Limited reasoning in first-order knowledge bases

Abstract

In traditional formal approaches to knowledge representation, agents are assumed to believe all the logical consequences of their knowledge bases. As a result, reasoning in the first-order case becomes undecidable. Since real agents are constrained by resource limitations, it seems appropriate to look for weaker forms of reasoning with better computational properties. One way to approach the problem is by modeling belief. Reasoning can then be understood as the question whether a belief follows from believing the sentences in the knowledge base. This paper proposes a model of belief, which combines features from both possible-world semantics and relevance logic. Among the important features of this logic are its treatment of quantifying-in, which allows us to distinguish between “knowing that” and “knowing who”, and the decidability of the implication problem for belief. The decidability result follows from a close connection between this notion of belief and an existing decidable form of first-order entailment.