A Proof-Theoretic Semantic Analysis of Dynamic Epistemic Logic

TL;DR

This paper analyzes proof systems for dynamic epistemic logic from a proof-theoretic semantics perspective, introduces a generalized cut elimination theorem, and revises the display calculus D.EAK to align with semantic principles.

Contribution

It generalizes Belnap's cut elimination theorem for display calculi and presents a revised display calculus D.EAK satisfying proof-theoretic semantic principles.

Findings

Revised display calculus D.EAK satisfies semantic principles.

Generalized cut elimination theorem for display calculi.

Cut elimination achieved for the revised calculus.

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.