Modal definability in enriched languages.
Valentin Goranko · Notre Dame Journal of Formal Logic · 1989
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 Δ-elementary classes of frames in this base and in some of its extensions, e.g., £(R,-R,R~ι,-R-1 ), £(R,-R,Φ) etc., is described, and numerous examples of conditions definable there, as well as undefinable ones, are adduced.