2949:
2944:
2912:
2910:
2909:
2904:
2872:
2870:
2869:
2864:
2837:
2835:
2834:
2829:
2802:
2800:
2799:
2794:
2769:
2767:
2766:
2761:
2745:
2743:
2742:
2737:
2717:
2715:
2714:
2709:
2697:
2695:
2694:
2689:
2677:
2675:
2674:
2669:
2657:
2655:
2654:
2649:
2631:
2629:
2628:
2623:
2611:
2609:
2608:
2603:
2591:
2589:
2588:
2583:
2571:
2569:
2568:
2563:
2551:
2549:
2548:
2543:
2525:
2523:
2522:
2517:
2499:
2497:
2496:
2491:
2479:
2477:
2476:
2471:
2459:
2457:
2456:
2451:
2439:
2437:
2436:
2431:
2419:
2417:
2416:
2411:
2399:
2397:
2396:
2391:
2373:
2371:
2370:
2365:
2353:
2351:
2350:
2345:
2333:
2331:
2330:
2325:
2312:Disjunction (or)
2307:
2305:
2304:
2299:
2287:
2285:
2284:
2279:
2267:
2265:
2264:
2259:
2247:
2245:
2244:
2239:
2221:
2219:
2218:
2213:
2201:
2199:
2198:
2193:
2181:
2179:
2178:
2173:
2161:
2159:
2158:
2153:
2141:
2139:
2138:
2133:
2103:More information
2097:
2066:
2035:
2009:
2007:
2006:
2001:
1986:
1955:
1924:
1893:
1862:
1831:
1810:
1808:
1807:
1802:
1784:
1763:
1761:
1760:
1755:
1724:
1722:
1721:
1716:
1688:
1686:
1685:
1680:
1660:
1635:
1620:
1618:
1617:
1612:
1585:
1583:
1582:
1577:
1555:
1527:
1492:
1479:
1478:
1459:
1443:truth-functional
1422:formal languages
1353:
1351:
1350:
1345:
1327:
1325:
1324:
1319:
1307:
1305:
1304:
1299:
1284:
1282:
1281:
1276:
1251:logical constant
1239:logical operator
1208:
1201:
1194:
1180:
1179:
1124:Boolean function
1090:Related concepts
1081:
1079:
1078:
1073:
1055:
1053:
1052:
1047:
1029:
1027:
1026:
1021:
995:
993:
992:
987:
969:
967:
966:
961:
956:
928:
926:
925:
920:
913:
912:
909:
905:
886:
884:
883:
878:
860:
858:
857:
852:
834:
832:
831:
826:
808:
806:
805:
800:
774:
772:
771:
766:
751:
749:
748:
743:
741:
733:
724:
722:
721:
716:
701:
699:
698:
693:
670:
668:
667:
662:
660:
655:
644:
635:
633:
632:
627:
609:
607:
606:
601:
596:
588:
568:
566:
565:
560:
542:
540:
539:
534:
516:
514:
513:
508:
484:
482:
481:
476:
474:
469:
458:
449:
447:
446:
441:
423:
421:
420:
415:
397:
395:
394:
389:
384:
376:
356:
354:
353:
348:
330:
328:
327:
322:
304:
302:
301:
296:
270:
268:
267:
262:
244:
242:
241:
236:
218:
216:
215:
210:
184:
182:
181:
176:
155:
153:
152:
147:
129:
127:
126:
121:
106:
104:
103:
98:
80:
78:
77:
72:
48:
47:
37:
36:
21:
11188:
11187:
11183:
11182:
11181:
11179:
11178:
11177:
11158:
11157:
11156:
11151:
11086:
10975:
10936:Lambda calculus
10868:
10839:Sloppy identity
10799:Opaque contexts
10734:Donkey anaphora
10699:Counterfactuals
10667:
10569:
10488:
10483:
10453:
10448:
10437:
10430:
10375:Category theory
10365:Algebraic logic
10348:
10319:Lambda calculus
10257:Church encoding
10243:
10219:Truth predicate
10075:
10041:Complete theory
9964:
9833:
9829:
9825:
9820:
9812:
9532: and
9528:
9523:
9509:
9485:New Foundations
9453:axiom of choice
9436:
9398:Gödel numbering
9338: and
9330:
9234:
9119:
9069:
9050:
8999:Boolean algebra
8985:
8949:Equiconsistency
8914:Classical logic
8891:
8872:Halting problem
8860: and
8836: and
8824: and
8823:
8818:Theorems (
8813:
8730:
8725:
8695:
8690:
8682:
8680:
8674:
8657:
8654:
8653:
8637:
8620:
8617:
8616:
8591:
8588:
8587:
8566:
8563:
8562:
8537:
8534:
8533:
8517:
8490:
8487:
8486:
8461:
8458:
8457:
8432:
8429:
8428:
8412:
8395:
8392:
8391:
8366:
8363:
8362:
8337:
8334:
8333:
8312:
8309:
8308:
8292:
8283:
8266:
8263:
8262:
8246:
8240:
8167:
8164:
8154:
8144:The Connectives
8135:
8079:
8037:
8032:
8031:
8022:
8020:
8014:
8010:
8001:
7999:
7993:
7989:
7980:
7978:
7970:
7969:
7962:
7953:
7951:
7945:
7941:
7932:
7930:
7928:web.mnstate.edu
7922:
7921:
7917:
7908:
7906:
7898:
7897:
7893:
7884:
7882:
7874:
7873:
7869:
7860:
7858:
7856:www.whitman.edu
7850:
7849:
7836:
7827:
7825:
7817:
7816:
7809:
7802:
7788:
7784:
7777:
7761:
7757:
7750:
7736:
7732:
7725:
7709:
7705:
7693:
7689:
7678:
7674:
7669:
7665:
7653:
7649:
7638:
7634:
7623:
7619:
7608:
7604:
7593:
7589:
7578:; Reprinted as
7570:
7566:
7555:
7551:
7535:
7528:
7514:
7510:
7498:
7489:
7478:
7474:
7463:
7459:
7448:
7441:
7426:
7422:
7412:
7410:
7400:
7396:
7391:
7386:
7291:
7286:
7284:
7277:
7272:
7270:
7267:
7189:
7186:
7185:
7120:
7117:
7116:
7058:
7056:
7053:
7052:
6981:
6978:
6977:
6906:
6903:
6902:
6866:
6858:Main articles:
6856:
6839:
6823:
6819:
6809:
6799:
6796:lazy evaluation
6741:
6735:
6719:
6683:
6663:
6654:
6631:
6607:
6604:
6603:
6587:
6584:
6583:
6561:
6558:
6557:
6546:
6516:
6513:
6512:
6490:
6487:
6486:
6464:
6461:
6460:
6438:
6435:
6434:
6412:
6409:
6408:
6337:
6334:
6333:
6308:
6294:
6291:
6290:
6283:
6274:
6268:
6265:
6258:needs expansion
6209:
6196:, ⊥, ⊄, ⊅ (see
6181:
6178:
6177:
6156:. E.g., ¬.
