Abstract
The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which have been successfully applied to diverse scientific disciplines, but the proof theoretic treatment of which presents many difficulties. After an illustration of the proof-theoretic semantic principles most relevant to the treatment of logical connectives, we turn to illustrating the main features of display calculi, a proof-theoretic paradigm which has been successfully employed to give a proof-theoretic semantic account of modal and substructural logics. Then, we review some of the most significant proposals of proof systems for dynamic epistemic logics, and we critically reflect on them in the light of the previously introduced proof-theoretic semantic principles. The contributions of the present paper include a generalisation of Belnap's cut elimination metatheorem for display calculi, and a revised version of the display-style calculus D.EAK. We verify that the revised version satisfies the previously mentioned proof-theoretic semantic principles, and show that it enjoys cut elimination as a consequence of the generalised metatheorem.
Highlights
In recent years, driven by applications in areas spanning from program semantics to game theory, the logical formalisms pertaining to the family of dynamic logics [31, 48] have been very intensely investigated, giving rise to a proliferation of variants.Typically, the language of a given dynamic logic is an expansion of classical propositional logic with an array of modal-type dynamic operators, each of which takes an action as a parameter
We provide an analysis, conducted adopting the viewpoint of proof-theoretic semantics, of the state-of-the-art deductive systems for dynamic epistemic logic, focusing mainly on Baltag-Moss-Solecki’s logic of epistemic actions and knowledge (EAK)
We start with an overview of the general research agenda in proof-theoretic semantics, and we focus on display calculi, as a proof-theoretic paradigm which has been successful in accounting for difficult logics, such as modal logics and substructural logics
Summary
Driven by applications in areas spanning from program semantics to game theory, the logical formalisms pertaining to the family of dynamic logics [31, 48] have been very intensely investigated, giving rise to a proliferation of variants. Prooftheoretic semantics has been very influential in an area of research in structural proof theory which aims at defining the meaning of logical connectives in terms of an analysis of the behaviour of the logical connectives inside the derivations of a given proof system. Such an analysis provides dynamic logics with sound methodological and foundational principles, and with an entirely novel perspective on the topic of dynamics and change, which is independent from the dominating model-theoretic methods Such an analysis provides structural proof theory with a novel array of case studies against which to test the generality of its proof-theoretic semantic principles, and with the opportunity to extend its modus operandi to still uncharted settings, such as the multi-type calculi introduced in [23]. Most of the proofs and derivations are collected in appendices A, B and C
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