Note on a system of Åqvist

Abstract

In [1, pp. 82–84] L. Åqvist considers a modal system which he calls S3.5 obtained by adding to S3 the axiom ∼□p⊃□∼□p. This system becomes S5 when the rule ├A→├□A is added to it. S3.5 is put forward to stand to S5 as S3 stands to S4 and S2 to T. In this note we show how a natural extension of the modelling for S3 in [2] can give a suitable semantics for S3.5.1An S3 model2 is an ordered quadruple (GKRφ) where Κ is a set, G ε K and R is transitive and quasi-reflexive over K.