Complexity of only knowing: The prepositional case

Abstract

We study the computational properties of the prepositional fragment of Levesque's logic of only knowing. In particular, we show that the problem of reasoning with only knowing in the prepositional case lies at the second level of the polynomial hierarchy. Thus, it is as hard as reasoning in the majority of propositional formalisms for nonmonotonic reasoning, like default logic, circumscription and autoepistemic logic, and it is easier than reasoning in propositional formalisms based on the minimal knowledge paradigm, which is strictly related to the notion of only knowing.