Bisimulation Quantified Logics: Undecidability

    Research output: Contribution to journalArticle

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    Abstract

    In this paper we introduce a general semantic interpretation for propositional quantification in all multi-modal logics based on bisimulations (bisimulation quantification). Bisimulation quantification has previously been considered in the context of isolated modal logics, such as PDL (D'Agostino and Hollenberg, 2000), intuitionistic logic (Pitts, 1992) and logics of knowledge (French 2003). We investigate the properties of bisimulation quantifiers in general modal logics, particularly the expressivity and decidability, and seek to motivate the use of bisimulation quantified modal logics. This paper addresses two important questions: when are bisimulation quantified logics bisimulation invariant; and do bisimulation quantifiers always preserve decidability? We provide a sufficient condition for bisimulation invariance, and give two examples of decidable modal logics which are undecidable when augmented with bisimulation quantifiers. This is part of a program of study to characterize the expressivity and decidability of bisimulation quantified modal logics.
    Original languageEnglish
    Pages (from-to)396-407
    JournalLecture Notes in Computer Science
    Volume3821
    DOIs
    Publication statusPublished - 2005

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    Computability and decidability
    Undecidability
    Bisimulation
    Logic
    Modal Logic
    Invariance
    Quantifiers
    Decidability
    Quantification
    Semantics
    Multi-modal Logic
    Intuitionistic Logic

    Cite this

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    title = "Bisimulation Quantified Logics: Undecidability",
    abstract = "In this paper we introduce a general semantic interpretation for propositional quantification in all multi-modal logics based on bisimulations (bisimulation quantification). Bisimulation quantification has previously been considered in the context of isolated modal logics, such as PDL (D'Agostino and Hollenberg, 2000), intuitionistic logic (Pitts, 1992) and logics of knowledge (French 2003). We investigate the properties of bisimulation quantifiers in general modal logics, particularly the expressivity and decidability, and seek to motivate the use of bisimulation quantified modal logics. This paper addresses two important questions: when are bisimulation quantified logics bisimulation invariant; and do bisimulation quantifiers always preserve decidability? We provide a sufficient condition for bisimulation invariance, and give two examples of decidable modal logics which are undecidable when augmented with bisimulation quantifiers. This is part of a program of study to characterize the expressivity and decidability of bisimulation quantified modal logics.",
    author = "Tim French",
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    language = "English",
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    Bisimulation Quantified Logics: Undecidability. / French, Tim.

    In: Lecture Notes in Computer Science, Vol. 3821, 2005, p. 396-407.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Bisimulation Quantified Logics: Undecidability

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    N2 - In this paper we introduce a general semantic interpretation for propositional quantification in all multi-modal logics based on bisimulations (bisimulation quantification). Bisimulation quantification has previously been considered in the context of isolated modal logics, such as PDL (D'Agostino and Hollenberg, 2000), intuitionistic logic (Pitts, 1992) and logics of knowledge (French 2003). We investigate the properties of bisimulation quantifiers in general modal logics, particularly the expressivity and decidability, and seek to motivate the use of bisimulation quantified modal logics. This paper addresses two important questions: when are bisimulation quantified logics bisimulation invariant; and do bisimulation quantifiers always preserve decidability? We provide a sufficient condition for bisimulation invariance, and give two examples of decidable modal logics which are undecidable when augmented with bisimulation quantifiers. This is part of a program of study to characterize the expressivity and decidability of bisimulation quantified modal logics.

    AB - In this paper we introduce a general semantic interpretation for propositional quantification in all multi-modal logics based on bisimulations (bisimulation quantification). Bisimulation quantification has previously been considered in the context of isolated modal logics, such as PDL (D'Agostino and Hollenberg, 2000), intuitionistic logic (Pitts, 1992) and logics of knowledge (French 2003). We investigate the properties of bisimulation quantifiers in general modal logics, particularly the expressivity and decidability, and seek to motivate the use of bisimulation quantified modal logics. This paper addresses two important questions: when are bisimulation quantified logics bisimulation invariant; and do bisimulation quantifiers always preserve decidability? We provide a sufficient condition for bisimulation invariance, and give two examples of decidable modal logics which are undecidable when augmented with bisimulation quantifiers. This is part of a program of study to characterize the expressivity and decidability of bisimulation quantified modal logics.

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