Modal Logic with “Most”

Studia Logica:1-41 (forthcoming)
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Abstract

In this paper, we axiomatize modal logic extended with the modal operator MφM\varphi saying that “there are strictly more φ\varphi -successors than ¬φ\lnot \varphi -successors”, both in the class of image-finite Kripke frames and in the class of all Kripke frames. We follow the proof strategy of van der Hoek (Int J Uncertain Fuzziness Knowl Based Syst 4(1):45–60, 1996.), and prove a characterization result of finite majority structures which are capable of representing finite cardinality measures and a characterization result of finite extended majority structures which are capable of representing cardinality measures.

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Zhiguang Zhao
Delft University of Technology

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References found in this work

Qualitative probability as an intensional logic.Peter Gärdenfors - 1975 - Journal of Philosophical Logic 4 (2):171 - 185.
Interleaving Logic and Counting.Johan van Benthem & Thomas Icard - 2023 - Bulletin of Symbolic Logic 29 (4):503-587.
Ways of branching quantifers.Gila Sher - 1990 - Linguistics and Philosophy 13 (4):393 - 422.
Axiomatization of modal logic with counting.Xiaoxuan Fu & Zhiguang Zhao - forthcoming - Logic Journal of the IGPL.

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