6153:
6144:
6133:
6124:
6114:
6086:
6083:
6082:
6072:
6063:
6054:
6047:
6040:
6033:
6026:
6017:
6010:
6001:
5994:
5985:
5974:
5965:
5944:
5940:
5900:
5897:
5896:
5876:
5872:
5868:
5837:
5809:
5781:
5778:
5777:
5745:
5742:
5741:
5709:
5706:
5705:
5673:
5670:
5669:
5637:
5634:
5633:
5604:
5601:
5600:
5568:
5565:
5564:
5532:
5529:
5528:
5496:
5493:
5492:
5460:
5457:
5456:
5407:donkey anaphora
5342:complementizers
5330:
5264:
5261:
5260:
5226:
5223:
5222:
5188:
5185:
5184:
5150:
5147:
5146:
5112:
5109:
5108:
5074:
5071:
5070:
5037:
5034:
5033:
5005:
5002:
5001:
4973:
4970:
4969:
4941:
4938:
4937:
4909:
4906:
4905:
4877:
4874:
4873:
4845:
4842:
4841:
4813:
4810:
4809:
4781:
4778:
4777:
4749:
4746:
4745:
4717:
4714:
4713:
4685:
4682:
4681:
4653:
4650:
4649:
4621:
4618:
4617:
4589:
4586:
4585:
4557:
4554:
4553:
4525:
4522:
4521:
4493:
4490:
4489:
4462:
4459:
4458:
4436:
4433:
4432:
4408:classical logic
4387:
4384:
4383:
4367:
4364:
4363:
4350:syntactic sugar
4333:
4330:
4329:
4313:
4310:
4309:
4293:
4290:
4289:
4273:
4270:
4269:
4247:
4244:
4243:
4218:
4215:
4214:
4203:classical logic
4182:
4179:
4178:
4171:
4140:
4137:
4136:
4114:
4111:
4110:
4088:
4085:
4084:
4062:
4059:
4058:
4036:
4033:
4032:
4013:
4010:
4009:
3990:
3988:
3985:
3984:
3965:
3963:
3960:
3959:
3939:
3937:
3934:
3933:
3917:
3914:
3913:
3897:
3894:
3893:
3874:
3872:
3869:
3868:
3840:
3837:
3836:
3817:
3814:
3813:
3797:
3794:
3793:
3773:
3770:
3769:
3749:
3746:
3745:
3729:
3726:
3725:
3705:
3702:
3701:
3678:
3675:
3674:
3658:
3655:
3654:
3634:
3631:
3630:
3607:
3604:
3603:
3575:
3572:
3571:
3555:
3552:
3551:
3535:
3532:
3531:
3504:
3501:
3500:
3473:
3470:
3469:
3449:
3446:
3445:
3429:
3426:
3425:
3402:
3399:
3398:
3376:
3374:
3371:
3370:
3345:
3343:
3340:
3339:
3319:
3316:
3315:
3312:Begriffsschrift
3287:
3284:
3283:
3279:
3239:negatum/negand
3197:Noun for parts
3166:
3164:
3161:
3160:
3144:
3141:
3140:
3124:
3121:
3120:
3104:
3101:
3100:
3078:
3076:
3073:
3072:
3056:
3053:
3052:
3036:
3033:
3032:
3016:
3013:
3012:
2967:
2964:
2963:
2962:it is raining (
2932:
2929:
2928:
2927:it is raining (
2892:
2889:
2888:
2881:it is raining,
2852:
2849:
2848:
2817:
2814:
2813:
2785:
2782:
2781:
2755:
2752:
2751:
2731:
2728:
2727:
2703:
2700:
2699:
2683:
2680:
2679:
2663:
2660:
2659:
2637:
2634:
2633:
2617:
2614:
2613:
2597:
2594:
2593:
2577:
2574:
2573:
2557:
2554:
2553:
2531:
2528:
2527:
2511:
2508:
2507:
2485:
2482:
2481:
2465:
2462:
2461:
2445:
2442:
2441:
2425:
2422:
2421:
2405:
2402:
2401:
2385:
2382:
2381:
2359:
2356:
2355:
2339:
2336:
2335:
2319:
2316:
2315:
2293:
2290:
2289:
2273:
2270:
2269:
2253:
2250:
2249:
2233:
2230:
2229:
2207:
2204:
2203:
2187:
2184:
2183:
2167:
2164:
2163:
2147:
2144:
2143:
2127:
2124:
2123:
2113:
1995:
1992:
1991:
1796:
1793:
1792:
1749:
1746:
1745:
1710:
1707:
1706:
1674:
1671:
1670:
1606:
1603:
1602:
1571:
1568:
1567:
1491:
1486:
1457:
1438:classical logic
1418:
1387:truth functions
1379:classical logic
1333:
1330:
1329:
1313:
1310:
1309:
1293:
1290:
1289:
1287:atomic formulas
1270:
1267:
1266:
1237:(also called a
1212:
1171:
1138:
1109:Boolean algebra
1104:Predicate logic
1061:
1058:
1057:
1035:
1032:
1031:
1009:
1006:
1005:
975:
972:
971:
947:
942:
939:
938:
908:
900:
897:
896:
866:
863:
862:
840:
837:
836:
814:
811:
810:
788:
785:
784:
757:
754:
753:
732:
730:
727:
726:
707:
704:
703:
684:
681:
680:
645:
643:
641:
638:
637:
615:
612:
611:
587:
582:
579:
578:
548:
545:
544:
522:
519:
518:
496:
493:
492:
459:
457:
455:
452:
451:
429:
426:
425:
403:
400:
399:
375:
370:
367:
366:
336:
333:
332:
310:
307:
306:
284:
281:
280:
250:
247:
246:
224:
221:
220:
198:
195:
194:
161:
158:
157:
135:
132:
131:
112:
109:
108:
86:
83:
82:
60:
57:
56:
35:
28:
23:
22:
15:
12:
11:
5:
11186:
11176:
11175:
11170:
11153:
11152:
11150:
11149:
11144:
11139:
11134:
11129:
11124:
11122:Inferentialism
11119:
11117:Formal grammar
11114:
11109:
11104:
11098:
11096:
11092:
11091:
11088:
11087:
11085:
11084:
11079:
11074:
11069:
11064:
11059:
11054:
11049:
11044:
11039:
11037:Possible world
11034:
11029:
11024:
11019:
11014:
11009:
11004:
10999:
10994:
10989:
10983:
10981:
10977:
10976:
10974:
10973:
10968:
10963:
10958:
10953:
10948:
10943:
10938:
10933:
10928:
10923:
10921:Glue semantics
10918:
10913:
10908:
10903:
10898:
10893:
10887:
10885:
10884:Formal systems
10878:
10874:
10873:
10870:
10869:
10867:
10866:
10861:
10856:
10851:
10846:
10841:
10836:
10831:
10826:
10821:
10816:
10811:
10809:Polarity items
10806:
10801:
10796:
10791:
10786:
10781:
10776:
10771:
10766:
10761:
10756:
10751:
10746:
10741:
10736:
10731:
10726:
10721:
10716:
10711:
10706:
10701:
10696:
10694:Conservativity
10691:
10686:
10681:
10675:
10673:
10669:
10668:
10666:
10665:
10660:
10658:Quantification
10655:
10650:
10645:
10640:
10635:
10630:
10625:
10620:
10615:
10610:
10605:
10600:
10595:
10590:
10584:
10582:
10575:
10571:
10570:
10568:
10567:
10562:
10557:
10552:
10547:
10542:
10537:
10535:Presupposition
10532:
10527:
10522:
10517:
10512:
10507:
10502:
10496:
10494:
10490:
10489:
10482:
10481:
10474:
10467:
10459:
10450:
10449:
10435:
10432:
10431:
10429:
10428:
10423:
10418:
10413:
10408:
10407:
10406:
10396:
10391:
10386:
10377:
10372:
10367:
10362:
10360:Abstract logic
10356:
10354:
10350:
10349:
10347:
10346:
10341:
10339:Turing machine
10336:
10331:
10326:
10321:
10316:
10311:
10310:
10309:
10304:
10299:
10294:
10289:
10279:
10277:Computable set
10274:
10269:
