Fuzzy bi-Gödel modal logic and its paraconsistent relatives
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910356657405952 |
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| author | Bilkova, Marta Frittella, Sabine Kozhemiachenko, Daniil |
| author_facet | Bilkova, Marta Frittella, Sabine Kozhemiachenko, Daniil |
| contents | We present the axiomatisation of the fuzzy bi-Gödel 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-Gödel modal logic and use them to prove their PSpace-completeness and obtain the characterisation of definable frames. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16250 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fuzzy bi-Gödel modal logic and its paraconsistent relatives Bilkova, Marta Frittella, Sabine Kozhemiachenko, Daniil Logic We present the axiomatisation of the fuzzy bi-Gödel 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-Gödel modal logic and use them to prove their PSpace-completeness and obtain the characterisation of definable frames. |
| title | Fuzzy bi-Gödel modal logic and its paraconsistent relatives |
| topic | Logic |
| url | https://arxiv.org/abs/2309.16250 |