Query Evaluation and Progression in AOL Knowledge Bases

Recently Lakemeyer and Levesque proposed the logic AOC, which amalgamates both the situation calculus and Levesques logic of only knowing. While very expressive the practical relevance of the formalism is unclear because it heavily relies on second-order logic. In this paper we demonstrate that the picture is not as bleak as it may seem. In particular, we show that for large classes of AOL knowledge bases and queries, including epistemic ones, query evaluation requires first-order reasoning only. We also provide a simple semantic definition of progressing a knowledge base. For a particular class of knowledge bases, adapted from earlier results by Lin and Reiter, we show that progression is first-order representable and easy to compute.