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Logical consequence (also entailment) is one of the most fundamental concepts in logic. It is the relationship between statements that holds true when one logically "follows from" one or more others. A valid logical argument is one in which the conclusions follow from its premises, and its conclusions are consequences of its premises. The philosophical analysis of logical consequence involves asking, 'in what sense does a conclusion follow from its premises?' and 'what does it mean for a conclusion to be a consequence of premises?'〔Beall, JC and Restall, Greg, ''(Logical Consequence )'' The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.).〕 All of philosophical logic can be thought of as providing accounts of the nature of logical consequence, as well as logical truth.〔Quine, Willard Van Orman, ''Philosophy of logic''〕 Logical consequence is taken to be both necessary and formal with examples explicated using models and proofs.〔 A sentence is said to be a logical consequence of a set of sentences, for a given language, if and only if, using logic alone (i.e. without regard to any interpretations of the sentences) the sentence must be true if every sentence in the set were to be true.〔McKeon, Matthew, ''(Logical Consequence )'' Internet Encyclopedia of Philosophy.〕 Logicians make precise accounts of logical consequence with respect to a given language by constructing a deductive system for , or by formalizing the intended semantics for . Alfred Tarski highlighted three salient features for which any adequate characterization of logical consequence needs to account: 1) that the logical consequence relation relies on the logical form of the sentences involved, 2) that the relation is a priori, i.e. it can be determined whether or not it holds without regard to sense experience, and 3) that the relation has a modal component.〔 == Formal accounts == The most widely prevailing view on how to best account for logical consequence is to appeal to formality. This is to say that whether statements follow from one another logically depends on the structure or logical form of the statements without regard to the contents of that form. Syntactic accounts of logical consequence rely on schemes using inference rules. For instance, we can express the logical form of a valid argument as "All are . All are . Therefore, All are ." This argument is formally valid, because every instance of arguments constructed using this scheme are valid. This is in contrast to an argument like "Fred is Mike's brother's son. Therefore Fred is Mike's nephew." Since this argument depends on the meanings of the words "brother", "son", and "nephew", the statement "Fred is Mike's nephew" is a so-called material consequence of "Fred is Mike's brother's son," not a formal consequence. A formal consequence must be true ''in all cases'', however this is an incomplete definition of formal consequence, since even the argument " is 's brother's son, therefore is 's nephew" is valid in all cases, but is not a ''formal'' argument.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Logical consequence」の詳細全文を読む スポンサード リンク
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