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arXiv · 2309.16250

Fuzzy bi-G\"{o}del modal logic and its paraconsistent relatives

Marta Bilkova·Sabine Frittella·Daniil Kozhemiachenko
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Abstract

We present the axiomatisation of the fuzzy bi-G\"{o}del modal logic (formulated in the language containing $\triangle$ and treating the coimplication as a defined connective) and establish its PSpace-completeness. We also consider its paraconsistent relatives defined on fuzzy frames with two valuations $e_1$ and $e_2$ standing for the support of truth and falsity, respectively, and equipped with \emph{two fuzzy relations} $R^+$ and $R^-$ used to determine supports of truth and falsity of modal formulas. We establish embeddings of these paraconsistent logics into the fuzzy bi-G\"{o}del modal logic and use them to prove their PSpace-completeness and obtain the characterisation of definable frames.

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Marta Bilkova, Sabine Frittella, Daniil Kozhemiachenko. 2023-09-28. Fuzzy bi-G\"{o}del modal logic and its paraconsistent relatives. https://doi.org/10.1093/logcom%2Fexae011

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