Semantical considerations on multiagent only knowing

Abstract

Levesque introduced the notion of “only knowing” to precisely capture the beliefs of a knowledge base. He also showed how only knowing can be used to formalize nonmonotonic behavior within a monotonic logic. Levesque's logic only deals with a single agent, and therefore, a number of attempts have been made to generalize only knowing to the many agent case. However, all these attempts have some undesirable features. Most significantly, these attempts are propositional and it is not clear how they are to be extended to the first-order case. In this work, we propose a new semantical account of multiagent only knowing which, for the first time, has a natural possible-world semantics for a quantified language with equality. Among other things, properties about Levesque's logic generalize faithfully to the many agent case with this account. For the propositional fragment, we also provide a sound and complete axiomatization. Finally, we obtain a multiagent first-order version of the nonmonotonicity exhibited by the logic of only knowing.