797:
845:
665:
530:
442:
595:
394:
703:
482:
738:
818:
624:
503:
415:
965:
206:
351:
is the principle that, if the negation of a conjunction holds and also one of its conjuncts, then the negation of its other conjunct holds."
913:
955:
220:
960:
257:
61:
261:
67:
248:
87:
74:
769:
252:
93:
80:
355:
292:
106:
28:
857:
760:
742:
303:
201:
182:
149:
100:
824:
638:
509:
421:
565:
364:
175:
168:
113:
669:
213:
196:
158:
119:
936:
682:
126:
905:
909:
288:
239:
232:
44:
35:
21:
457:
720:
285:
707:
189:
898:
803:
609:
488:
448:
400:
949:
132:
882:
Politzer, Guy & Carles, Laure. 2001. 'Belief
Revision and Uncertain Reasoning'.
928:
344:
297:
50:
863:
451:(alternative denial), "|", the inference can also be formalized in this way:
120:
114:
94:
900:
Latin for the
Illiterati: Exorcizing the Ghosts of a Dead Language
281:
183:
141:
107:
62:
133:
101:
214:
169:
75:
51:
827:
806:
772:
723:
685:
641:
612:
568:
512:
491:
460:
424:
403:
367:
897:
839:
812:
791:
732:
697:
659:
618:
589:
524:
497:
476:
436:
409:
388:
127:
207:
176:
68:
315:MPT is usually described as having the form:
221:
190:
88:
81:
8:
17:
826:
805:
776:
771:
763:instead of non-conjunction as a premise:
722:
684:
640:
611:
567:
511:
490:
470:
465:
464:
459:
423:
402:
366:
339:Therefore, Bill cannot have won the race.
539:
284:: "mode that denies by affirming") is a
875:
238:
231:
157:
34:
27:
20:
792:{\displaystyle A{\underline {\lor }}B}
333:Ann and Bill cannot both win the race.
7:
831:
724:
689:
686:
651:
642:
569:
516:
428:
368:
14:
840:{\displaystyle \therefore \neg B}
660:{\displaystyle \neg A\lor \neg B}
525:{\displaystyle \therefore \neg B}
437:{\displaystyle \therefore \neg B}
966:Theorems in propositional logic
590:{\displaystyle \neg (A\land B)}
389:{\displaystyle \neg (A\land B)}
759:can be made stronger by using
584:
572:
466:
383:
371:
1:
904:. London: Routledge. p.
358:this can be represented as:
698:{\displaystyle \neg \neg A}
295:. It is closely related to
982:
258:Existential generalization
63:Biconditional introduction
249:Universal generalization
89:Disjunction introduction
76:Conjunction introduction
46:Implication introduction
477:{\displaystyle A\,|\,B}
896:Stone, Jon R. (1996).
884:Thinking and Reasoning
841:
814:
793:
734:
733:{\displaystyle \neg B}
699:
661:
620:
591:
526:
499:
478:
438:
411:
390:
108:hypothetical syllogism
29:Propositional calculus
956:Latin logical phrases
858:Modus tollendo ponens
842:
815:
794:
761:exclusive disjunction
757:Modus ponendo tollens
743:Disjunctive syllogism
735:
700:
662:
621:
592:
527:
500:
479:
439:
412:
391:
349:Modus ponendo tollens
304:modus tollendo ponens
273:Modus ponendo tollens
150:Negation introduction
143:modus ponendo tollens
825:
804:
770:
721:
683:
639:
610:
566:
510:
489:
458:
422:
401:
365:
208:Material implication
159:Rules of replacement
22:Transformation rules
929:Lemmon, Edward John
293:propositional logic
121:destructive dilemma
961:Rules of inference
939:/CRC Press, p. 61.
937:Taylor and Francis
837:
810:
789:
784:
730:
695:
657:
616:
587:
522:
495:
474:
434:
407:
386:
240:Rules of inference
36:Rules of inference
813:{\displaystyle A}
777:
749:
748:
619:{\displaystyle A}
498:{\displaystyle A}
410:{\displaystyle A}
336:Ann won the race.
