Axiomatization of Crisp Gödel Modal Logic

0525276 - ÚI 2022 RIV NL eng J - Článek v odborném periodiku
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
Grant CEP: GA MŠMT(CZ) EF17_050/0008361
GRANT EU: European Commission(XE) 689176 - SYSMICS
Institucionální podpora: RVO:67985807
Klíčová slova: Modal many-valued logics * Axiomatic systems * Gödel logic * Modal Gödel logic * Lattice-valued Kripke semantics
Obor OECD: Pure mathematics
Impakt faktor: 0.833, rok: 2021
Způsob publikování: Omezený přístup
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.
Trvalý link: http://hdl.handle.net/11104/0309456