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The Epistemic View of Concurrency Theory

Sophia Knight 1
1 COMETE - Concurrency, Mobility and Transactions
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : This dissertation describes three distinct but complementary ways in which epistemic reasoning plays a role in concurrency theory. The first and perhaps the one least explored so far is the idea of using epistemic modalities as programming constructs. Logic programming emerged under the slogan ''Logic as a programming language'' and the connection was manifest in a very clear way in the concurrent constraint programming paradigm. In the first part of the present thesis, we explore the role of epistemic, and closely related spatial modalities, as part of the programming language and not just as part of the meta-language for reasoning about protocols. The next part explores a variant of dynamic epistemic logic adapted to labelled transition systems. In contrast to the previous part, one might be tempted to think that everything that can be said on this topic has already been said. However, the new ingredient that we propose is a tight connection between epistemic logic and Hennessy-Milner logic: \emph{the} logic of labelled transition systems. We provide an axiomatization and prove a weak completeness theorem. This proof follows the general plan that one uses for logics like dynamic logic but requires some non-trivial adaptations. The final part of the thesis focuses on the study of interacting agents in concurrent processes. We present a game semantics for agents' interaction which makes manifest the role of knowledge and information flow in the interactions between agents, and makes it possible to control the information available to the interacting agents. We use processes as the game board and define strategies for the agents so that two agents interacting according to their strategies determine the execution of the process, replacing the traditional scheduler. We show that different restrictions on the strategies represent different amounts of information being available to the scheduler. These restrictions on the strategies have an explicit epistemic flavour, and we present a modal logic for strategies and a logical characterization of several different possible restrictions on strategies. These three approaches to the analysis and representation of epistemic information in concurrency theory provide a new way to understand agents' knowledge in concurrent processes, which is vital in today's world of ubiquitous distributed multi-agent systems.
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Sophia Knight. The Epistemic View of Concurrency Theory. Logic in Computer Science [cs.LO]. Ecole Polytechnique X, 2013. English. ⟨tel-00940413⟩

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