10264:
10259:
10253:
10251:
10245:
10244:
10242:
10241:
10236:
10231:
10226:
10221:
10216:
10211:
10206:
10205:
10204:
10199:
10194:
10184:
10179:
10174:
10172:Satisfiability
10169:
10164:
10159:
10158:
10157:
10147:
10146:
10145:
10135:
10134:
10133:
10128:
10123:
10118:
10113:
10103:
10102:
10101:
10096:
10089:Interpretation
10085:
10083:
10077:
10076:
10074:
10073:
10068:
10063:
10058:
10053:
10043:
10038:
10037:
10036:
10035:
10034:
10024:
10019:
10009:
10004:
9999:
9994:
9989:
9984:
9978:
9976:
9970:
9969:
9966:
9965:
9963:
9962:
9954:
9953:
9952:
9951:
9946:
9945:
9944:
9939:
9934:
9914:
9913:
9912:
9910:minimal axioms
9907:
9896:
9895:
9894:
9883:
9882:
9881:
9876:
9871:
9866:
9861:
9856:
9843:
9841:
9822:
9821:
9819:
9818:
9817:
9816:
9804:
9799:
9798:
9797:
9792:
9787:
9782:
9772:
9767:
9762:
9757:
9756:
9755:
9750:
9740:
9739:
9738:
9733:
9728:
9723:
9713:
9708:
9707:
9706:
9701:
9696:
9686:
9685:
9684:
9679:
9674:
9669:
9664:
9659:
9649:
9644:
9639:
9634:
9633:
9632:
9627:
9622:
9617:
9607:
9602:
9600:Formation rule
9597:
9592:
9591:
9590:
9585:
9575:
9574:
9573:
9563:
9558:
9553:
9548:
9542:
9536:
9519:Formal systems
9515:
9514:
9511:
9510:
9508:
9507:
9502:
9497:
9492:
9487:
9482:
9477:
9472:
9467:
9462:
9461:
9460:
9455:
9444:
9442:
9438:
9437:
9435:
9434:
9433:
9432:
9422:
9417:
9416:
9415:
9408:Large cardinal
9405:
9400:
9395:
9390:
9385:
9371:
9370:
9369:
9364:
9359:
9344:
9342:
9332:
9331:
9329:
9328:
9327:
9326:
9321:
9316:
9306:
9301:
9296:
9291:
9286:
9281:
9276:
9271:
9266:
9261:
9256:
9251:
9245:
9243:
9236:
9235:
9233:
9232:
9231:
9230:
9225:
9220:
9215:
9210:
9205:
9197:
9196:
9195:
9190:
9180:
9175:
9173:Extensionality
9170:
9168:Ordinal number
9165:
9155:
9150:
9149:
9148:
9137:
9131:
9125:
9124:
9121:
9120:
9118:
9117:
9112:
9107:
9102:
9097:
9092:
9087:
9086:
9085:
9075:
9074:
9073:
9060:
9058:
9052:
9051:
9049:
9048:
9047:
9046:
9041:
9036:
9026:
9021:
9016:
9011:
9006:
9001:
8995:
8993:
8987:
8986:
8984:
8983:
8978:
8973:
8968:
8963:
8958:
8953:
8952:
8951:
8941:
8936:
8931:
8926:
8921:
8916:
8910:
8908:
8899:
8893:
8892:
8890:
8889:
8884:
8879:
8874:
8869:
8864:
8852:Cantor's
8850:
8845:
8840:
8830:
8828:
8815:
8814:
8812:
8811:
8806:
8801:
8796:
8791:
8786:
8781:
8776:
8771:
8766:
8761:
8756:
8751:
8750:
8749:
8738:
8736:
8732:
8731:
8724:
8723:
8716:
8709:
8701:
8692:
8691:
8679:
8676:
8675:
8673:
8672:
8661:
8642:
8639:
8638:
8636:
8635:
8624:
8606:
8595:
8581:
8570:
8555:Nonimplication
8552:
8541:
8522:
8519:
8518:
8516:
8515:
8512:Digital buffer
8505:
8494:
8476:
8465:
8447:
8436:
8417:
8414:
8413:
8411:
8410:
8399:
8381:
8370:
8352:
8341:
8327:
8316:
8297:
8294:
8293:
8286:
8284:
8282:
8281:
8270:
8251:
8248:
8247:
8239:
8238:
8231:
8224:
8216:
8210:
8209:
8198:
8183:
8163:
8162:External links
8160:
8159:
8158:
8152:
8139:
8133:
8105:Rautenberg, W.
8101:
8082:
8077:
8061:
8048:
8036:
8033:
8030:
8029:
8008:
7987:
7960:
7939:
7915:
7891:
7867:
7834:
7807:
7800:
7782:
7775:
7755:
7748:
7730:
7723:
7703:
7687:
7672:
7663:
7647:
7632:
7617:
7602:
7587:
7564:
7549:
7526:
7508:
7487:
7472:
7457:
7439:
7420:
7408:Stack Overflow
7393:
7392:
7390:
7387:
7385:
7384:
7379:
7374:
7372:Truth function
7369:
7364:
7359:
7354:
7352:Modal operator
7349:
7344:
7339:
7334:
7329:
7324:
7319:
7314:
7309:
7304:
7302:Boolean domain
7298:
7297:
7296:
7282:
7266:
7263:
7253:
7252:
7241:
7238:
7235:
7232:
7229:
7226:
7223:
7220:
7217:
7214:
7211:
7208:
7205:
7202:
7199:
7196:
7193:
7183:
7178:
7172:
7171:
7160:
7157:
7154:
7151:
7148:
7145:
7142:
7139:
7136:
7133:
7130:
7127:
7124:
7114:
7109:
7103:
7102:
7091:
7088:
7085:
7082:
7079:
7076:
7073:
7070:
7065:
7062:
7050:
7045:
7039:
7038:
7027:
7024:
7021:
7018:
7015:
7012:
7009:
7006:
7003:
7000:
6997:
6994:
6991:
6988:
6985:
6975:
6970:
6964:
6963:
6952:
6949:
6946:
6943:
6940:
6937:
6934:
6931:
6928:
6925:
6922:
6919:
6916:
6913:
6910:
6900:
6895:
6889:
6888:
6885:
6882:
6881:Set operation
6872:, as follows:
6855:
6852:
6848:constructivist
6840:if (P) then Q;
6737:Main article:
6734:
6731:
6718:
6715:
6712:
6711:
6698:
6696:
6688:
6687:
6660:
6658:
6614:
6611:
6591:
6571:
6568:
6565:
6545:
6542:
6535:
6534:
6531:
6520:
6509:
6508:
6505:
6494:
6483:
6482:
6479:
6468:
6457:
6456:
6453:
6442:
6431:
6430:
6427:
6416:
6405:
6404:
6401:
6380:
6377:
6374:
6371:
6368:
6365:
6362:
6359:
6356:
6353:
6350:
6347:
6344:
6341:
6321:
6318:
6314:
6311:
6307:
6304:
6301:
6298:
6282:
6279:
6276:
6275:
6255:
6253:
6228:
6227:
6207:
6201:
6185:
6174:contradictions
6170:
6167:
6160:
6157:
6149:
6142:
6129:
6122:
6107:
6102:
6090:
6079:
6074:
6068:
6059:
6052:
6045:
6038:
6031:
6022:
6015:
6006:
5999:
5990:
5983:
5970:
5963:
5953:
5948:
5928:
5925:
5922:
5919:
5916:
5913:
5910:
5907:
5904:
5893:
5888:
5885:
5880:
5834:
5832:Distributivity
5829:
5826:
5821:
5818:
5808:
5805:
5802:
5801:
5796:
5785:
5775:
5770:
5766:
5765:
5760:
5749:
5739:
5734:
5730:
5729:
5724:
5713:
5703:
5698:
5694:
5693:
5688:
5677:
5667:
5662:
5661:if and only if
5658:
5657:
5652:
5641:
5631:
5626:
5622:
5621:
5619:
5608:
5598:
5593:
5589:
5588:
5583:
5572:
5562:
5557:
5553:
5552:
5547:
5536:
5526:
5521:
5517:
5516:
5511:
5500:
5490:
5485:
5481:
5480:
5475:
5464:
5454:
5449:
5445:
5444:
5441:
5438:
5435:
5329:
5326:
5299:
5298:
5286:
5283:
5280:
5277:
5274:
5271:
5268:
5248:
5245:
5242:
5239:
5236:
5233:
5230:
5210:
5207:
5204:
5201:
5198:
5195:
5192:
5172:
5169:
5166:
5163:
5160:
