Quantifying over epistemic updates

James Colin Hales

    Research output: ThesisDoctoral Thesis

    Abstract

    Dynamic epistemic logics reason about the knowledge belonging to a collectionof agents and how that knowledge changes in response to epistemic updates,events that provide agents with additional information. Previous work in dynamicepistemic logic, such as public announcement logic [76, 47] and actionmodel logic [15, 14], introduced models for epistemic updates and logics for reasoning about the effects of specific epistemic updates using these models. However many natural questions about epistemic updates are not questions about specific epistemic updates. For example, given a desired change in knowledge we might ask \Is there an epistemic update that results in the desired change in knowledge?", and if there is we might also ask \What is a specific epistemic update that results in the desired change in knowledge?". More recent works in dynamic epistemic logic, such as arbitrary public announcement logic [11] and group announcement logic [74], have considered logics for quantifying over epistemic updates. In principle these logics allow us to answer such questions using model-checking or satisfiability procedures, although these particular logics are undecidable [45, 3], and quantify over relatively restricted forms of epistemic updates.
    In the present work we consider logics for quantifying over very general formsof epistemic updates: arbitrary action model logic, which quantities over actionmodels; and refinement modal logic, which quantities over refinements, whichhave a partial correspondence with the results of action models, but are moregeneral. We present sound and complete axiomatisations, expressivity results,and decidability results for these logics in various multi-agent modal settings.
    LanguageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • The University of Western Australia
    Award date31 May 2016
    StateUnpublished - 2016

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    Logic
    Public Announcement
    Dynamic Epistemic Logic
    Model Checking
    Decidability
    Satisfiability
    Expressivity
    Sound
    Modal Logic

    Cite this

    Hales, James Colin. / Quantifying over epistemic updates. 2016.
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    title = "Quantifying over epistemic updates",
    abstract = "Dynamic epistemic logics reason about the knowledge belonging to a collectionof agents and how that knowledge changes in response to epistemic updates,events that provide agents with additional information. Previous work in dynamicepistemic logic, such as public announcement logic [76, 47] and actionmodel logic [15, 14], introduced models for epistemic updates and logics for reasoning about the effects of specific epistemic updates using these models. However many natural questions about epistemic updates are not questions about specific epistemic updates. For example, given a desired change in knowledge we might ask \Is there an epistemic update that results in the desired change in knowledge?{"}, and if there is we might also ask \What is a specific epistemic update that results in the desired change in knowledge?{"}. More recent works in dynamic epistemic logic, such as arbitrary public announcement logic [11] and group announcement logic [74], have considered logics for quantifying over epistemic updates. In principle these logics allow us to answer such questions using model-checking or satisfiability procedures, although these particular logics are undecidable [45, 3], and quantify over relatively restricted forms of epistemic updates.In the present work we consider logics for quantifying over very general formsof epistemic updates: arbitrary action model logic, which quantities over actionmodels; and refinement modal logic, which quantities over refinements, whichhave a partial correspondence with the results of action models, but are moregeneral. We present sound and complete axiomatisations, expressivity results,and decidability results for these logics in various multi-agent modal settings.",
    keywords = "Modal logic, decision procedures, Dynamic epistemic logic, Refinement quantifier, Multi-agent systems, Automated reasoning",
    author = "Hales, {James Colin}",
    year = "2016",
    language = "English",
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    Hales, JC 2016, 'Quantifying over epistemic updates', Doctor of Philosophy, The University of Western Australia.

    Quantifying over epistemic updates. / Hales, James Colin.

    2016.

    Research output: ThesisDoctoral Thesis

    TY - THES

    T1 - Quantifying over epistemic updates

    AU - Hales,James Colin

    PY - 2016

    Y1 - 2016

    N2 - Dynamic epistemic logics reason about the knowledge belonging to a collectionof agents and how that knowledge changes in response to epistemic updates,events that provide agents with additional information. Previous work in dynamicepistemic logic, such as public announcement logic [76, 47] and actionmodel logic [15, 14], introduced models for epistemic updates and logics for reasoning about the effects of specific epistemic updates using these models. However many natural questions about epistemic updates are not questions about specific epistemic updates. For example, given a desired change in knowledge we might ask \Is there an epistemic update that results in the desired change in knowledge?", and if there is we might also ask \What is a specific epistemic update that results in the desired change in knowledge?". More recent works in dynamic epistemic logic, such as arbitrary public announcement logic [11] and group announcement logic [74], have considered logics for quantifying over epistemic updates. In principle these logics allow us to answer such questions using model-checking or satisfiability procedures, although these particular logics are undecidable [45, 3], and quantify over relatively restricted forms of epistemic updates.In the present work we consider logics for quantifying over very general formsof epistemic updates: arbitrary action model logic, which quantities over actionmodels; and refinement modal logic, which quantities over refinements, whichhave a partial correspondence with the results of action models, but are moregeneral. We present sound and complete axiomatisations, expressivity results,and decidability results for these logics in various multi-agent modal settings.

    AB - Dynamic epistemic logics reason about the knowledge belonging to a collectionof agents and how that knowledge changes in response to epistemic updates,events that provide agents with additional information. Previous work in dynamicepistemic logic, such as public announcement logic [76, 47] and actionmodel logic [15, 14], introduced models for epistemic updates and logics for reasoning about the effects of specific epistemic updates using these models. However many natural questions about epistemic updates are not questions about specific epistemic updates. For example, given a desired change in knowledge we might ask \Is there an epistemic update that results in the desired change in knowledge?", and if there is we might also ask \What is a specific epistemic update that results in the desired change in knowledge?". More recent works in dynamic epistemic logic, such as arbitrary public announcement logic [11] and group announcement logic [74], have considered logics for quantifying over epistemic updates. In principle these logics allow us to answer such questions using model-checking or satisfiability procedures, although these particular logics are undecidable [45, 3], and quantify over relatively restricted forms of epistemic updates.In the present work we consider logics for quantifying over very general formsof epistemic updates: arbitrary action model logic, which quantities over actionmodels; and refinement modal logic, which quantities over refinements, whichhave a partial correspondence with the results of action models, but are moregeneral. We present sound and complete axiomatisations, expressivity results,and decidability results for these logics in various multi-agent modal settings.

    KW - Modal logic

    KW - decision procedures

    KW - Dynamic epistemic logic

    KW - Refinement quantifier

    KW - Multi-agent systems

    KW - Automated reasoning

    M3 - Doctoral Thesis

    ER -