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#REDIRECT [[Logical consequence]] ...

#REDIRECT [[Logical consequence]] ...

#REDIRECT [[Logical consequence]] ...

[[Category:Logical consequence]] ...

*[[Logical consequence]] (or entailment), the relationship between statements that holds true when *[[Result]] (or upshot), the final consequence of a sequence of actions or events ...

...ath>P</math> is true, and the proposition <math>Q</math> is true, then the logical conjunction of the two propositions <math>P</math> and <math>Q</math> is tr ...ath>P</math> is true, and the proposition <math>Q</math> is true, then the logical conjunction of the two propositions <math>P</math> and <math>Q</math> is tr ...

{{wiktionary|consequence}} '''Consequence''' may refer to: ...

* [[Logical consequence]] (also entailment or logical implication), the relationship between statements that holds true when one * [[Material conditional]] (also material implication), a logical connective and binary truth function typically interpreted as "If ''p'', th ...

...law of [[classical logic]]. It is the principle that the conjuncts of a [[logical conjunction]] may switch places with each other, while preserving the [[tru ...sequence of <math>(Q \land P)</math> in the other, in some [[formal system|logical system]]; ...

...s it possible to introduce a biconditional statement into a [[formal proof|logical proof]]. If <math>P \to Q</math> is true, and if <math>Q \to P</math> is tr ...that <math>P \leftrightarrow Q</math> is a [[logical consequence|syntactic consequence]] when <math>P \to Q</math> and <math>Q \to P</math> are both in a proof; ...

...m]] and [[rule of inference]] which makes the [[inference]] that, if the [[Logical conjunction|conjunction]] ''A and B'' is true, then ''A'' is true, and ''B' ...also a syntactic consequence of <math>P \land Q</math> in [[formal system|logical system]]; ...

A '''multiple-conclusion logic''' is one in which [[logical consequence]] is a [[relation (mathematics)|relation]], <math>\vdash</math>, between tw Some [[logician]]s favor a multiple-conclusion consequence relation over the more traditional single-conclusion relation on the ground ...

...00mend/page/n63 56]|publisher=Van Nostrand |isbn=9780442253073}}</ref> The logical equivalence of <math>p</math> and <math>q</math> is sometimes expressed as ...erial equivalence]], so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concep ...

{{Short description|Inference introducing a disjunction in logical proofs}} ...ssible to introduce [[logical disjunction|disjunctions]] to [[formal proof|logical proofs]]. It is the [[inference]] that if ''P'' is true, then ''P or Q'' mu ...

...her answers and test them alone – the others are eliminated as a [[logical consequence]]; this is the idea behind optimizations for computerized searches when the ...

{{about|propositions which are logically true|the logical property|Truth}} ...as providing accounts of the nature of logical truth, as well as [[logical consequence]].<ref>[[Willard Van Orman Quine|Quine, Willard Van Orman]], ''Philosophy o ...

...nate a [[logical disjunction|disjunctive statement]] from a [[formal proof|logical proof]]. It is the [[inference]] that if a statement <math>P</math> implie ...P \to Q</math>, and <math>R \to Q</math> and <math>P \lor R</math> in some logical system; ...

...arski]]an approaches to semantics, but in the role that the proposition or logical connective plays within a [[Formal system|system of inference]]. ..., and some provocative philosophical remarks about locating the meaning of logical connectives in their [[Natural_deduction#Introduction_and_elimination|intro ...

...st one of their consequents must be too. ''Constructive dilemma'' is the [[Logical disjunction|disjunctive]] version of [[modus ponens]], whereas [[destructiv ...>, <math>R \to S</math>, and <math>P \lor R</math> in some [[formal system|logical system]]; ...

...one to [[inference|infer]] a [[Material conditional|conditional]] from a [[Logical biconditional|biconditional]]. If <math>P \leftrightarrow Q</math> is true, ...consequences]] of <math>P \leftrightarrow Q</math> in some [[formal system|logical system]]; ...