Efficient computation of the degree of belief in a propositional theory

We design a novel model-based approach for reasoning, considering the reasoning process as the computation of the degree of belief of an intelligent agent. We assume a Knowledge Base (KB) expressed by a two Conjunctive Form (2-CF) Σ. We represent Σ using an appropriate logical structure. Our representation of a 2-CF is highly expressive since it supports efficient reasoning, even in the cases where the formula-based representation does not allow to do it. Indeed, we can compute the degree of belief with new information (a literal or a binary clause) efficiently, providing an efficient scheme of inductive reasoning. Exploiting this logical structure of a 2-CF, we propose a way to determine the relative value for every element in the KB which is an essential problem when new knowledge is aggregated and is necessary to maintain the consistency of the KB.