5157:
5154:
5134:
5131:
5128:
5125:
5122:
5119:
5116:
5096:
5093:
5090:
5087:
5084:
5081:
5078:
5068:
5067:Three elements
5065:
5053:
5050:
5047:
5044:
5041:
5021:
5018:
5015:
5012:
5009:
4989:
4986:
4983:
4980:
4977:
4957:
4954:
4951:
4948:
4945:
4925:
4922:
4919:
4916:
4913:
4893:
4890:
4887:
4884:
4881:
4861:
4858:
4855:
4852:
4849:
4829:
4826:
4823:
4820:
4817:
4797:
4794:
4791:
4788:
4785:
4765:
4762:
4759:
4756:
4753:
4733:
4730:
4727:
4724:
4721:
4701:
4698:
4695:
4692:
4689:
4669:
4666:
4663:
4660:
4657:
4637:
4634:
4631:
4628:
4625:
4605:
4602:
4599:
4596:
4593:
4573:
4570:
4567:
4564:
4561:
4541:
4538:
4535:
4532:
4529:
4509:
4506:
4503:
4500:
4497:
4487:
4484:
4472:
4469:
4466:
4446:
4443:
4440:
4430:
4391:
4371:
4337:
4317:
4297:
4277:
4257:
4254:
4251:
4231:
4228:
4225:
4222:
4186:
4170:
4167:
4150:
4147:
4144:
4124:
4121:
4118:
4098:
4095:
4092:
4072:
4069:
4066:
4046:
4043:
4040:
4031:for negation,
4020:
4017:
3996:
3993:
3971:
3968:
3956:
3955:
3942:
3921:
3901:
3890:
3877:
3844:
3833:
3821:
3801:
3777:
3753:
3733:
3709:
3698:
3682:
3662:
3638:
3627:
3611:
3579:
3559:
3550:); the symbol
3539:
3508:
3497:
3477:
3453:
3444:); the symbol
3433:
3406:
3395:
3382:
3379:
3352:
3349:
3323:
3314:); the symbol
3291:
3278:
3275:
3272:
3271:
3268:
3265:
3262:
3261:Biconditional
3258:
3257:
3254:
3251:
3248:
3244:
3243:
3240:
3237:
3234:
3230:
3229:
3226:
3223:
3220:
3216:
3215:
3212:
3209:
3206:
3202:
3201:
3198:
3195:
3192:
3183:
3182:
3169:
3148:
3128:
3108:
3094:
3081:
3060:
3040:
3020:
2990:
2989:
2977:
2974:
2971:
2959:if and only if
2954:
2942:
2939:
2936:
2921:I am indoors,
2914:
2902:
2899:
2896:
2887:I am indoors (
2874:
2862:
2859:
2856:
2847:I am indoors (
2841:It is raining
2839:
2827:
2824:
2821:
2812:I am indoors (
2806:It is raining
2804:
2792:
2789:
2759:
2735:
2720:
2719:
2707:
2687:
2667:
2647:
2641:
2621:
2601:
2581:
2561:
2541:
2535:
2515:
2501:
2489:
2469:
2449:
2429:
2409:
2389:
2375:
2363:
2343:
2323:
2309:
2297:
2277:
2257:
2237:
2223:
2211:
2191:
2171:
2151:
2131:
2120:Negation (not)
2112:
2109:
2106:
2105:
2099:
2098:
2091:
2088:
2085:
2082:
2079:
2077:
2072:
2068:
2067:
2060:
2057:
2054:
2051:
2048:
2046:
2041:
2037:
2036:
2029:
2026:
2023:
2020:
2017:
2015:
2010:
1999:
1988:
1987:
1980:
1977:
1974:
1971:
1968:
1966:
1961:
1957:
1956:
1949:
1946:
1943:
1940:
1937:
1935:
1930:
1926:
1925:
1918:
1915:
1912:
1909:
1906:
1904:
1899:
1895:
1894:
1887:
1884:
1881:
1878:
1875:
1873:
1868:
1864:
1863:
1856:
1853:
1850:
1847:
1844:
1842:
1837:
1833:
1832:
1825:
1822:
1819:
1816:
1813:
1811:
1800:
1789:
1786:
1785:
1778:
1775:
1772:
1769:
1766:
1764:
1753:
1742:
1739:
1738:
1735:
1732:
1729:
1726:
1714:
1703:
1702:
1699:
1696:
1693:
1690:
1678:
1667:
1666:
1662:
1661:
1654:
1651:
1648:
1646:
1641:
1637:
1636:
1629:
1626:
1623:
1621:
1610:
1599:
1596:
1595:
1593:
1590:
1587:
1575:
1565:
1562:
1561:
1557:
1556:
1549:
1546:
1544:
1542:
1533:
1529:
1528:
1521:
1518:
1516:
1514:
1505:
1501:
1500:
1496:
1495:
1488:
1483:
1417:
1414:
1401:with a robust
1343:
1340:
1337:
1317:
1297:
1274:
1214:
1213:
1211:
1210:
1203:
1196:
1188:
1185:
1184:
1173:
1172:
1170:
1169:
1164:
1159:
1154:
1148:
1145:
1144:
1140:
1139:
1137:
1136:
1131:
1126:
1121:
1119:Truth function
1116:
1111:
1106:
1101:
1095:
1092:
1091:
1087:
1086:
1083:
1082:
1071:
1068:
1065:
1045:
1042:
1039:
1019:
1016:
1013:
1003:
997:
996:
985:
982:
979:
959:
954:
951:
946:
936:
930:
929:
918:
904:
894:
888:
887:
876:
873:
870:
850:
847:
844:
824:
821:
818:
798:
795:
792:
782:
776:
775:
764:
761:
739:
736:
714:
711:
691:
688:
678:
672:
671:
658:
654:
651:
648:
625:
622:
619:
599:
594:
591:
586:
576:
570:
569:
558:
555:
552:
532:
529:
526:
506:
503:
500:
490:
486:
485:
472:
468:
465:
462:
439:
436:
433:
413:
410:
407:
387:
382:
379:
374:
364:
358:
357:
346:
343:
340:
320:
317:
314:
294:
291:
288:
278:
272:
271:
260:
257:
254:
234:
231:
228:
208:
205:
202:
192:
186:
185:
174:
171:
168:
165:
145:
142:
139:
119:
116:
96:
93:
90:
70:
67:
64:
54:
44:
43:
26:
9:
6:
4:
3:
2:
11185:
11174:
11173:Logic symbols
11171:
11169:
11166:
11165:
11163:
11148:
11145:
11143:
11140:
11138:
11135:
11133:
11130:
11128:
11125:
11123:
11120:
11118:
11115:
11113:
11110:
11108:
11105:
11103:
11100:
11099:
11097:
11093:
11083:
11080:
11078:
11075:
11073:
11070:
11068:
11065:
11063:
11060:
11058:
11055:
11053:
11050:
11048:
11045:
11043:
11040:
11038:
11035:
11033:
11030:
11028:
11025:
11023:
11020:
11018:
11015:
11013:
11010:
11008:
11005:
11003:
11000:
10998:
10995:
10993:
10990:
10988:
10985:
10984:
10982:
10978:
10972:
10969:
10967:
10964:
10962:
10959:
10957:
10954:
10952:
10949:
10947:
10944:
10942:
10939:
10937:
10934:
10932:
10929:
10927:
10924:
10922:
10919:
10917:
10914:
10912:
10909:
10907:
10904:
10902:
10899:
10897:
10894:
10892:
10889:
10888:
10886:
10882:
10879:
10875:
10865:
10862:
10860:
10857:
10855:
10852:
10850:
10847:
10845:
10842:
10840:
10837:
10835:
10832:
10830:
10827:
10825:
10822:
10820:
10817:
10815:
10812:
10810:
10807:
10805:
10804:Performatives
10802:
10800:
10797:
10795:
10792:
10790:
10787:
10785:
10784:Logophoricity
10782:
10780:
10777:
10775:
10772:
10770:
10767:
10765:
10762:
10760:
10757:
10755:
10752:
10750:
10747:
10745:
10742:
10740:
10737:
10735:
10732:
10730:
10727:
10725:
10722:
10720:
10717:
10715:
10712:
10710:
10707:
10705:
10702:
10700:
10697:
10695:
10692:
10690:
10687:
10685:
10682:
10680:
10677:
10676:
10674:
