Public announcement logic with distributed knowledge. (English) Zbl 1298.03061
van Ditmarsch, Hans (ed.) et al., Logic, rationality, and interaction. Third international workshop, LORI 2011, Guangzhou, China, October 10–13, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-24129-1/pbk). Lecture Notes in Computer Science 6953. Lecture Notes in Artificial Intelligence, 328-341 (2011).
Summary: 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.
See also the authors’ paper [Synthese 190, Suppl. 1, 135–162 (2013; doi:10.1007/s11229-012-0243-3)].
For the entire collection see [Zbl 1223.68013].
See also the authors’ paper [Synthese 190, Suppl. 1, 135–162 (2013; doi:10.1007/s11229-012-0243-3)].
For the entire collection see [Zbl 1223.68013].
MSC:
| 03B42 | Logics of knowledge and belief (including belief change) |
| 68T27 | Logic in artificial intelligence |
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