Transaction Logic: Unifying Declarative and Procedural Knowledge (Extended Abstract)

This paper presents AI applications of the recently proposed Transaction Logic (abbr., 7-7z) [2]. Transaction Logic is a novel formalism that accounts in a clean and declarative fashion for the phenomenon of updating first-order knowledge bases, most notably, databases and logic programs. Transaction Logic has a natural model theory and a sound-and-complete proof theory. Unlike many other logics, Tn allows users to program transactions that modify the state of a knowledge base. This is possible because, like classical logic, Tn has a "Horn" version which has both a procedural and a declarative semantics, as well as an efficient SLD-style proof procedure. As a result, Tn is a unifying, logical formalism for specifying both declarative and procedural knowledge. Furthermore, for a wide range of practical problems, the frame problem [18] is not an issue for "/-n. This is because Tn performs real updates on materialized databases, much as procedural languages like Pascal do. A key contribution of ~-n is capturing these procedural updates in a logical framework with an efficient proof theory. A full development of the proof theory, a discussion of the frame problem, and applications to database systems can be found in [2, 3]. This paper presents the model theory of 7-~¢, and then focuses on applications of Tn to problems in AI, especially planning, temporal reasoning, constraint satisfaction, hypothetical and counterfactual reasoning, and the representation and use of procedural knowledge. The importance of procedural knowledge has been extensively argued in the AI literature (see e.g., [8]). For instance, the well-known SHRDLU program [26] is largely based on procedural knowledge. In fact, Winograd argues in [26] that procedural knowledge is inherent in automated natural language understanding. For example, the meaning of "the" is a collection of procedures