A SEMANTICS FOR THE CALCULUS E OF ENTAILMENT
Larisa Maksimowa · 2013
In this paper a semantics for the calculus E of entailment is constructed. This semantics is based on a notion of E-structure which is a generalization of Kripke S4 models. We use this semantics to prove that a hypothesis of D. Prawitz [3] and R. K. Meyer [5] on the equivalence of calculus E and NR-theory of entailment is false. We begin from the definition of EICD-structure which gives a semantics for the calculus EICDthe positive fragment of E. Axioms for E and EICD can be found for example in [1]. Let S be a set, P be a non-empty subset of S, R be a ternary relation on S. The system 〈S, P,R〉 is called an EICD-structure, if it satisfies the following conditions for all U , V , W , X, Y in S.