Fuzzy bi-Godel modal logic and its paraconsistent relatives

Autoři: Mgr. Marta Bílková, Ph.D.
Rok vydání: 2025
Typ publikace: Článek v odborném periodiku
Periodikum: Journal of Logic and Computation
Projekty: Metamatematika substrukturálních modálních logik
Bibliografická citace: BÍLKOVÁ, Marta, FRITTELLA, S., KOZHEMIACHENKO, D. Fuzzy bi-Godel modal logic and its paraconsistent relatives. Journal of Logic and Computation. 2025, 35(2), exae011. ISSN 0955-792X. E-ISSN 1465-363X
Dostupné z: doi:10.1093/logcom/exae011.
DOI: 10.1093/logcom/exae011
ID: 604115
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Abstrakt

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.