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Journal Article

Toward a general frame semantics for modal many-valued logics

Cintula Petr, Menchón P., Noguera Carles

: Soft Computing vol.23, 7 (2019), p. 2233-2241

: GA17-04630S, GA ČR

: Modal many-valued logics, Mathematical fuzzy logic, Neighborhood frames, Kripke semantics, General frames

: 10.1007/s00500-018-3369-5

: http://dx.doi.org/10.1007/s00500-018-3369-5

(eng): Frame semantics, given by Kripke or neighborhood frames, do not give completeness theorems for all modal logics extending, respectively, K and E. Such shortcoming can be overcome by means of general frames, i.e., frames equipped with a collection of admissible sets of worlds (which is the range of possible valuations over such frame). We export this approach from the classical paradigm to modal many-valued logics by defining general A-frames over a given residuated lattice AA (i.e., the usual frames with a collection of admissible A-valued sets). We describe in detail the relation between general Kripke and neighborhood A-frames and prove that, if the logic of A is finitary, all extensions of the corresponding logic E of A are complete w.r.t. general neighborhood frames. Our work provides a new approach to the current research trend of generalizing relational semantics for non-classical modal logics to circumvent axiomatization problems.

: BA

: 10201

07.01.2019 - 08:39