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A Proof-Theoretic Semantic Analysis of Dynamic Epistemic Logic

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posted on 04.02.2015, 16:21 by S. Frittella, G. Greco, Alexander H. Kurz, A. Palmigiano, V. Sikimić
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 generalization of Belnap's cut-elimination metatheorem for display calculi, and a revised version of the display-style calculus D.EAK [30]. 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 generalized metatheorem.

History

Citation

Journal of Logic and Computation, 2014, Special Issue on Substructural Logic and Information Dynamics

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Computer Science

Version

AM (Accepted Manuscript)

Published in

Journal of Logic and Computation

Publisher

Oxford University Press (OUP)

issn

0955-792X

eissn

1465-363X

Copyright date

2014

Available date

03/11/2015

Publisher version

http://logcom.oxfordjournals.org/content/early/2014/11/03/logcom.exu063

Editors

Aucher, G.;Hjortland, O.;Roy, O.

Language

en