An extension of J\'{o}nsson-Tarski representation and model existence in predicate non-normal modal logics
| Autor: | Tanaka, Yoshihito |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Mathematical Logic Quarterly, 68-2, 2022, 189-201 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1002/malq.202100018 |
| Popis: | In this paper, we give an extension of the J\'{o}nsson-Tarski representation theorem for both normal and non-normal modal algebras so that it preserves countably many infinitary meets and joins. To extend the J\'{o}nsson-Tarski representation to non-normal modal algebras we consider neighborhood frames instead of Kripke frames just as Do\v{s}en's duality theorem for modal algebras, and to deal with infinite meets and joins, we make use of Q-filters instead of prime filters. Then, we show that every predicate modal logic, whether it is normal or non-normal, has a model defined on a neighborhood frame with constant domains, and give completeness theorem for some predicate modal logics. We also show the same results for infinitary modal logics. Comment: The previous version of this paper is submitted by error |
| Databáze: | arXiv |
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