587:(i.e. everything becomes provable) and paraconsistent logic tries to avoid explosion and to be able to reason with contradictions. One of the solutions is to introduce disjunction with over rules. See
511:
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572:, this means that if the premise is true, then the conclusion is also true as any rule of inference should be, and an
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Therefore, Socrates is a man or pigs are flying in formation over the
English Channel.
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because in combination with other rules of logic, it leads to
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Copi, Irving M.; Cohen, Carl; McMahon, Kenneth (2014).
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880:(11th ed.). New York: McGraw Hill. p. 311.
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Inference introducing a disjunction in logical proofs
576:, as it has a single proposition in its premises.
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849:(12th ed.). Cengage. pp. 401–402, 707.
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873:"Deductive Arguments II Truth-Functional Logic"
579:Disjunction introduction is not a rule in some
506:{\displaystyle {\frac {P}{\therefore P\lor Q}}}
316:
208:
146:{\displaystyle {\frac {P}{\therefore P\lor Q}}}
516:where the rule is that whenever instances of "
905:(14th ed.). Pearson. pp. 370, 618.
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870:Moore, Brooke Noel; Parker, Richard (2015).
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434:. The rule makes it possible to introduce
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562:" can be placed on a subsequent line.
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589:Paraconsistent logic § Tradeoffs
7:
732:and expressed as a truth-functional
824:are propositions expressed in some
565:More generally it's also a simple
14:
641:{\displaystyle P\vdash (P\lor Q)}
943:Theorems in propositional logic
847:A Concise Introduction to Logic
536:" appear on lines of a proof, "
774:{\displaystyle P\to (P\lor Q)}
768:
756:
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635:
623:
472:The rule can be expressed as:
1:
845:Hurley, Patrick J. (2014).
959:
398:Existential generalization
203:Biconditional introduction
740:of propositional logic:
601:disjunction introduction
412:Disjunction introduction
389:Universal generalization
229:Disjunction introduction
216:Conjunction introduction
186:Implication introduction
20:Disjunction introduction
694:{\displaystyle P\lor Q}
664:{\displaystyle \vdash }
603:rule may be written in
555:{\displaystyle P\lor Q}
430:and almost every other
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248:hypothetical syllogism
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39:Propositional calculus
903:Introduction to Logic
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703:syntactic consequence
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290:Negation introduction
283:modus ponendo tollens
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938:Paraconsistent logic
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348:Material implication
299:Rules of replacement
162:Transformation rules
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261:destructive dilemma
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933:Rules of inference
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465:Socrates is a man.
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113:Symbolic statement
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912:978-1-292-02482-0
887:978-0-07-811914-9
878:Critical Thinking
856:978-1-285-19654-1
817:{\displaystyle Q}
797:{\displaystyle P}
718:{\displaystyle P}
529:{\displaystyle P}
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101:{\displaystyle Q}
81:{\displaystyle P}
61:{\displaystyle P}
29:Rule of inference
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595:Formal notation
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420:or introduction
373:Predicate logic
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331:Double negation
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454:must be true.
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68:is true, then
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826:formal system
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310:Associativity
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192:elimination (
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108:must be true.
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442:. It is the
436:disjunctions
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410:
400: /
391: /
282:
279: /
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271: /
258: /
255:Constructive
245: /
232: /
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219: /
206: /
194:modus ponens
193:
189: /
673:metalogical
355:Exportation
242:Disjunctive
235:elimination
222:elimination
209:elimination
927:Categories
832:References
607:notation:
268:Absorption
763:∨
754:→
734:tautology
686:∨
659:⊢
630:∨
621:⊢
585:explosion
547:∨
495:∨
489:∴
444:inference
362:Tautology
135:∨
129:∴
45:Statement
725:in some
446:that if
416:addition
738:theorem
605:sequent
459:English
422:) is a
909:
884:
853:
784:where
651:where
452:P or Q
701:is a
671:is a
567:valid
35:Field
907:ISBN
882:ISBN
851:ISBN
804:and
599:The
25:Type
736:or
705:of
438:to
426:of
414:or
88:or
48:If
929::
876:.
828:.
729:;
591:.
461::
915:.
890:.
859:.
812:Q
792:P
769:)
766:Q
760:P
757:(
751:P
713:P
689:Q
683:P
636:)
633:Q
627:P
624:(
618:P
550:Q
544:P
524:P
498:Q
492:P
485:P
448:P
196:)
138:Q
132:P
125:P
96:Q
76:P
56:P
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