Quantifying over epistemic updates
This thesis was presented to the School of Computer Science and Software Engineering for the degree of Doctor of Philosophy from The University of Western Australia in May 2016.
Dynamic epistemic logics reason about the knowledge belonging to a collection of agents and how that knowledge changes in response to epistemic updates, events that provide agents with additional information. Previous work in dynamic epistemic logic, such as public announcement logic and action model logic, 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 and group announcement logic, 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, and quantify over relatively restricted forms of epistemic updates.
In the present work we consider logics for quantifying over very general forms of epistemic updates: arbitrary action model logic, which quantifies over action models; and refinement modal logic, which quantifies over refinements, which have a partial correspondence with the results of action models, but are more general. We present sound and complete axiomatisations, expressivity results, and decidability results for these logics in various multi-agent modal settings.
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