Referential Matrix Semantics for Propositional Calculi
نویسنده
چکیده
Let L be a propositional language, and let F1, . . . , Fn be all propositional connectives it involves. We shall denote the set of all formulas of L as L, and identify L with the algebra of formulas (L,F1, . . . , Fn) freely generated by the propositional letters p1, . . . , pi, . . .. Assume that T is a non-empty set of indices (points of reference, possible worlds) and assume that a certain set H of functions of the form v : L × T → {0, 1} is selected to play the role of admissible valuations for L (i.e. the valuations that conform to the intended meaning of Fi’s). v(α, t) = 1 (= 0) reads: the formula α is true (is false) at the point t under v. The set H determines uniquely the consequence operation CnH on L defined by
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