A proof-theoretic semantic analysis of dynamic epistemic logic

Sabine Frittella (1) , Giuseppe Greco (2) , Alexander Kurz (3) , Alessandra Palmigiano (4) , Vlasta Sikimic

1 LIF - Laboratoire d'informatique Fondamentale de Marseille
2 TU Delft - Delft University of Technology
3 University of Leicester
4 Applied Logic

The present article 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 that 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 that 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 article include a generalisation of Belnap's cut-elimination meta-theorem 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 meta-theorem.

Mots clés: Display calculus; dynamic epistemic logic; proof-theoretic semantics

Domaines: Logique en informatique [cs.LO]

Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano, Vlasta Sikimic. A proof-theoretic semantic analysis of dynamic epistemic logic . Journal of Logic and Computation, 2016, J Logic Computation 2016, 26 (6), ⟨10.1093/logcom/exu063⟩. ⟨hal-01509388⟩