10670:
10664:
10661:
10659:
10656:
10654:
10651:
10649:
10646:
10644:
10641:
10639:
10636:
10634:
10631:
10629:
10626:
10624:
10621:
10619:
10618:Evidentiality
10616:
10614:
10611:
10609:
10606:
10604:
10601:
10599:
10596:
10594:
10591:
10589:
10586:
10585:
10583:
10579:
10576:
10572:
10566:
10563:
10561:
10558:
10556:
10553:
10551:
10548:
10546:
10543:
10541:
10538:
10536:
10533:
10531:
10528:
10526:
10523:
10521:
10518:
10516:
10513:
10511:
10508:
10506:
10503:
10501:
10498:
10497:
10495:
10491:
10487:
10480:
10475:
10473:
10468:
10466:
10461:
10460:
10457:
10447:
10446:
10441:
10433:
10427:
10424:
10422:
10419:
10417:
10414:
10412:
10409:
10405:
10402:
10401:
10400:
10397:
10395:
10392:
10390:
10387:
10385:
10381:
10378:
10376:
10373:
10371:
10368:
10366:
10363:
10361:
10358:
10357:
10355:
10351:
10345:
10342:
10340:
10337:
10335:
10334:Recursive set
10332:
10330:
10327:
10325:
10322:
10320:
10317:
10315:
10312:
10308:
10305:
10303:
10300:
10298:
10295:
10293:
10290:
10288:
10285:
10284:
10283:
10280:
10278:
10275:
10273:
10270:
10268:
10265:
10263:
10260:
10258:
10255:
10254:
10252:
10250:
10246:
10240:
10237:
10235:
10232:
10230:
10227:
10225:
10222:
10220:
10217:
10215:
10212:
10210:
10207:
10203:
10200:
10198:
10195:
10193:
10190:
10189:
10188:
10185:
10183:
10180:
10178:
10175:
10173:
10170:
10168:
10165:
10163:
10160:
10156:
10153:
10152:
10151:
10148:
10144:
10143:of arithmetic
10141:
10140:
10139:
10136:
10132:
10129:
10127:
10124:
10122:
10119:
10117:
10114:
10112:
10109:
10108:
10107:
10104:
10100:
10097:
10095:
10092:
10091:
10090:
10087:
10086:
10084:
10082:
10078:
10072:
10069:
10067:
10064:
10062:
10059:
10057:
10054:
10051:
10050:from ZFC
10047:
10044:
10042:
10039:
10033:
10030:
10029:
10028:
10025:
10023:
10020:
10018:
10015:
10014:
10013:
10010:
10008:
10005:
10003:
10000:
9998:
9995:
9993:
9990:
9988:
9985:
9983:
9980:
9979:
9977:
9975:
9971:
9961:
9960:
9956:
9955:
9950:
9949:non-Euclidean
9947:
9943:
9940:
9938:
9935:
9933:
9932:
9928:
9927:
9925:
9922:
9921:
9919:
9915:
9911:
9908:
9906:
9903:
9902:
9901:
9897:
9893:
9890:
9889:
9888:
9884:
9880:
9877:
9875:
9872:
9870:
9867:
9865:
9862:
9860:
9857:
9855:
9852:
9851:
9849:
9845:
9844:
9842:
9837:
9831:
9826:Example
9823:
9815:
9810:
9809:
9808:
9805:
9803:
9800:
9796:
9793:
9791:
9788:
9786:
9783:
9781:
9778:
9777:
9776:
9773:
9771:
9768:
9766:
9763:
9761:
9758:
9754:
9751:
9749:
9746:
9745:
9744:
9741:
9737:
9734:
9732:
9729:
9727:
9724:
9722:
9719:
9718:
9717:
9714:
9712:
9709:
9705:
9702:
9700:
9697:
9695:
9692:
9691:
9690:
9687:
9683:
9680:
9678:
9675:
9673:
9670:
9668:
9665:
9663:
9660:
9658:
9655:
9654:
9653:
9650:
9648:
9645:
9643:
9640:
9638:
9635:
9631:
9628:
9626:
9623:
9621:
9618:
9616:
9613:
9612:
9611:
9608:
9606:
9603:
9601:
9598:
9596:
9593:
9589:
9586:
9584:
9583:by definition
9581:
9580:
9579:
9576:
9572:
9569:
9568:
9567:
9564:
9562:
9559:
9557:
9554:
9552:
9549:
9547:
9544:
9543:
9540:
9537:
9535:
9531:
9526:
9520:
9516:
9506:
9503:
9501:
9498:
9496:
9493:
9491:
9488:
9486:
9483:
9481:
9478:
9476:
9473:
9471:
9470:Kripke–Platek
9468:
9466:
9463:
9459:
9456:
9454:
9451:
9450:
9449:
9446:
9445:
9443:
9439:
9431:
9428:
9427:
9426:
9423:
9421:
9418:
9414:
9411:
9410:
9409:
9406:
9404:
9401:
9399:
9396:
9394:
9391:
9389:
9386:
9383:
9379:
9375:
9372:
9368:
9365:
9363:
9360:
9358:
9355:
9354:
9353:
9349:
9346:
9345:
9343:
9341:
9337:
9333:
9325:
9322:
9320:
9317:
9315:
9314:constructible
9312:
9311:
9310:
9307:
9305:
9302:
9300:
9297:
9295:
9292:
9290:
9287:
9285:
9282:
9280:
9277:
9275:
9272:
9270:
9267:
9265:
9262:
9260:
9257:
9255:
9252:
9250:
9247:
9246:
9244:
9242:
9237:
9229:
9226:
9224:
9221:
9219:
9216:
9214:
9211:
9209:
9206:
9204:
9201:
9200:
9198:
9194:
9191:
9189:
9186:
9185:
9184:
9181:
9179:
9176:
9174:
9171:
9169:
9166:
9164:
9160:
9156:
9154:
9151:
9147:
9144:
9143:
9142:
9139:
9138:
9135:
9132:
9130:
9126:
9116:
9113:
9111:
9108:
9106:
9103:
9101:
9098:
9096:
9093:
9091:
9088:
9084:
9081:
9080:
9079:
9076:
9072:
9067:
9066:
9065:
9062:
9061:
9059:
9057:
9053:
9045:
9042:
9040:
9037:
9035:
9032:
9031:
9030:
9027:
9025:
9022:
9020:
9017:
9015:
9012:
9010:
9007:
9005:
9002:
9000:
8997:
8996:
8994:
8992:
8991:Propositional
8988:
8982:
8979:
8977:
8974:
8972:
8969:
8967:
8964:
8962:
8959:
8957:
8954:
8950:
8947:
8946:
8945:
8942:
8940:
8937:
8935:
8932:
8930:
8927:
8925:
8922:
8920:
8919:Logical truth
8917:
8915:
8912:
8911:
8909:
8907:
8903:
8900:
8898:
8894:
8888:
8885:
8883:
8880:
8878:
8875:
8873:
8870:
8868:
8865:
8863:
8859:
8855:
8851:
8849:
8846:
8844:
8841:
8839:
8835:
8832:
8831:
8829:
8827:
8821:
8816:
8810:
8807:
8805:
8802:
8800:
8797:
8795:
8792:
8790:
8787:
8785:
8782:
8780:
8777:
8775:
8772:
8770:
8767:
8765:
8762:
8760:
8757:
8755:
8752:
8748:
8745:
8744:
8743:
8740:
8739:
8737:
8733:
8729:
8722:
8717:
8715:
8710:
8708:
8703:
8702:
8699:
8689:
8677:
8651:
8647:
8646:Contradiction
8644:
8643:
8640:
8622:
8614:
8610:
8607:
8593:
8585:
8582:
8568:
8560:
8556:
8553:
8531:
8527:
8524:
8523:
8520:
8513:
8509:
8506:
8484:
8480:
8479:Biconditional
8477:
8463:
8455:
8451:
8448:
8426:
8422:
8419:
8418:
8415:
8397:
8389:
8385:
8382:
8360:
8356:
8353:
8331:
8328:
8306:
8302:
8299:
8298:
8295:
8290:
8260:
8256:
8253:
8252:
8249:
8245:
8237:
8232:
8230:
8225:
8223:
8218:
8217:
8214:
8207:
8203:
8199:
8196:
8192:
8188:
8184:
8180:
8176:
8175:
8170:
8166:
8165:
8155:
8149:
8146:. MIT Press.
