Public announcement logic with distributed knowledge: expressivity, completeness and complexity

作     者：Wang, Yi N. Agotnes, Thomas 

作者机构：Bergen Univ Coll Dept Comp Math & Phys Bergen Norway Univ Bergen Dept Informat Sci & Media Studies Bergen Norway 

出 版 物：《SYNTHESE》 (Synthese)

年 卷 期：2013年第190卷第1期

页      面：135-162页

核心收录：

学科分类：01[哲学] 0101[哲学-哲学] 0712[理学-科学技术史(分学科，可授理学、工学、农学、医学学位)] 

基　　金：National Office for Philosophy and Social Sciences  NPOPSS  (11&ZD088) 

主　　题：Public announcement logic Distributed knowledge Expressivity Completeness Decidability Computational complexity Unravelling Folding Trans-bisimulation 

摘      要：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 () with distributed knowledge, in particular their expressivity, axiomatisations and complexity. extended only with distributed knowledge is not more expressive than standard epistemic logic with distributed knowledge. Our focus is therefore on , the result of adding both common and distributed knowledge to , which is more expressive than each of its component logics. We introduce an axiomatisation of , which 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 knowledge, distributed knowledge, common knowledge and public announcements at the same time. We furthermore show that is decidable, more precisely that it is -complete. This result also carries over to with common and distributed knowledge operators for all coalitions (and not only the grand coalition). Finally, we propose a notion of a trans-bisimulation to generalise certain results and give deeper insight into the proofs.