Truth-value semantics

In the semantics of logic, truth-value semantics is an alternative to Tarskian semantics. It has been primarily championed by H. Leblanc, and M. Dunn and N. Belnap. It is also called the substitution interpretation (of the quantifiers).

A theorem of Beth, stating that in models all members in the domain except those that have been assigned constants may be discounted, supports the idea that the 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.