8145:
8140:
8136:
8130:
8126:
8122:
8118:
8114:
8110:
8106:
8102:
8099:
8095:
8091:
8087:
8083:
8080:
8074:
8070:
8066:
8062:
8058:
8054:
8053:数理逻辑：形式化方法的应用
8049:
8046:
8042:
8039:
8038:
8019:
8012:
7998:
7991:
7977:
7973:
7967:
7965:
7950:
7943:
7929:
7925:
7919:
7905:
7901:
7895:
7881:
7877:
7871:
7857:
7853:
7847:
7845:
7843:
7841:
7839:
7824:
7820:
7814:
7812:
7803:
7797:
7793:
7786:
7778:
7776:9780262017152
7772:
7768:
7767:
7759:
7751:
7745:
7741:
7734:
7726:
7724:9781846285981
7720:
7716:
7715:
7707:
7700:
7696:
7691:
7683:
7676:
7667:
7660:
7656:
7651:
7643:
7636:
7628:
7621:
7613:
7606:
7598:
7591:
7583:
7575:
7568:
7562:
7558:
7553:
7546:
7542:
7538:
7533:
7531:
7523:
7522:
7517:
7512:
7505:
7501:
7496:
7494:
7492:
7483:
7476:
7469:
7468:
7461:
7453:
7446:
7444:
7435:
7431:
7430:数理逻辑：形式化方法的应用
7424:
7409:
7405:
7398:
7394:
7383:
7380:
7378:
7375:
7373:
7370:
7368:
7365:
7363:
7360:
7358:
7355:
7353:
7350:
7348:
7345:
7343:
7340:
7338:
7335:
7333:
7330:
7328:
7325:
7323:
7320:
7318:
7315:
7313:
7312:Boolean logic
7310:
7308:
7305:
7303:
7300:
7299:
7294:
7283:
7280:
7269:
7262:
7260:
7236:
7233:
7230:
7224:
7221:
7218:
7209:
7197:
7194:
7191:
7184:
7182:
7181:Biconditional
7179:
7177:
7174:
7173:
7155:
7152:
7149:
7143:
7140:
7137:
7128:
7125:
7122:
7115:
7113:
7110:
7108:
7105:
7104:
7086:
7083:
7080:
7077:
7074:
7068:
7060:
7051:
7049:
7046:
7044:
7041:
7040:
7022:
7019:
7016:
7013:
7010:
7007:
7004:
7001:
6998:
6992:
6989:
6986:
6983:
6976:
6974:
6971:
6969:
6966:
6965:
6947:
6944:
6941:
6938:
6935:
6932:
6929:
6926:
6923:
6917:
6914:
6911:
6908:
6901:
6899:
6896:
6894:
6891:
6890:
6886:
6883:
6880:
6879:
6873:
6871:
6865:
6861:
6851:
6849:
6845:
6837:
6833:
6829:
6816:
6812:
6806:
6802:
6797:
6793:
6788:
6786:
6782:
6778:
6774:
6770:
6766:
6762:
6758:
6754:
6750:
6746:
6740:
6730:
6728:
6724:
6709:
6705:
6703:
6699:
6697:
6694:
6690:
6689:
6661:
6629:
6628:
6625:
6612:
6609:
6589:
6569:
6566:
6563:
6555:
6554:Hasse diagram
6551:
6541:
6532:
6511:
6510:
6506:
6485:
6484:
6480:
6466:
6459:
6458:
6454:
6440:
6433:
6432:
6428:
6407:
6406:
6402:
6399:
6398:
6395:
6392:
6378:
6363:
6354:
6351:
6345:
6342:
6332:is short for
6319:
6312:
6305:
6302:
6299:
6296:
6288:
6272:
6263:
6259:
6256:This section
6254:
6251:
6247:
6246:
6243:
6240:
6236:
6234:
6224:
6220:
6216:
6212:
6208:
6205:
6202:
6199:
6183:
6175:
6171:
6168:
6165:
6161:
6158:
6152:
6148:
6141:
6137:
6132:
6128:
6121:
6117:
6112:
6108:
6106:
6103:
6088:
6080:
6078:
6075:
6071:
6067:
6062:
6058:
6051:
6044:
6037:
6030:
6025:
6021:
6014:
6009:
6005:
5998:
5993:
5989:
5982:
5978:
5973:
5969:
5962:
5958:
5954:
5952:
5949:
5926:
5923:
5917:
5914:
5911:
5905:
5902:
5894:
5892:
5889:
5886:
5884:
5881:
5864:
5860:
5856:
5852:
5848:
5844:
5840:
5835:
5833:
5830:
5827:
5825:
5824:Commutativity
5822:
5819:
5817:
5816:Associativity
5814:
5813:
5812:
5800:
5797:
5783:
5776:
5774:
5771:
5768:
5767:
5764:
5761:
5740:
5738:
5735:
5733:neither...nor
5732:
5731:
5728:
5725:
5704:
5702:
5699:
5696:
5695:
5692:
5689:
5668:
5666:
5665:biconditional
5663:
5660:
5659:
5656:
5653:
5639:
5632:
5630:
5627:
5624:
5623:
5620:
5599:
5597:
5594:
5591:
5590:
5587:
5584:
5563:
5561:
5558:
5555:
5554:
5551:
5548:
5534:
5527:
5525:
5522:
5519:
5518:
5515:
5512:
5498:
5491:
5489:
5486:
5483:
5482:
5479:
5476:
5455:
5453:
5450:
5447:
5446:
5443:Logical gate
5442:
5439:
5436:
5433:
5432:
5429:
5426:
5424:
5420:
5416:
5412:
5408:
5404:
5399:
5397:
5393:
5389:
5385:
5381:
5377:
5373:
5369:
5364:
5362:
5358:
5354:
5350:
5347:
5343:
5339:
5335:
5325:
5323:
5319:
5314:
5312:
5308:
5304:
5278:
5275:
5272:
5269:
5243:
5240:
5234:
5231:
5202:
5196:
5193:
5164:
5161:
5158:
5155:
5129:
5126:
5120:
5117:
5088:
5082:
5079:
5069:
5066:
5045:
5042:
5013:
5010:
4981:
4978:
4949:
4946:
4917:
4914:
4885:
4882:
4856:
4853:
4824:
4821:
4792:
4789:
4760:
4757:
4728:
4725:
4696:
4693:
4661:
4629:
4597:
4565:
4533:
4530:
4501:
4498:
4488:
4485:
4431:
4428:
4427:
4426:
4424:
4420:
4415:
4413:
4409:
4405:
4389:
4369:
4362:
4358:
4353:
4351:
4315:
4308:" (not) and "
4255:
4249:
4229:
4226:
4223:
4212:
4208:
4204:
4200:
4176:
4166:
4164:
4148:
4145:
4142:
4122:
4119:
4116:
4096:
4093:
4090:
4070:
4067:
4064:
4044:
4041:
4038:
4018:
4015:
3994:
3969:
3899:
3891:
3866:
3862:
3858:
3842:
3834:
3819:
3799:
3791:
3775:
3767:
3723:
3707:
3699:
3696:
3660:
3652:
3628:
3625:
3609:
3601:
3597:
3593:
3577:
3557:
3537:
3530:
3526:
3522:
3506:
3498:
3495:
3491:
3475:
3467:
3431:
3424:
3420:
3404:
3396:
3380:
3377:
3368:
3347:
3337:
3321:
3313:
3309:
3305:
3281:
3280:
3269:
3266:
3263:
3260:
3259:
3255:
3252:
3250:If A, then B
3249:
3246:
3245:
3242:A is negated
3241:
3238:
3235:
3232:
3231:
3227:
3224:
3221:
3218:
3217:
3213:
3210:
3208:Both A and B
3207:
3204:
3203:
3199:
3196:
3193:
3190:
3189:
3186:
3159:(prefix), or
3146:
3126:
3098:
3095:
3071:(prefix), or
3058:
3038:
3010:
3007:
3006:
3005:
3003:
2999:
2995:
2975:
2969:
2961:
2960:
2956:I am indoors
2955:
2940:
2934:
2926:
2925:
2920:
2919:
2915:
2900:
2894:
2886:
2885:
2880:
2879:
2875:
2860:
2857:
2854:
2846:
2845:
2840:
2825:
2822:
2819:
2811:
2810:
2805:
2790:
2779:
2778:
2773:
2772:
2771:
2757:
2749:
2733:
2725:
2724:it is raining
2665:
2645:
2639:
2599:
2579:
2539:
2533:
2505:
2502:
2487:
2447:
2407:
2379:
2376:
2361:
2341:
2321:
2313:
2310:
2295:
2275:
2235:
2227:
2224:
2209:
2169:
2149:
2121:
2118:
2117:
2116:
2104:
2100:
2096:
2092:
2089:
2086:
2083:
2080:
2078:
2076:
2073:
2070:
2069:
2065:
2061:
2058:
2055:
2052:
2049:
2047:
2045:
2044:Biconditional
2042:
2039:
2038:
2034:
2030:
2027:
2024:
2021:
2018:
2016:
2014:
2011:
1997:
1990:
1989:
1985:
1981:
1978:
1975:
1972:
1969:
1967:
