Axiomatization of Crisp Gödel Modal Logic

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00525276" target="_blank" >RIV/67985807:_____/21:00525276 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11225-020-09910-5" target="_blank" >http://dx.doi.org/10.1007/s11225-020-09910-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11225-020-09910-5" target="_blank" >10.1007/s11225-020-09910-5</a>

Result language
angličtina
Original language name
Axiomatization of Crisp Gödel Modal Logic
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/EF17_050%2F0008361" target="_blank" >EF17_050/0008361: Enhancing human resources for research in theoretical computer science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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