Modal Logic for Reasoning About Uncertainty and Confusion
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915641051578368 |
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| author | Bílková, Marta Ferguson, Thomas M. Kozhemiachenko, Daniil |
| author_facet | Bílková, Marta Ferguson, Thomas M. Kozhemiachenko, Daniil |
| contents | We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we expand Gödel modal logic KG with the involutive negation ~ defined as v(~A,w)=1-v(A,w). We provide semantics with the finite model property for our new logic that we call KG_inv and show its equivalence to the standard semantics over [0,1]-valued Kripke models. Namely, we show that a formula is valid in the standard semantics of KG_inv iff it is valid in the new semantics. Using this new semantics, we construct a constraint tableaux calculus for KG_inv that allows for an explicit extraction of countermodels from complete open branches and then employ the tableaux calculus to obtain the PSPACE-completeness of the validity in KG_inv. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modal Logic for Reasoning About Uncertainty and Confusion Bílková, Marta Ferguson, Thomas M. Kozhemiachenko, Daniil Logic Logic in Computer Science We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we expand Gödel modal logic KG with the involutive negation ~ defined as v(~A,w)=1-v(A,w). We provide semantics with the finite model property for our new logic that we call KG_inv and show its equivalence to the standard semantics over [0,1]-valued Kripke models. Namely, we show that a formula is valid in the standard semantics of KG_inv iff it is valid in the new semantics. Using this new semantics, we construct a constraint tableaux calculus for KG_inv that allows for an explicit extraction of countermodels from complete open branches and then employ the tableaux calculus to obtain the PSPACE-completeness of the validity in KG_inv. |
| title | Modal Logic for Reasoning About Uncertainty and Confusion |
| topic | Logic Logic in Computer Science |
| url | https://arxiv.org/abs/2505.02548 |