## Reasoning about Knowledge and Probability (1994)

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Venue: | Journal of the ACM |

Citations: | 160 - 16 self |

### BibTeX

@ARTICLE{Fagin94reasoningabout,

author = {Ronald Fagin and Joseph Y. Halpern},

title = {Reasoning about Knowledge and Probability},

journal = {Journal of the ACM},

year = {1994},

volume = {41},

pages = {340--367}

}

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### Abstract

: We provide a model for reasoning about knowledge and probability together. We allow explicit mention of probabilities in formulas, so that our language has formulas that essentially say "according to agent i, formula ' holds with probability at least b." The language is powerful enough to allow reasoning about higher-order probabilities, as well as allowing explicit comparisons of the probabilities an agent places on distinct events. We present a general framework for interpreting such formulas, and consider various properties that might hold of the interrelationship between agents' probability assignments at different states. We provide a complete axiomatization for reasoning about knowledge and probability, prove a small model property, and obtain decision procedures. We then consider the effects of adding common knowledge and a probabilistic variant of common knowledge to the language. A preliminary version of this paper appeared in the Proceedings of the Second Conference on T...