All You Ever Wanted to Know about Tweety (But Were Afraid to Ask)

We propose a formalization of only-knowing-about, which captures the idea that something is all an agent knows about some subject matter. The work extends a previous formalization of only-knowing by Levesque. Besides discussing some of the logical properties of the new concept, we also address the issue of computing what is known about some subject matter for a given knowledge base. In this context, we are able to relate only-knowing-about to deKleer's ATMS. Finally , we show that only-knowing-about is eeciently computable, if we weaken the underlying model of belief. In Lev90], Levesque proposes a formalization of the concept of only-knowing. This notion, which captures the idea that something is all an agent knows, 1 has proven very valuable in characterizing the knowledge of a fully introspective agent. In particular, Levesque uses it to reconstruct and in fact generalize Moore's autoepistemic logic within the framework of a classical (monotonic) logic. While a logic of only-knowing is thus very useful from a theoretical point of view, being able to talk about all an agent knows does not seem very relevant from a practical point of view, say, as part of a query language. After all, hardly anybody is interested in all I know. 2 A much more useful concept in this regard seems to be the notion of only-knowing-about, where one is interested in all the agent knows about a certain subject matter. Thus queries like is this all you know about Tweety or what do you know about Tweety seem very appropriate. Another application is a multi-agent scenario where agents reason about other agents, possibly applying defaults. For example, assume there are two agents, Jack and Jill, with the default that birds y unless known otherwise being common knowledge. If Jill knows 1 We will freely use the terms knowledge and belief interchangeably. While all of the logics discussed here allow an agent to have false beliefs, none of our results hinges on this choice. 2 Besides, for a knowledge-based agent it is a trivial matter to tell a user all it knows. It only needs to hand over a copy of its knowledge base.