Abstract
In the paper we define a generic many valued modal logic, in which modalities are defined in the most general way possible following the idea of Thomason. Both the valuation of formulae and the accessibility predicates — replacing the usual accessibility relations — can be many valued. We present two types of semantics of the logic: the standard (Kripke) one and a relational one. In connection with the latter, we define a special calculus of relations corresponding to the connectives and modalities of the logic, and we develop a complete deduction system in Rasiowa-Sikowski style for this calculus. We illustrate the results by applying our formalisation to the two-valued modalities of possibility and necessity, and to a general class of many-valued modal logics defined by Fitting.
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© 2001 Springer-Verlag Berlin Heidelberg
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Konikowska, B., Orłowska, E. (2001). A Relational Formalisation of a Generic Many—Valued Modal Logic. In: Orłowska, E., Szałas, A. (eds) Relational Methods for Computer Science Applications. Studies in Fuzziness and Soft Computing, vol 65. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1828-4_11
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DOI: https://doi.org/10.1007/978-3-7908-1828-4_11
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