Abstract

By an algebraic semantics we shall mean a class K of matrices M = for a propositional language L such that D is a singleton, D = fdg. A logic has an algebraic semantics i C =6 ; and there exists an algebraic semantics K strongly adequate for C, i.e., C = CnK. Proposition. If a logic has an algebraic semantics, then every factorial matrix M 2 M atr has the following properties: M is of the form, where 1A 2 A each formula 2 C denes the constant 1A in A, that is, A[a1; : : : ; an] = 1A for any a1; : : : ; an 2 A.