Natural Frames and Self-dual Logics

Abstract

The paper revisits a class of model structures introduced by the author in 1974, with particular attention to the system SCon, which axiomatizes the universal class. SCon, which independently deserves notice as an algebraically plausible weakest modal system, is self-dual; that is, its □ and ◊ have the same logic. The paper gives a semantic analysis of the system on model structures capable of an axiological interpretation, presenting a number of determination- and correspondence-theoretic results. Some intriguing consequences of self-duality for the axiological interpretation of natural frames are discussed.