Extending Defeasibility for Propositional Standpoint Logics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916842577068032 |
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| author | Leisegang, Nicholas Meyer, Thomas Varzinczak, Ivan |
| author_facet | Leisegang, Nicholas Meyer, Thomas Varzinczak, Ivan |
| contents | In this paper, we introduce a new defeasible version of propositional standpoint logic by integrating Kraus et al.'s defeasible conditionals, Britz and Varzinczak's notions of defeasible necessity and distinct possibility, along with Leisegang et al.'s approach to defeasibility into the standpoint logics of Gómez Álvarez and Rudolph. The resulting logical framework allows for the expression of defeasibility on the level of implications, standpoint modal operators, and standpoint-sharpening statements. We provide a preferential semantics for this extended language and propose a tableaux calculus, which is shown to be sound and complete with respect to preferential entailment. We also establish the computational complexity of the tableaux procedure to be in PSpace. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_10133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Defeasibility for Propositional Standpoint Logics Leisegang, Nicholas Meyer, Thomas Varzinczak, Ivan Logic in Computer Science Artificial Intelligence In this paper, we introduce a new defeasible version of propositional standpoint logic by integrating Kraus et al.'s defeasible conditionals, Britz and Varzinczak's notions of defeasible necessity and distinct possibility, along with Leisegang et al.'s approach to defeasibility into the standpoint logics of Gómez Álvarez and Rudolph. The resulting logical framework allows for the expression of defeasibility on the level of implications, standpoint modal operators, and standpoint-sharpening statements. We provide a preferential semantics for this extended language and propose a tableaux calculus, which is shown to be sound and complete with respect to preferential entailment. We also establish the computational complexity of the tableaux procedure to be in PSpace. |
| title | Extending Defeasibility for Propositional Standpoint Logics |
| topic | Logic in Computer Science Artificial Intelligence |
| url | https://arxiv.org/abs/2507.10133 |