Negative Definability in Modal Logic

Abstract

The aim of this paper is to give characterizations of the notion of negative definability as introduced in Venema [14]. This notion can be seen as an alternative way of defining classes of Kripke frames via a modal language, one that enables us, for instance, to define the previously undefinable class of irreflexive frames. Besides a list of closure conditions for negatively definable classes, the paper contains two main theorems. First, a characterization is given of negatively defined classes of finite transitive Kripke frames. Second, we characterize the negatively defined classes of general frames.