Open Access
The logic of public announcements, common knowledge, and private suspicions
Alexandru Baltag,Lawrence S. Moss,Sławomir Solecki +2 more
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In this paper, the authors present a logical system in which various group-level epistemic actions are incorporated into the object language, such as announcements to groups privately, announcements with suspicious outsiders, etc.Abstract:
This paper presents a logical system in which various group-level epistemic actions are incorporated into the object language That is, we consider the standard modeling of knowledge among a set of agents by multi-modal Kripke structures One might want to consider actions that take place, such as announcements to groups privately, announcements with suspicious outsiders, etc In our system, such actions correspond to additional modalities in the object language That is, we do not add machinery on top of models (as in Fagin et alia), but we reify aspects of the machinery in the logical language Special cases of our logic have been considered in Plaza, Gerbrandy, and Gerbrandy and Groeneveld The latter group of papers introduce a language in which one can faithfully represent all of the reasoning in examples such as the Muddy Children scenario In that paper we find operators for updating worlds via announcements to groups of agents who are isolated from all others We advance this by considering many more actions, and by using a more general semantics Our logic contains the infinitary operators used in the standard modeling of common knowledge We present a sound and complete logical system for the logic, and we study its expressive powerread more
Citations
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Book
Dynamic Epistemic Logic
TL;DR: This book provides various logics to support formal specifications of multi-agent systems, including proof systems, and discusses various results on the expressive power of the logics presented.
Journal ArticleDOI
Dynamic logic for belief revision
TL;DR: This work shows how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added, and obtains complete logics for concrete mechanisms of belief revision based on compositional reduction axioms.
Book
Logical Dynamics of Information and Interaction
TL;DR: A new view of logic as a theory of information-driven agency and intelligent interaction between many agents is developed, unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory.
Journal ArticleDOI
Logics of communication and change
TL;DR: New systems that extend the epistemic base language with a new notion of 'relativized common knowledge' are proposed, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous 'reduction axioms'.
Book ChapterDOI
Logics for epistemic programs
TL;DR: This work constructs logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting by formalizing these changes by defining a notion of epistemic program, a Kripke model of ‘actions’.
References
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Book
Reasoning About Knowledge
TL;DR: Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed systems, artificial intelligence, and game theory.
Journal ArticleDOI
Orderings for term-rewriting systems☆
TL;DR: Methods of proving that a term-rewriting system terminates are presented, based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable in another is smaller than the other.
Proceedings ArticleDOI
Orderings for term-rewriting systems
TL;DR: Methods of proving that a term-rewriting system terminates are presented, based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable in another is smaller than the other.