Reasoning About Common Knowledge with Infinitely Many Agents

Details Reasoning About Common Knowledge with Infinitely Many Agents Reasoning About Common Knowledge with Infinitely Many Agents

1999-09-21

arxiv.org/abs/cs/9909014v1

Computer Science

Logic in Computer Science

Preliminary version appears in 14th IEEE Symposium on Logic in Computer Science, 1999. This is the full version

Scientific paper

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.

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