A Computationally Attractive First-Order Logic of Belief

Logics of belief play an essential role in formal approaches to knowledge representation (KR). Such logics allow us to formalize the idea that a knowledge base (KB) represents an epistemic state, that is, a set of beliefs. In its simplest form, an epistemic state can be defined as the set of all beliefs that logically follow from believing the sentences that are explicitly stored in the KB. Reasoning can be understood as computing whether a belief follows logically from believing the sentences in the KB. Since the classical model of belief, possible-world semantics, renders reasoning undecidable, it is important to find weaker models with better computational properties.