Axiomatization of Crisp Gödel Modal Logic

0525276 - ÚI 2022 RIV NL eng J - Journal Article
Rodriguez, R. O. - Vidal, Amanda
Axiomatization of Crisp Gödel Modal Logic.
Studia Logica. Roč. 109, č. 2 (2021), s. 367-395. ISSN 0039-3215. E-ISSN 1572-8730
R&D Projects: GA MŠMT(CZ) EF17_050/0008361
EU Projects: European Commission(XE) 689176 - SYSMICS
Institutional support: RVO:67985807
Keywords : Modal many-valued logics * Axiomatic systems * Gödel logic * Modal Gödel logic * Lattice-valued Kripke semantics
OECD category: Pure mathematics
Impact factor: 0.833, year: 2021
Method of publishing: Limited access
http://dx.doi.org/10.1007/s11225-020-09910-5

In this paper we consider the modal logic with both [] and arising from Kripke models with a crisp accessibility and whose propositions are valued over the standard Gödel algebra [0,1]G. We provide an axiomatic system extending the one from Caicedo and Rodriguez (J Logic Comput 25(1):37–55, 2015) for models with a valued accessibility with Dunn axiom from positive modal logics, and show it is strongly complete with respect to the intended semantics. The axiomatizations of the most usual frame restrictions are given too. We also prove that in the studied logic it is not possible to get ◊ as an abbreviation of [], nor vice-versa, showing that indeed the axiomatic system we present does not coincide with any of the mono-modal fragments previously axiomatized in the literature.
Permanent Link: http://hdl.handle.net/11104/0309456