1965:
1962:
1959:
1958:
1954:
1950:
1947:
1944:
1941:
1938:
1936:
1934:
1931:
1928:
1927:
1923:
1919:
1916:
1913:
1910:
1907:
1905:
1903:
1900:
1897:
1896:
1892:
1888:
1885:
1882:
1879:
1876:
1874:
1872:
1869:
1866:
1865:
1861:
1857:
1854:
1851:
1848:
1845:
1843:
1841:
1838:
1835:
1834:
1830:
1826:
1823:
1820:
1817:
1814:
1812:
1798:
1790:
1788:
1787:
1783:
1779:
1776:
1773:
1770:
1767:
1765:
1751:
1743:
1741:
1740:
1736:
1733:
1730:
1727:
1712:
1705:
1704:
1700:
1697:
1694:
1691:
1676:
1669:
1668:
1663:
1659:
1655:
1647:
1645:
1642:
1639:
1638:
1634:
1630:
1622:
1608:
1600:
1598:
1597:
1594:
1573:
1566:
1563:
1558:
1554:
1550:
1543:
1541:
1540:contradiction
1537:
1534:
1531:
1530:
1526:
1522:
1515:
1513:
1509:
1506:
1503:
1502:
1497:
1489:
1482:Symbol, name
1480:
1477:
1475:
1471:
1467:
1463:
1461:
1452:
1450:
1446:
1444:
1439:
1435:
1431:
1427:
1423:
1413:
1411:
1406:
1404:
1400:
1396:
1392:
1388:
1384:
1380:
1376:
1372:
1368:
1364:
1360:
1355:
1341:
1338:
1335:
1315:
1295:
1288:
1272:
1264:
1260:
1256:
1252:
1248:
1244:
1240:
1236:
1232:
1224:
1223:Hasse diagram
1220:
1209:
1204:
1202:
1197:
1195:
1190:
1189:
1187:
1186:
1183:
1175:
1174:
1168:
1165:
1163:
1160:
1158:
1155:
1153:
1152:Digital logic
1150:
1149:
1147:
1146:
1142:
1141:
1135:
1134:Scope (logic)
1132:
1130:
1127:
1125:
1122:
1120:
1117:
1115:
1112:
1110:
1107:
1105:
1102:
1100:
1097:
1096:
1094:
1093:
1089:
1088:
1069:
1063:
1043:
1040:
1037:
1017:
1011:
1004:
1002:
999:
998:
983:
980:
977:
957:
952:
949:
944:
937:
935:
932:
931:
916:
902:
895:
893:
890:
889:
874:
871:
868:
848:
845:
842:
822:
819:
816:
796:
793:
790:
783:
781:
778:
777:
762:
759:
734:
712:
709:
689:
679:
677:
674:
673:
652:
649:
646:
623:
617:
597:
589:
584:
577:
575:
572:
571:
556:
553:
550:
530:
527:
524:
504:
501:
498:
491:
489:nonequivalent
488:
487:
466:
463:
460:
437:
434:
431:
411:
405:
385:
377:
372:
365:
363:
360:
359:
344:
338:
318:
315:
312:
292:
286:
279:
277:
274:
273:
258:
252:
232:
226:
206:
203:
200:
193:
191:
188:
187:
172:
163:
143:
137:
117:
114:
94:
91:
88:
68:
65:
62:
55:
53:
50:
49:
46:
45:
42:
39:
38:
33:
19:
11077:Type shifter
11047:Quantization
10997:Continuation
10864:Veridicality
10744:Exhaustivity
10709:Cumulativity
10628:Indexicality
10608:Definiteness
10603:Conditionals
10530:Logical form
10436:
10234:Ultraproduct
10081:Model theory
10046:Independence
9982:Formal proof
9974:Proof theory
9957:
9930:
9887:real numbers
9859:second-order
9770:Substitution
9651:
9647:Metalanguage
9588:conservative
9561:Axiom schema
9505:Constructive
9475:Morse–Kelley
9441:Set theories
9420:Aleph number
9413:inaccessible
9319:Grothendieck
9203:intersection
9090:Higher-order
9078:Second-order
9024:Truth tables
9008:
8981:Venn diagram
8764:Formal proof
8526:Joint denial
8450:Exclusive or
8243:
8172:
8143:
8108:
8089:
8086:Gamut, L.T.F
8068:
8056:
8052:
8044:
8021:. Retrieved
8011:
8000:. Retrieved
7990:
7979:. Retrieved
7976:www.siue.edu
7975:
7952:. Retrieved
7942:
7931:. Retrieved
7927:
7918:
7907:. Retrieved
7903:
7894:
7883:. Retrieved
7879:
7876:"Theory Set"
7870:
7859:. Retrieved
7855:
7826:. Retrieved
7823:www.siue.edu
7822:
7791:
7785:
7765:
7758:
7740:Logic primer
7739:
7733:
7713:
7706:
7698:
7690:
7681:
7675:
7666:
7658:
7650:
7641:
7635:
7626:
7620:
7611:
7605:
7596:
7590:
7581:
7573:
7567:
7560:
7552:
7544:
7540:
7519:
7511:
7503:
7481:
7475:
7465:
7460:
7451:
7433:
7429:
7423:
7411:. Retrieved
7407:
7397:
7382:Truth values
7256:
6893:Intersection
6867:
6828:side effects
6814:
6810:
6804:
6800:
6789:
6742:
6720:
6717:Applications
6547:
6538:
6393:
6284:
6266:
6262:adding to it
6257:
6241:
6237:
6229:
6222:
6218:
6214:
6210:
6204:Involutivity
6150:
6146:
6139:
6135:
6130:
6126:
6119:
6115:
6069:
6065:
6060:
6056:
6049:
6042:
6035:
6028:
6023:
6019:
6012:
6007:
6003:
5996:
5991:
5987:
5980:
5976:
5971:
5967:
5960:
5956:
5951:Monotonicity
5862:
5858:
5854:
5850:
5846:
5842:
5838:
5810:
5737:joint denial
5434:English word
5427:
5400:
5376:nonclassical
5365:
5331:
5315:
5302:
5300:
4486:Two elements
4418:
4416:
4361:truth values
4354:
4348:" only as a
4172:
3957:
3764:appeared in
3693:appeared in
3649:appeared in
3596:exclusive or
3590:of ordinary
3519:appeared in
3423:intersection
3367:prime symbol
3334:appeared in
3302:appeared in
3267:equivalents
3247:Conditional
3219:Disjunction
3205:Conjunction
3200:Verb phrase
3184:
2998:always false
2997:
2993:
2991:
2958:
2957:
2923:
2922:
2917:
2916:
2883:
2882:
2877:
2876:
2843:
2842:
2808:
2807:
2776:
2775:
2750:(denoted by
2748:I am indoors
2747:
2726:(denoted by
2723:
2721:
2114:
2013:Exclusive or
1933:Joint denial
1791:Proposition
1744:Proposition
1601:Proposition
1473:
1469:
1455:
1453:
1441:
1433:
1429:
1425:
1419:
1407:
1356:
1246:
1242:
1238:
1234:
1228:
1143:Applications
40:
10992:Context set
10966:Type theory
10849:Subtrigging
10613:Disjunction
10540:Proposition
10344:Type theory
10292:undecidable
10224:Truth value
10111:equivalence
9790:non-logical
9403:Enumeration
9393:Isomorphism
9340:cardinality
9324:Von Neumann
9289:Ultrafilter
9254:Uncountable
9188:equivalence
9105:Quantifiers
9095:Fixed-point
9064:First-order
8944:Consistency
8929:Proposition
8906:Traditional
8877:Lindström's
8867:Compactness
8809:Type theory
8754:Cardinality
8609:Conjunction
8559:NIMPLY gate
8384:Disjunction
8355:Implication
8016:Cooper, A.
7995:Cooper, A.
7947:Cooper, A.
7537:Schönfinkel
7377:Truth table
7327:Dialetheism
7112:Implication
6973:Disjunction
6898:Conjunction
6887:Definition
6884:Connective
6832:conditional
6777:bit vectors
6745:logic gates
6403:Precedence
6111:truth table
5883:Idempotence
5625:either...or
5524:disjunction
5488:conjunction
5425:operators.
