MoL-2021-20: The Expressive Power of Derivational Modal Logic

MoL-2021-20: Gougeon, Quentin (2021) The Expressive Power of Derivational Modal Logic. [Report]

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Alongside the traditional Kripke semantics, modal logic also enjoys a topological interpretation, which is becoming increasingly influential. We present various developments related to the topological derivational semantics based on the Cantor derivative operator. We establish useful characterizations of the validity of the axioms of bounded depth, and prove results of soundness and completeness for many other classical modal logics. We also address the expressivity of the topological μ-calculus, an extension of modal logic with fixpoint operators. We examine the tangled fragments of μ-calculus and show that they are not expressively complete. We also exhibit a large collection of classes of spaces that are definable in μ-calculus, but not in plain modal logic, thus demonstrating the strength of the former.

Item Type: Report
Report Nr: MoL-2021-20
Series Name: Master of Logic Thesis (MoL) Series
Year: 2021
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 05 Oct 2021 15:49
Last Modified: 07 Oct 2021 22:23

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