First Order Theory Re

This paper summarizes the current state of the art in the topics of rst-order theory revision and theory restructuring. The various tasks involved in rst-order theory reenement (revision vs. restructuring) are deened and then discussed in turn. For theory revision, the issue of minimality is discussed in detail, and a general outline algorithm is given which identiies the major places of diierence between diierent algorithms. The paper then describes the various options that have been explored by diierent researchers. For theory restructuring, two approaches developed in the ILP project are discussed, one devoted to understandability, and the other devoted to eeciency. First-order methods of inductive learning have witnessed considerable interest in recent years, and the eld of Inductive Logic Programming (ILP) 26] has developed rapidly. While the original ILP learning task deals with learning rst-order clausal theories from scratch given examples and background knowledge, the eld is also focusing increasingly on the task of theory reenement, i.e., using an existing rst-order theory as a departure point and revising it to match a given set of examples, or restructuring it to meet external criteria such as understandability or eeciency. The goal of this document is to summarize the current state of the art in the topics of rst-order theory revision and theory restructuring. As a nal deliverable of the ESPRIT basic research project \Inductive Logic Programming", this paper surveys the state of the art worldwide with a special emphasis on the contributions made by the ILP project partners over the lifetime of the project. A large number of systems for propositional knowledge base maintenance have been developed in the expert systems eld (see 14] for an overview). In this paper, however, we are concentrating on systems in which the theory to be reened is of a rst-order nature, usually consisting of rst-order clauses. The paper is organized as follows. Following a more detailed description of the various tasks involved in theory reenement, we will discuss the two broad subtasks revision and restructuring in turn. For theory revision, we give a general outline algorithm which clearly identiies the major places of diierence between diierent algorithms. We then discuss each of these, describing the various options that have been explored by diierent researchers. For theory restructuring, we discuss two approaches developed in the ILP project, one devoted to understandability, and the other devoted to eeciency. 1 Theory reenement terminology and tasks Theory revision …