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- Truth-value_semantics abstract "In formal semantics, truth-value semantics is an alternative to Tarskian semantics. It has been primarily championed by Ruth Barcan Marcus, H. Leblanc, and M. Dunn and N. Belnap. It is also called the substitution interpretation (of the quantifiers) or substitutional quantification.The idea of these semantics is that universal (existential) quantifier may be read as a conjunction (disjunction) of formulas in which constants replace the variables in the scope of the quantifier. E.g. ∀xPx may be read (Pa & Pb & Pc &...) where a,b,c are individual constants replacing all occurrences of x in Px.The main difference between truth-value semantics and the standard semantics for predicate logic is that there are no domains for truth-value semantics. Only the truth clauses for atomic and for quantificational formulas differ from those of the standard semantics. Whereas in standard semantics atomic formulas like Pb or Rca are true if and only if (the referent of) b is a member of the extension of the predicate P, respectively, if and only if the pair (c,a) is a member of the extension of R, in truth-value semantics the truth-values of atomic formulas are basic. A universal (existential) formula is true if and only if all (some) substitution instances of it are true. Compare this with the standard semantics, which says that a universal (existential) formula is true if and only if for all (some) members of the domain, the formula holds for all (some) of them; e.g. ∀xA is true (under an interpretation) if and only if for all k in the domain D, A(k/x) is true (where A(k/x) is the result of substituting k for all occurrences of x in A). (Here we are assuming that constants are names for themselves—i.e. they are also members of the domain.)Truth-value semantics is not without its problems. First, the strong completeness theorem and compactness fail. To see this consider the set {F(1), F(2),...}. Clearly the formula ∀xF(x) is a logical consequence of the set, but it is not a consequence of any finite subset of it (and hence it is not deducible from it). It follows immediately that both compactness and the strong completeness theorem fail for truth-value semantics. This is rectified by a modified definition of logical consequence as given in Dunn and Belnap 1968.Another problem occurs in free logic. Consider a language with one individual constant c that is nondesignating and a predicate F standing for 'does not exist'. Then ∃xFx is false even though a substitution instance (in fact every such instance under this interpretation) of it is true. To solve this problem we simply add the proviso that an existentially quantified statement is true under an interpretation for at least one substitution instance in which the constant designates something that exists.".
- Truth-value_semantics wikiPageID "2165388".
- Truth-value_semantics wikiPageLength "3291".
- Truth-value_semantics wikiPageOutDegree "20".
- Truth-value_semantics wikiPageRevisionID "656459846".
- Truth-value_semantics wikiPageWikiLink Atomic_formula.
- Truth-value_semantics wikiPageWikiLink Category:Semantics.
- Truth-value_semantics wikiPageWikiLink Compactness_theorem.
- Truth-value_semantics wikiPageWikiLink Completeness_(logic).
- Truth-value_semantics wikiPageWikiLink Formal_semantics_(logic).
- Truth-value_semantics wikiPageWikiLink Free_logic.
- Truth-value_semantics wikiPageWikiLink Game_semantics.
- Truth-value_semantics wikiPageWikiLink Kripke_semantics.
- Truth-value_semantics wikiPageWikiLink Logical_consequence.
- Truth-value_semantics wikiPageWikiLink Model-theoretic_semantics.
- Truth-value_semantics wikiPageWikiLink Predicate_logic.
- Truth-value_semantics wikiPageWikiLink Proof-theoretic_semantics.
- Truth-value_semantics wikiPageWikiLink Quantifier_(logic).
- Truth-value_semantics wikiPageWikiLink Quasi-quotation.
- Truth-value_semantics wikiPageWikiLink Ruth_Barcan_Marcus.
- Truth-value_semantics wikiPageWikiLink Semantic_theory_of_truth.
- Truth-value_semantics wikiPageWikiLink Standard_semantics.
- Truth-value_semantics wikiPageWikiLink Truth-conditional_semantics.
- Truth-value_semantics wikiPageWikiLink Truth_clause.
- Truth-value_semantics wikiPageWikiLink Universal_quantification.
- Truth-value_semantics wikiPageWikiLink Universal_quantifier.
- Truth-value_semantics wikiPageWikiLinkText "Truth-value semantics".
- Truth-value_semantics wikiPageWikiLinkText "substitution interpretation".
- Truth-value_semantics hasPhotoCollection Truth-value_semantics.
- Truth-value_semantics wikiPageUsesTemplate Template:Unreferenced.
- Truth-value_semantics subject Category:Semantics.
- Truth-value_semantics hypernym Alternative.
- Truth-value_semantics type Article.
- Truth-value_semantics type Organisation.
- Truth-value_semantics type Article.
- Truth-value_semantics comment "In formal semantics, truth-value semantics is an alternative to Tarskian semantics. It has been primarily championed by Ruth Barcan Marcus, H. Leblanc, and M. Dunn and N. Belnap. It is also called the substitution interpretation (of the quantifiers) or substitutional quantification.The idea of these semantics is that universal (existential) quantifier may be read as a conjunction (disjunction) of formulas in which constants replace the variables in the scope of the quantifier. E.g.".
- Truth-value_semantics label "Truth-value semantics".
- Truth-value_semantics sameAs Semântica_de_Valor-verdade.
- Truth-value_semantics sameAs m.06rpy5.
- Truth-value_semantics sameAs Q14477759.
- Truth-value_semantics sameAs Q14477759.
- Truth-value_semantics sameAs 真值语义.
- Truth-value_semantics wasDerivedFrom Truth-value_semantics?oldid=656459846.
- Truth-value_semantics isPrimaryTopicOf Truth-value_semantics.