The Modelwise Interpolation Property of Semantic Logics
| Autor: | Zalán Gyenis, Zalán Molnár, Övge Öztürk |
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| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Bulletin of the Section of Logic, Vol 52, Iss 1, Pp 59-83 (2023) |
| Druh dokumentu: | article |
| ISSN: | 0138-0680 2449-836X |
| DOI: | 10.18778/0138-0680.2023.09 |
| Popis: | In this paper we introduce the modelwise interpolation property of a logic that states that whenever \(\models\phi\to\psi\) holds for two formulas \(\phi\) and \(\psi\), then for every model \(\mathfrak{M}\) there is an interpolant formula \(\chi\) formulated in the intersection of the vocabularies of \(\phi\) and \(\psi\), such that \(\mathfrak{M}\models\phi\to\chi\) and \(\mathfrak{M}\models\chi\to\psi\), that is, the interpolant formula in Craig interpolation may vary from model to model. We compare the modelwise interpolation property with the standard Craig interpolation and with the local interpolation property by discussing examples, most notably the finite variable fragments of first order logic, and difference logic. As an application we connect the modelwise interpolation property with the local Beth definability, and we prove that the modelwise interpolation property of an algebraizable logic can be characterized by a weak form of the superamalgamation property of the class of algebras corresponding to the models of the logic. |
| Databáze: | Directory of Open Access Journals |
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