From Kripke to Neighborhood Semantics for Modal Fuzzy Logics

0460686 - ÚI 2017 RIV CH eng C - Conference Paper (international conference)
Cintula, Petr - Noguera, Carles - Roger, J.
From Kripke to Neighborhood Semantics for Modal Fuzzy Logics.
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Vol. 2. Cham: Springer, 2016 - (Carvalho, J.; Lesot, M.; Kaymak, U.; Vieira, S.; Bouchon-Meunier, B.; Yager, R.), s. 95-107. Communications in Computer and Information Science, 611. ISBN 978-3-319-40581-0. ISSN 1865-0929. E-ISSN 1865-0937.
[IPMU 2016 /16./. Eindhoven (NL), 20.06.2016-24.06.2016]
R&D Projects: GA ČR(CZ) GF15-34650L
Grant - others:Austrian Science Fund(AT) I1897-N25
Institutional support: RVO:67985807 ; RVO:67985556
Keywords : mathematical fuzzy logic * modal fuzzy logics * neighborhood frames * Kripke semantics * many-valued logics
Subject RIV: BA - General Mathematics

The majority of works on modal fuzzy logics consider Kripke-style possible worlds semantics as the principal semantics despite its well known axiomatizability issues when considering fuzzy accessibility relations. The present work offers the first (two) steps towards exploring a more general semantical picture, namely a fuzzified version of the classical neighborhood semantics. First we prove the fuzzy version of the classical relationship between Kripke and neighborhood semantics. Second, for any axiomatic extension of MTL (one of the main fuzzy logics), we define its modal expansion by a box-like modality, and, in the presence of some additional conditions, we prove that the resulting logic can be axiomatized by adding the E-rule to the corresponding Hilbert-style calculus of the starting logic.
Permanent Link: http://hdl.handle.net/11104/0260702