Modal definability in enriched languages

Abstract

The paper deals with polymodal languages combined with standard semantics defined by means of some conditions on the frames. So a notion of “polymodal base” arises which provides various enrichments of the classical modal language. One of these enrichments, viz. the base £(R,-R), with modalities over a relation and over its complement, is the paper’s main paradigm. The modal definability (in the spirit of van Benthem’s correspondence theory) of arbitrary and -elementary classes of frames in this base and in some of its extensions, e.g., £(R,— R,R-1,—R-1), £(R,—R,) etc., is described, and numerous examples of conditions definable there, as well as undefinable ones, are adduced. © 1990 by the University of Notre Dame. All rights reserved.