Paraconsistent Gödel Modal Logic
| Autor: | Marta Bílková, Sabine Frittella, Daniil Kozhemiachenko |
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| Rok vydání: | 2022 |
| Zdroj: | Automated Reasoning ISBN: 9783031107689 Part of the Lecture Notes in Computer Science book series (LNAI) Lecture Notes in Computer Science Lecture Notes in Computer Science-Automated Reasoning |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-031-10769-6_26 |
| Popis: | We introduce a paraconsistent modal logic $$\mathbf {K}\mathsf {G}^2$$ K G 2 , based on Gödel logic with coimplication (bi-Gödel logic) expanded with a De Morgan negation $$\lnot $$ ¬ . We use the logic to formalise reasoning with graded, incomplete and inconsistent information. Semantics of $$\mathbf {K}\mathsf {G}^2$$ K G 2 is two-dimensional: we interpret $$\mathbf {K}\mathsf {G}^2$$ K G 2 on crisp frames with two valuations $$v_1$$ v 1 and $$v_2$$ v 2 , connected via $$\lnot $$ ¬ , that assign to each formula two values from the real-valued interval [0, 1]. The first (resp., second) valuation encodes the positive (resp., negative) information the state gives to a statement. We obtain that $$\mathbf {K}\mathsf {G}^2$$ K G 2 is strictly more expressive than the classical modal logic $$\mathbf {K}$$ K by proving that finitely branching frames are definable and by establishing a faithful embedding of $$\mathbf {K}$$ K into $$\mathbf {K}\mathsf {G}^2$$ K G 2 . We also construct a constraint tableau calculus for $$\mathbf {K}\mathsf {G}^2$$ K G 2 over finitely branching frames, establish its decidability and provide a complexity evaluation. |
| Databáze: | OpenAIRE |
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