Public announcement logic with distributed knowledge

Authors:
Yí N. Wáng;Thomas Ågotnes
Affiliations:
Department of Computer Engineering, Bergen University College, Norway and Department of Information Science and Media Studies, University of Bergen, Norway;Department of Information Science and Media Studies, University of Bergen, Norway
Venue:
LORI'11 Proceedings of the Third international conference on Logic, rationality, and interaction
Year:
2011

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Abstract

While dynamic epistemic logics with common knowledge have been extensively studied, dynamic epistemic logics with distributed knowledge have so far received far less attention. In this paper we study extensions of public announcement logic (PAL) with distributed knowledge, in particular their expressivity and axiomatisations. PAL extended only with distributed knowledge is not more expressive than standard epistemic logic with distributed knowledge. Our focus is therefore on PACD, the result of adding both common and distributed knowledge to PAL, which is more expressive than each of its component logics. Our main result is a completeness result for PACD. The axiomatisation is not surprising: it is the combination of well-known axioms. The completeness proof, however, is not trivial, and requires novel combinations and extensions of techniques for dealing with S5 knowledge, distributed knowledge, common knowledge and public announcements at the same time.