Decidable Reasoning in First-Order Knowledge Bases with Perfect Introspection

Since knowledge bases (KBs) are usually incomplete, they should be able to provide information regarding their own incompleteness, which requires them to introspect on what they know and do not know. An important area of research is to devise models of introspective reasoning that take into account resource limitations. Under the view that a KB is completely characterized by the set of beliefs it represents (its epistemic state), it seems natural to model KBs in terms of belief. Reasoning can then be understood as the problem of computing membership in the epistemic state of a KB. The best understood models of belief are based on possible-world semantics. However, their computational properties are unacceptable. In particular, they render reasoning in firstorder KBs undecidable. In this paper, we propose a novel model of belief, which preserves many of the advantages of possible-world semantics yet, at the same time, guarantees reasoning to be decidable, where a KB may contain sentences in full first-order logic. Moreover, such KBs have perfect knowledge about their own beliefs even though their beliefs about the world are limited.