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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2501.00486 |
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| _version_ | 1866916547045359616 |
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| author | Sawasaki, Takahiro |
| author_facet | Sawasaki, Takahiro |
| contents | In this paper, we prove the semantic incompleteness of the Hilbert-style system for the minimal normal term-modal logic with equality and non-rigid terms that was proposed in Liberman et al. (2020) "Dynamic Term-modal Logics for First-order Epistemic Planning." Term-modal logic is a family of first-order modal logics having term-modal operators indexed with terms in the first-order language. While some first-order formula is valid over the class of all frames in the Kripke semantics for the term-modal logic proposed there, it is not derivable in Liberman et al. (2020)'s Hilbert-style system. We show this fact by introducing a non-standard Kripke semantics which makes the meanings of constants and function symbols relative to the meanings of relation symbols combined with them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00486 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semantic Incompleteness of Liberman et al. (2020)'s Hilbert-style System for Term-modal Logic K with Equality and Non-rigid Terms Sawasaki, Takahiro Logic in Computer Science In this paper, we prove the semantic incompleteness of the Hilbert-style system for the minimal normal term-modal logic with equality and non-rigid terms that was proposed in Liberman et al. (2020) "Dynamic Term-modal Logics for First-order Epistemic Planning." Term-modal logic is a family of first-order modal logics having term-modal operators indexed with terms in the first-order language. While some first-order formula is valid over the class of all frames in the Kripke semantics for the term-modal logic proposed there, it is not derivable in Liberman et al. (2020)'s Hilbert-style system. We show this fact by introducing a non-standard Kripke semantics which makes the meanings of constants and function symbols relative to the meanings of relation symbols combined with them. |
| title | Semantic Incompleteness of Liberman et al. (2020)'s Hilbert-style System for Term-modal Logic K with Equality and Non-rigid Terms |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2501.00486 |