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Decidability of four modal logics

Theoria 34 (1):21-25 (1968)

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  1. Canonicity in Power and Modal Logics of Finite Achronal Width.Robert Goldblatt & Ian Hodkinson - 2024 - Review of Symbolic Logic 17 (3):705-735.
    We develop a method for showing that various modal logics that are valid in their countably generated canonical Kripke frames must also be valid in their uncountably generated ones. This is applied to many systems, including the logics of finite width, and a broader class of multimodal logics of ‘finite achronal width’ that are introduced here.
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  • Selective filtration in modal logic Part A. Semantic tableaux method.Dovm Gabbay - 1970 - Theoria 36 (3):323-330.
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  • Filtration Safe Operations on Frames.Stanislav Kikot, Ilya Shapriovsky & Evgeny Zolin - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10: Papers From the Tenth Aiml Conference, Held in Groningen, the Netherlands, August 2014. London, England: CSLI Publications. pp. 333-352.
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  • Another proof for the decidability of four modal logics.Brian F. Chellas - 1980 - Philosophia 9 (2):251-264.
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  • A general filtration method for modal logics.Dov M. Gabbay - 1972 - Journal of Philosophical Logic 1 (1):29 - 34.
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  • Existential definability of modal frame classes.Tin Perkov & Luka Mikec - 2020 - Mathematical Logic Quarterly 66 (3):316-325.
    We prove an existential analogue of the Goldblatt‐Thomason Theorem which characterizes modal definability of elementary classes of Kripke frames using closure under model theoretic constructions. The less known version of the Goldblatt‐Thomason Theorem gives general conditions, without the assumption of first‐order definability, but uses non‐standard constructions and algebraic semantics. We present a non‐algebraic proof of this result and we prove an analogous characterization for an alternative notion of modal definability, in which a class is defined by formulas which are satisfiable (...)
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  • Decidability by filtrations for graded normal logics (graded modalities V).Claudio Cerrato - 1994 - Studia Logica 53 (1):61 - 73.
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