Toward a general frame semantics for modal many-valued logics

0491819 - ÚI 2020 RIV DE eng J - Journal Article
Cintula, Petr - Menchón, P. - Noguera, Carles
Toward a general frame semantics for modal many-valued logics.
Soft Computing. Roč. 23, č. 7 (2019), s. 2233-2241. ISSN 1432-7643. E-ISSN 1433-7479
R&D Projects: GA ČR GA17-04630S
Institutional support: RVO:67985807 ; RVO:67985556
Keywords : Modal many-valued logics * Mathematical fuzzy logic * Neighborhood frames * Kripke semantics * General frames
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8); Pure mathematics (UTIA-B)
Impact factor: 3.050, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1007/s00500-018-3369-5

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.
Permanent Link: http://hdl.handle.net/11104/0285436