Truth-value semantics

substitutional quantification
In formal semantics, truth-value semantics is an alternative to Tarskian semantics.wikipedia
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Semantics of logic

formal semanticssemanticslogical semantics
In formal semantics, truth-value semantics is an alternative to Tarskian semantics.
Truth-value semantics (also commonly referred to as substitutional quantification) was advocated by Ruth Barcan Marcus for modal logics in the early 1960s and later championed by Dunn, Belnap, and Leblanc for standard first-order logic. James Garson has given some results in the areas of adequacy for intensional logics outfitted with such a semantics. The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever (and hence its name truth-value semantics).

Quasi-quotation

Oxford bracketsquasiquote
Quasi-quotation
For example, one can use quasi-quotation to illustrate an instance of substitutional quantification, like the following:

Semantic theory of truth

Convention Tsemantic theoryTarski's theory of truth
In formal semantics, truth-value semantics is an alternative to Tarskian semantics.

Ruth Barcan Marcus

tag theory of namesMarcus
It has been primarily championed by Ruth Barcan Marcus, H. Leblanc, and M. Dunn and N. Belnap.

Universal quantification

universal quantifieruniversally quantifieduniversal
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.

Quantifier (logic)

quantifierquantifiersquantification
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.

First-order logic

predicate logicfirst-orderpredicate calculus
The main difference between truth-value semantics and the standard semantics for predicate logic is that there are no domains for truth-value semantics.

Atomic formula

atomatomicatomic expressions
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.

Completeness (logic)

completecompletenessincompleteness
First, the strong completeness theorem and compactness fail.

Compactness theorem

compactnesscompact(countable) compactness property
First, the strong completeness theorem and compactness fail.

Logical consequence

entailsentailmentfollows from
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).

Free logic

inclusive logic
Another problem occurs in free logic.

Game semantics

game semantics for first-order logicgame theoretic semanticsGame-theoretical semantics
Game semantics

Kripke semantics

Kripke modelsrelational semanticsframe semantics
Kripke semantics

Truth-conditional semantics

truthtruth conditioningtruth-conditional theory of meaning
Truth-conditional semantics

Truth value

truth-valuelogical valuetruth values
Truth-value semantics