On transitive modal many-valued logics

0522276 - ÚI 2022 RIV NL eng J - Journal Article
Vidal, Amanda
On transitive modal many-valued logics.
Fuzzy Sets and Systems. Roč. 407, 1 March (2021), s. 97-114. ISSN 0165-0114. E-ISSN 1872-6801
R&D Projects: GA ČR GA17-04630S; GA MŠMT(CZ) EF17_050/0008361
EU Projects: European Commission(XE) 689176 - SYSMICS
Institutional support: RVO:67985807
Keywords : non-classical logics * computability * modal logics
OECD category: Pure mathematics
Impact factor: 4.462, year: 2021
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.fss.2020.01.011

This paper is focused on the study of modal logics defined from valued Kripke frames, and particularly, on computability and expressivity questions of modal logics of transitive Kripke frames evaluated over certain residuated lattices. It is shown that a large family of those logics -including the ones arising from the standard MV and Product algebras- yields an undecidable consequence relation. Later on, the behavior of transitive modal Łukasiewicz logic is compared with that of its non-transitive counterpart, exhibiting some particulars concerning computability and equivalence with other logics. We conclude the article by showing the undecidability of the validity and the local SAT questions over transitive models when the Delta operation is added to the logic.
Permanent Link: http://hdl.handle.net/11104/0306795