289:rule of inference
269:
268:
973:
940:
926:
920:
919:
903:
893:
887:
880:
846:
844:
843:
838:
819:
817:
816:
811:
798:
796:
795:
790:
785:
739:
737:
736:
731:
704:
702:
701:
696:
670:De Morgan's laws
666:
664:
663:
658:
625:
623:
622:
617:
596:
594:
593:
588:
540:
531:
529:
528:
523:
504:
502:
501:
496:
483:
481:
480:
475:
469:
443:
441:
440:
435:
416:
414:
413:
408:
395:
393:
392:
387:
325:Therefore, not B
319:Not both A and B
223:
216:
209:
197:De Morgan's laws
192:
185:
178:
171:
145:
137:
129:
122:
116:
109:
103:
96:
90:
83:
77:
70:
64:
57:
47:
18:
981:
980:
976:
975:
974:
972:
971:
970:
946:
945:
944:
943:
933:Beginning Logic
927:
923:
916:
895:
894:
890:
881:
877:
872:
853:
823:
822:
802:
801:
768:
767:
754:
719:
718:
708:Double negation
681:
680:
637:
636:
608:
607:
564:
563:
538:
508:
507:
487:
486:
456:
455:
420:
419:
399:
398:
363:
362:
347:describes it: "
313:
233:Predicate logic
227:
191:Double negation
45:
12:
11:
5:
979:
977:
969:
968:
963:
958:
948:
947:
942:
941:
921:
914:
888:
874:
873:
871:
868:
867:
866:
861:
852:
849:
848:
847:
836:
833:
830:
820:
809:
799:
788:
783:
780:
775:
753:
750:
747:
746:
740:
729:
726:
716:
712:
711:
705:
694:
691:
688:
678:
674:
673:
667:
656:
653:
650:
647:
644:
634:
630:
629:
626:
615:
605:
601:
600:
597:
586:
583:
580:
577:
574:
571:
561:
557:
556:
551:
546:
537:
534:
533:
532:
521:
518:
515:
505:
494:
484:
473:
468:
463:
449:Sheffer Stroke
445:
444:
433:
430:
427:
417:
406:
396:
385:
382:
379:
376:
373:
370:
356:logic notation
341:
340:
337:
334:
327:
326:
323:
320:
312:
309:
267:
266:
265:
264:
255:
243:
242:
236:
235:
229:
228:
226:
225:
218:
211:
204:
199:
194:
187:
184:Distributivity
180:
173:
165:
162:
161:
155:
154:
153:
152:
147:
124:
111:
98:
85:
72:
59:
39:
38:
32:
31:
25:
24:
13:
10:
9:
6:
4:
3:
2:
978:
967:
964:
962:
959:
957:
954:
953:
951:
938:
934:
930:
925:
922:
917:
915:0-415-91775-1
911:
907:
902:
901:
892:
889:
885:
879:
876:
869:
865:
862:
860:
859:
855:
854:
850:
834:
828:
821:
807:
800:
786:
781:
778:
773:
766:
765:
764:
762:
758:
751:
744:
741:
727:
717:
714:
713:
709:
706:
692:
679:
676:
675:
671:
668:
654:
648:
645:
635:
632:
631:
627:
613:
606:
603:
602:
598:
581:
578:
575:
562:
559:
558:
555:
552:
550:
547:
545:
542:
541:
535:
519:
513:
506:
492:
485:
471:
461:
454:
453:
452:
450:
447:Based on the
431:
425:
418:
404:
397:
380:
377:
374:
361:
360:
359:
357:
352:
350:
346:
338:
335:
332:
331:
330:
329:For example:
324:
321:
318:
317:
316:
310:
308:
306:
305:
300:
299:
294:
290:
287:
283:
279:
275:
274:
263:
262:instantiation
259:
256:
254:
253:instantiation
250:
247:
246:
245:
244:
241:
237:
234:
230:
224:
219:
217:
212:
210:
205:
203:
202:Transposition
200:
198:
195:
193:
188:
186:
181:
179:
177:Commutativity
174:
172:
170:Associativity
167:
166:
164:
163:
160:
156:
151:
148:
146:
144:
138:
136:
135:modus tollens
130:
125:
123:
117:
112:
110:
104:
99:
97:
91:
86:
84:
78:
73:
71:
65:
60:
58:
55:
52:elimination (
48:
43:
42:
41:
40:
37:
33:
30:
26:
23:
19:
16:
932:
924:
899:
891:
886:. 7:217–234.
883:
878:
856:
756:
755:
553:
548:
543:
446:
353:
348:
345:E. J. Lemmon
342:
328:
314:
302:
298:modus ponens
296:
277:
272:
271:
270:
260: /
251: /
142:
140:
139: /
134:
131: /
118: /
115:Constructive
105: /
92: /
79: /
66: /
54:modus ponens
53:
49: /
15:
864:Stoic logic
752:Strong form
549:Proposition
215:Exportation
102:Disjunctive
95:elimination
82:elimination
69:elimination
950:Categories
870:References
554:Derivation
128:Absorption
832:¬
829:∴
782:_
779:∨
725:¬
690:¬
687:¬
652:¬
649:∨
643:¬
579:∧
570:¬
517:¬
514:∴
429:¬
426:∴
378:∧
369:¬
222:Tautology
931:. 2001.
851:See also
311:Overview
912:
745:(3,4)
628:Given
599:Given
536:Proof
286:valid
282:Latin
910:ISBN
710:(2)
672:(1)
544:Step
301:and
291:for
354:In
343:As
307:.
278:MPT
952::
935:.
908:.
906:60
280:;
918:.
835:B
808:A
787:B
774:A
728:B
715:5
693:A
677:4
655:B
646:A
633:3
614:A
604:2
585:)
582:B
576:A
573:(
560:1
520:B
493:A
472:B
467:|
462:A
432:B
405:A
384:)
381:B
375:A
372:(
322:A
276:(
56:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.