THE AXIOMATIC STRUCTURE OF KNOWLEDGE AND PERCEPTION

Standard models of knowledge treat either information partitions or knowledge operators as primitives. The present paper starts with a new and arguably more intuitive primitive which is a binary relation (here called the imperceptions relation) on the states space. This relation expresses an individual's inability to distinguish between pairs of social states. Equivalences between axioms on this binary relation and the standard axioms for knowledge operators are established. Theorems concerning common knowledge and the convergence of posterior probabilities are worked out in the new framework. It is shown that Aumann's "agreeing-to disagree" theorem remains valid even if we dispense with the axioms of Knowledge, Transparency and Wisdom, as long as the imperceptions relation satisfies a property called triangularity.