## Invited Talk: Reasoning About Common Knowledge with Infinitely Many Agents (at LICS 1999)

Authors:**Joseph Y. Halpern Richard A. Shore**

### Abstract

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 and G1 ,where G and G1 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.

### BibTeX

@InProceedings{HalpernShore-ReasoningAboutCommo, author = {Joseph Y. Halpern and Richard A. Shore}, title = {Reasoning About Common Knowledge with Infinitely Many Agents}, booktitle = {Proceedings of the Fourteenth Annual IEEE Symp. on Logic in Computer Science, {LICS} 1999}, year = 1999, editor = {Giuseppe Longo}, month = {July}, pages = {384--393}, location = {Trento, Italy}, note = {Invited Talk}, publisher = {IEEE Computer Society Press} }