Notre Dame Journal of Formal Logic 31 (1):81-105 (1989)

Authors
Valentin Goranko
Stockholm University
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,=I=) etc., is described, and numerous examples of conditions definable there, as well as undefinable ones, are adduced.
Keywords modal definability  extended modal languages  correspondence theory
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Reprint years 1990
DOI 10.1305/ndjfl/1093635335
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References found in this work BETA

Semantic Analysis of Orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
Reduction of Second‐Order Logic to Modal Logic.S. K. Thomason - 1975 - Mathematical Logic Quarterly 21 (1):107-114.
Inaccessible Worlds.I. L. Humberstone - 1983 - Notre Dame Journal of Formal Logic 24 (3):346-352.
Minimal Deontic Logics.Jfak van Benthem - 1979 - Bulletin of the Section of Logic 8 (1):36-42.

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Citations of this work BETA

Modal Logic with Names.George Gargov & Valentin Goranko - 1993 - Journal of Philosophical Logic 22 (6):607 - 636.
The Modal Logic of Inequality.Maarten de Rijke - 1992 - Journal of Symbolic Logic 57 (2):566-584.
The Range of Modal Logic: An Essay in Memory of George Gargov.Johan van Benthem - 1999 - Journal of Applied Non-Classical Logics 9 (2):407-442.

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