5357:denotations
5303:not minimal
4429:One element
4163:Łukasiewicz
3855:comes from
3832:in Chazal,
3488:comes from
3466:Schönfinkel
3194:In English
3191:Connective
2994:always true
1902:Disjunction
1840:Conjunction
1445:connectives
1383:interpreted
1375:equivalence
1371:implication
1367:conjunction
1363:disjunction
1265:connective
1114:Truth table
11162:Categories
11142:Pragmatics
10789:Mirativity
10555:Speech act
10510:Entailment
10505:Denotation
10155:elementary
9848:arithmetic
9716:Quantifier
9694:functional
9566:Expression
9284:Transitive
9228:identities
9213:complement
9146:hereditary
9129:Set theory
8359:IMPLY gate
8023:2024-06-11
8002:2024-06-11
7981:2024-06-11
7954:2024-06-11
7933:2024-06-11
7909:2024-06-11
7885:2024-06-11
7861:2024-06-11
7828:2024-06-11
7402:Cogwheel.
7389:References
7367:Tetralemma
7362:Term logic
7043:Complement
6870:set theory
6860:Set theory
6854:Set theory
6844:antecedent
6830:. Also, a
6739:Logic gate
6727:set theory
6269:March 2012
5995:) for all
5891:Absorption
5807:Properties
5437:Connective
4169:Redundancy
1468:constants
1403:pragmatics
190:equivalent
10941:Mereology
10877:Formalism
10759:Givenness
10684:Cataphora
10672:Phenomena
10663:Vagueness
10593:Ambiguity
10545:Reference
10525:Intension
10515:Extension
10426:Supertask
10329:Recursion
10287:decidable
10121:saturated
10099:of models
10022:deductive
10017:axiomatic
9937:Hilbert's
9924:Euclidean
9905:canonical
9828:axiomatic
9760:Signature
9689:Predicate
9578:Extension
9500:Ackermann
9425:Operation
9304:Universal
9294:Recursive
9269:Singleton
9264:Inhabited
9249:Countable
9239:Types of
9223:power set
9193:partition
9110:Predicate
9056:Predicate
8971:Syllogism
8961:Soundness
8934:Inference
8924:Tautology
8826:paradoxes
8660:⊥
8623:∧
8594:↚
8569:↛
8540:↓
8508:Statement
8493:↔
8483:XNOR gate
8435:¬
8398:∨
8369:→
8340:←
8315:↑
8305:NAND gate
8269:⊤
8255:Tautology
8179:EMS Press
7701:, passim.
7695:Bocheński
7322:Catuṣkoṭi
7234:∈
7228:↔
7222:∈
7207:∀
7201:↔
7153:∈
7147:→
7141:∈
7132:↔
7126:⊆
7084:∉
7064:¯
7020:∈
7014:∨
7008:∈
6987:∪
6945:∈
6939:∧
6933:∈
6912:∩
6567:≤
6519:↔
6493:→
6467:∨
6441:∧
6415:¬
6376:→
6361:¬
6355:∧
6346:∨
6317:→
6310:¬
6306:∧
6300:∨
6184:↮
6089:↮
5915:∨
5906:∧
5748:↓
5712:↑
5676:↔
5640:⊕
5607:←
5571:→
5556:if...then
5535:∨
5499:∧
5463:¬
5380:pragmatic
5372:semantics
5353:particles
5282:⊤
5276:↮
5270:∧
5244:↮
5238:↔
5232:∧
5206:⊥
5200:↔
5194:∧
5168:⊤
5162:↮
5156:∨
5130:↮
5124:↔
5118:∨
5092:⊥
5086:↔
5080:∨
5049:↔
5043:↚
5017:↔
5011:↛
4985:⊤
4979:↚
4953:⊤
4947:↛
4921:¬
4915:↚
4889:¬
4883:↛
4857:↚
4851:←
4825:↛
4819:←
4793:↚
4787:→
4761:↛
4755:→
4729:↮
4723:←
4697:↮
4691:→
4665:⊥
4659:←
4633:⊥
4627:→
4601:¬
4595:←
4569:¬
4563:→
4537:¬
4531:∧
4505:¬
4499:∨
4468:↓
4442:↑
4336:→
4316:∨
4296:¬
4276:→
4253:→
4227:∨
4221:¬
4209:. A less
4185:←
4165:in 1929.
3932:(rotated
3920:Λ
3863:over the
3800:∼
3752:⇔
3732:↔
3724:in 1879;
3708:≡
3681:⇒
3661:⊃
3653:in 1918;
3637:→
3538:∪
3507:∨
3476:⋅
3452:&
3432:∩
3405:∧
3351:¯
3322:∼
3290:¬
3233:Negation
3225:disjunct
3211:conjunct
3107:⊥
3099:formula:
3019:⊤
3011:formula:
2973:↔
2938:→
2898:→
2858:∨
2823:∧
2788:¬
2780:raining (
2706:→
2686:↔
2666:⊃
2646:⊃
2640:⊂
2620:↔
2580:≡
2560:⇔
2540:⊃
2534:⊂
2514:↔
2488:⊃
2468:→
2428:⇒
2408:⊃
2388:→
2362:∨
2322:∨
2296:∧
2256:&
2236:∧
2210:∼
2190:¬
2150:∼
2130:¬
1998:↮
1512:tautology
1436:, or, in
1339:∨
1273:∨
1067:←
1041:⊂
1015:⇐
981:⊕
953:_
950:∨
872:∥
846:∣
794:∨
760:∼
738:¯
710:−
687:¬
657:¯
621:↓
593:¯
590:∨
554:↮
471:¯
464:⋅
435:∣
409:↑
381:¯
378:∧
342:→
316:⊃
290:⇒
256:⇋
230:⇔
204:≡
170:&
167:&
141:&
92:⋅
66:∧
11095:See also
10980:Concepts
10854:Telicity
10689:Coercion
10643:Negation
10638:Modality
10588:Anaphora
10411:Logicism
10404:timeline
10380:Concrete
10239:Validity
10209:T-schema
10202:Kripke's
10197:Tarski's
10192:semantic
10182:Strength
10131:submodel
10126:spectrum
10094:function
9942:Tarski's
9931:Elements
9918:geometry
9874:Robinson
9795:variable
9780:function
9753:spectrum
9743:Sentence
9699:variable
9642:Language
9595:Relation
9556:Automata
9546:Alphabet
9530:language
9384:-jection
9362:codomain
9348:Function
9309:Universe
9279:Infinite
9183:Relation
8966:Validity
8956:Argument
8854:theorem,
8613:AND gate
8530:NOR gate
8464:↮
8454:XOR gate
8425:NOT gate
8421:Negation
8113:New York
8107:(2010),
8098:21372380
8067:(2001),
8043:(1959),
7697:(1959),
7265:See also
7176:Equality
7048:Negation
6400:Operator
6198:validity
6164:validity
6125:, ..., ¬
6077:Affinity
5784:↛
5697:not both
5452:negation
5349:suffixes
3766:Bourbaki
3697:in 1954.
3695:Bourbaki
3381:′
1725: =
1689: =
1644:Negation
1586: =
1416:Overview
1359:negation
1182:Category
1001:converse
528:⇎
502:≢
10598:Binding
10353:Related
10150:Diagram
10048: (
10027:Hilbert
10012:Systems
10007:Theorem
9885:of the
9830:systems
9610:Formula
9605:Grammar
9521: (
9465:General
9178:Forcing
9163:Element
9083:Monadic
8858:paradox
8799:Theorem
8735:General
8615:)
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8303: (
8242:Common
8181:, 2001
8035:Sources
7657:(1934)
7655:Gentzen
7559:(1867)
7539:(1924)
7518:(1889)
7502:(1908)
7500:Russell
7413:9 April
6725:and in
6145:, ...,
6116:g̃
6105:Duality
6101:, ⊤, ⊥.
6055:, ...,
6018:, ...,
6002:, ...,
5986:, ...,
5966:, ...,
5769:but not
5423:dynamic
5334:English
4419:minimal
4211:trivial
3790:Gentzen
3651:Hilbert
3521:Russell
3336:Russell
3304:Heyting
3002:nullary
1536:Falsity
1493:diagram
1466:boolean
1395:English
1249:) is a
276:implies
11027:Monads
10574:Topics
10116:finite
9879:Skolem
9832:
9807:Theory
9775:Symbol
9765:String
9748:atomic
9625:ground
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10719:De se
10623:Focus
10581:Areas
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10106:Model
9854:Peano
9711:Proof
9551:Arity
9480:Naive
9367:image
9299:Fuzzy
9259:Empty
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8650:False
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8259:True
8193:(An
8148:ISBN
8129:ISBN
8094:OCLC
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7796:ISBN
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7415:2015
6862:and
6808:and
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5975:) ≤
5727:NAND
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3009:True
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