Crisp Bi-Gödel modal logic and its paraconsistent expansion
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00604125" target="_blank" >RIV/67985807:_____/25:00604125 - isvavai.cz</a>
Result on the web
<a href="https://dx.doi.org/10.1093/jigpal/jzad017" target="_blank" >https://dx.doi.org/10.1093/jigpal/jzad017</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/jigpal/jzad017" target="_blank" >10.1093/jigpal/jzad017</a>
Alternative languages
Result language
angličtina
Original language name
Crisp Bi-Gödel modal logic and its paraconsistent expansion
Original language description
In this paper, we provide a Hilbert-style axiomatization for the crisp bi-Gödel modal logic KbiG. We prove its completeness w.r.t. crisp Kripke models where formulas at each state are evaluated over the standard bi-Gödel algebra on [0, 1]. We also consider a paraconsistent expansion of KbiG with a De Morgan negation ¬, which we dub KG2. We devise a Hilbert-style calculus for this logic and, as a consequence of a conservative translation from KbiG to KG2, prove its completeness w.r.t. crisp Kripke models with two valuations over [0, 1] connected via ¬. For these two logics, we establish that their decidability and validity are PSPACE-complete. We also study the semantical properties of KbiG and KG2. In particular, we show that Glivenko’s theorem holds only in finitely branching frames. We also explore the classes of formulas that define the same classes of frames both in K (the classical modal logic) and the crisp Gödel modal logic BKc. We show that, among others, all Sahlqvist formulas and all formulas ϕ → χ where ϕ and χ are monotone define the same classes of frames in K and BKc.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA22-01137S" target="_blank" >GA22-01137S: Metamathematics of substructural modal logics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Logic Journal of the IGPL
ISSN
1367-0751
e-ISSN
1368-9894
Volume of the periodical
33
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
30
Pages from-to
jzad017
UT code for WoS article
001074713800001
EID of the result in the Scopus database
2-s2.0-105017431379