REASONING WITH BACKGROUND KNOWLEDGE–A THREE-LEVEL THEORY

We address the problem of reasoning in cases when knowledge bases containing background knowledge are understood not as sets of formulas (rules and facts) but as collections of partially ordered theories. In our system, the usual, two-part logical structures, consisting of a metalevel and an object level, are augmented by a third level–a referential level. The referential level is a partially ordered collection of theories; it encodes background knowledge. As usual, current situations are described on the object level, and the metalevel is a place for rules that can eliminate some of the models permitted by the object level and the referential level. As a logic of reasoning the system generalizes the standard model of a rational agent: deducing actions and deriving new information about the world from a logical theory–its knowledge base. It is a natural logical system in which priorities on the possible readings of predicates, not special rules of inference, are the main source of nonmonotonicity. We introduce a theory forming operator PT(x) to exploit the priorities, and we investigate its basic logical properties. Then we show how such a system can be augmented by metarules. Although this paper concentrates on basic logical properties of the new theory, this formalism has already been applied to model a number of natural language phenomena such as the notion of text coherence, Gricean maxims, vagueness, and a few others. The paper also briefly compares it with the model of background knowledge of CYC, as proposed by Lenat and Guha.