Neighborhood semantics for modal many-valued logics

0480886 - ÚI 2019 RIV NL eng J - Journal Article
Cintula, Petr - Noguera, Carles
Neighborhood semantics for modal many-valued logics.
Fuzzy Sets and Systems. Roč. 345, 15 August (2018), s. 99-112. ISSN 0165-0114. E-ISSN 1872-6801
R&D Projects: GA ČR(CZ) GF15-34650L
EU Projects: European Commission(XE) 689176 - SYSMICS
Grant - others:AV ČR(CZ) JSPS-16-08; Austrian Science Fund(AT) I1897-N25
Program: Bilaterální spolupráce
Institutional support: RVO:67985807 ; RVO:67985556
Keywords : mathematical fuzzy logic * modal fuzzy logics * neighborhood frames * Kripke semantics * many-valued logics
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: 2.907, year: 2018

The majority of works on modal many-valued logics consider Kripke-style possible worlds frames as the principal semantics despite their well-known axiomatizability issues when considering non-Boolean accessibility relations. The present work explores a more general semantical picture, namely a many-valued version of the classical neighborhood semantics. We present it in two levels of generality. First, we work with modal languages containing only the two usual unary modalities, define neighborhood frames over algebras of the logic FLew with operators, and show their relation with the usual Kripke semantics (this is actually the highest level of generality where one can give a straightforward definition of the Kripke-style semantics). Second, we define generalized neighborhood frames for arbitrary modal languages over a given class of algebras for an arbitrary protoalgebraic logic and, assuming certain additional conditions, axiomatize the logic of all such frames (which generalizes the completeness theorem of the classical modal logic E with respect to classical neighborhood frames).
Permanent Link: http://hdl.handle.net/11104/0276553