1999/09/21 by Joseph Y. Halpern, Halpern, Joseph Y., Richard A. Shore +1
Computer Science · #Artificial Intelligence (cs.AI) #Computability, Logic, AI Algorithms #F.4.1 #FOS: Computer and information sciences #I.2.4 #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Multi-Agent Systems and Negotiation #cs.AI #cs.LO
paper · pdf · doi:10.48550/arxiv.cs/9909014
Preliminary version appears in 14th IEEE Symposium on Logic in Computer Science, 1999. This is the full version
arxiv created 1999/09/21 · openalex publication_date 1999/09/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.