Fuzzy bi-Godel modal logic and its paraconsistent relatives

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00604115" target="_blank" >RIV/67985807:_____/25:00604115 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1093/logcom/exae011" target="_blank" >https://doi.org/10.1093/logcom/exae011</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/logcom/exae011" target="_blank" >10.1093/logcom/exae011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Fuzzy bi-Godel modal logic and its paraconsistent relatives

Popis výsledku v původním jazyce

We present the axiomatisation of the fuzzy bi-Godel modal logic KbiG(f) (formulated in the language containing Delta (Baaz delta operator) and treating < (co-implication) as a defined connective). We also consider its paraconsistent relatives KbiG(f) KG(2 +/- f) and G(square,lozenge)(2 +/- f). respectively, and equipped with two fuzzy relations R+ and R- used to determine supports of truth and falsity of modal formulas. We construct embeddings of KG(2 +/- f) and G(square,lozenge)(2 +/- f) into KbiG(f) and use them to obtain the characterization of KG(2)- and G(square,lozenge)(2)-definable frames. Moreover, we study the transfer of KbiG(f) formulas into KG(2 +/- f), i.e., formulas that are KbiG(f)-valid on mono-relational frames F and F' iff they are KG(2 +/- f)-valid on their bi-relational counterparts. Finally, we establish PSpace-completeness of all considered logics.

Název v anglickém jazyce

Fuzzy bi-Godel modal logic and its paraconsistent relatives

Popis výsledku anglicky

We present the axiomatisation of the fuzzy bi-Godel modal logic KbiG(f) (formulated in the language containing Delta (Baaz delta operator) and treating < (co-implication) as a defined connective). We also consider its paraconsistent relatives KbiG(f) KG(2 +/- f) and G(square,lozenge)(2 +/- f). respectively, and equipped with two fuzzy relations R+ and R- used to determine supports of truth and falsity of modal formulas. We construct embeddings of KG(2 +/- f) and G(square,lozenge)(2 +/- f) into KbiG(f) and use them to obtain the characterization of KG(2)- and G(square,lozenge)(2)-definable frames. Moreover, we study the transfer of KbiG(f) formulas into KG(2 +/- f), i.e., formulas that are KbiG(f)-valid on mono-relational frames F and F' iff they are KG(2 +/- f)-valid on their bi-relational counterparts. Finally, we establish PSpace-completeness of all considered logics.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA22-01137S" target="_blank" >GA22-01137S: Metamatematika substrukturálních modálních logik</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Logic and Computation

ISSN

0955-792X

e-ISSN

1465-363X

Svazek periodika

35

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

37

Strana od-do

exae011

Kód UT WoS článku

001195311900001

EID výsledku v databázi Scopus

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