On the progression of situation calculus basic action theories: Resolving a 10-year-old conjecture

In a seminal paper, Lin and Reiter introduced a modeltheoretic definition for the progression of the initial knowledge base of a basic action theory. This definition comes with a strong negative result, namely that for certain kinds of action theories, first-order logic is not expressive enough to correctly characterize this form of progression, and secondorder axioms are necessary. However, Lin and Reiter also considered an alternative definition for progression which is always first-order definable. They conjectured that this alternative definition is incorrect in the sense that the progressed theory is too weak and may sometimes lose information. This conjecture, and the status of first-order definable progression, has remained open since then. In this paper we present two significant results about this alternative definition of progression. First, we prove the Lin and Reiter conjecture by presenting a case where the progressed theory indeed does lose information. Second, we prove that the alternative definition is nonetheless correct for reasoning about a large class of sentences, including some that quantify over situations. In this case the alternative definition is a preferred option due to its simplicity and the fact that it is always first-order

Temporal Data Modeling and Reasoning for Information Systems

Temporal knowledge representation and reasoning is a major research field in Artificial Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to model and process time and calendar data is essential for many applications like appointment scheduling, planning, Web services, temporal and active database systems, adaptive Web applications, and mobile computing applications. This article aims at three complementary goals. First, to provide with a general background in temporal data modeling and reasoning approaches. Second, to serve as an orientation guide for further specific reading. Third, to point to new application fields and research perspectives on temporal knowledge representation and reasoning in the Web and Semantic Web