Reasoning about common knowledge with infinitely many agents

Complete axiomatizations and exponential-time decision procedures are provided for reasoning about knowledge and common knowledge when there are infinitely many agents. The results show that reasoning about knowledge and common knowledge with infinitely many agents is no harder than when there are f...

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Bibliographic Details
Main Authors: Halpern, J.Y., Shore, R.A.
Format: Conference Proceeding
Language:English
Subjects:
Application software
Artificial intelligence
Computer science
Distributed computing
Game theory
Internet
Mathematics
Software agents
Tellurium
US Department of Defense
Online Access:Request full text
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Summary:Complete axiomatizations and exponential-time decision procedures are provided for reasoning about knowledge and common knowledge when there are infinitely many agents. The results show that reasoning about knowledge and common knowledge with infinitely many agents is no harder than when there are finitely many agents, provided that we can check the cardinality of certain set differences G G' where G and G' are sets of agents. Since our complexity results are independent of the cardinality of the sets G involved, they represent improvements over the previous results even with the sets of agents involved are finite. Moreover, our results make clear the extent to which issues of complexity and completeness depend on how the sets of agents involved are represented.
ISSN:1043-6871
2575-5528
DOI:10.1109/LICS.1999.782633