Modal definability in enriched languages

Notre Dame Journal of Formal Logic 31 (1):81-105 (1989)
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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,=I=) etc., is described, and numerous examples of conditions definable there, as well as undefinable ones, are adduced.
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Modal Logic with Names.George Gargov & Valentin Goranko - 1993 - Journal of Philosophical Logic 22 (6):607 - 636.

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