From Logic Programming Semantics to the Consistency of Syntactical Treatments of Knowledge and Belief

This paper concerns formal theories for reasoning about the knowledge and belief of agents. It has seemed attractive to researchers in artificial intelligence to formalise these propositional attitudes as predicates of first-order predicate logic. This allows the agents to express stronger introspective beliefs and engage in stronger meta-reasoning than in the classical modal operator approach. Results by Montague [1963] and Thomason [1980] show, however, that the predicate approach is prone to inconsistency. More recent results by des Rivieres & Levesque [1986] and Morreau & Kraus [1998] show that we can keep the predicate approach if we make suitable restrictions to our set of epistemic axioms. Their results are proved by careful translations from corresponding modal formalisms. In the present paper we show that their results fit nicely into the framework of logic programming semantics, in that we show their results to be corollaries of well-known results in this field. This does not only allow us to demonstrate a close connection between consistency problems in the syntactic treatment of propositional attitudes and problems in semantics for logic programs, but it also allows us to strengthen the results of Rivieres and Levesque [1986] and Morreau and Kraus [1998].