Abstract
In this paper, we consider the non-normal modal logics over monotonic modal logic \(\textsf{M}\) with extensions of any combination of (N), (P), (T), and (4) i.e. \(\{\textsf{M},\textsf{MN},\ldots ,\textsf{MNPT4}\}\). We study the algebras corresponding to these logics and give some examples of them. We further introduce the Gentzen-style sequent calculi with soundness and completeness proved. Finally, we prove the FMP of these logics and thus decidability based on our systems by algebraic proof-theoretic methods.
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This work of both authors was supported by the Chinese National Funding of Social Sciences (Grant no. 18ZDA033).
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Peng, Y., Wang, Y. (2023). On the Finite Model Property of Non-normal Modal Logics. In: Alechina, N., Herzig, A., Liang, F. (eds) Logic, Rationality, and Interaction. LORI 2023. Lecture Notes in Computer Science, vol 14329. Springer, Cham. https://doi.org/10.1007/978-3-031-45558-2_16
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