S is Constructively Complete

The logic S (Symmetric Propositional Relatedness Logic) was introduced in the late 1970s by Richard Epstein, and thoroughly studied over the subsequent decade by Epstein himself and his collaborators a clear outline of this work is presented in [2]. Epstein’s starting point was a semantical analysis of the concept of subject matter relatedness among propositions, which eventually led to an axiomatization and a nonconstructive completeness proof with respect to that semantics. We shall provide the axiom system S devised by Epstein with a constructive completeness proof, extending thereby to the full system of propositional logic some of our results on first degree relatedness conditionals (cp. [3]). For this purpose, however, we shall make use of Epstein’s semantics, as well as of a syntactic counterpart of a normal form theorem, already proved by Epstein in a semantic guise.