One Logic or Many Logics? ( Epstein's Set-Assignment Semantics for Logical Calculi)

Abstract

A philosophically motivated uniform semantical framework for various propositional calculae is sketched, following Richard L. Espstei's book The Semantic Foundations of Logic. The main idea is that a conditional can be true only if there is some connection between its antecedent and its consequent. Also a new concept of translations between logics (a joint work with Epstein) is presented. One theorem from the book is simplified and strengthened. The problem how to extend the approach to the predicate case (also a joint work, not included in the book) is discussed for the most natural system - the relatedness logic.