Efficient Computation of the Degree of Belief for a Subclass of Two Conjunctive Forms

Assuming a Knowledge Base (KB) Σ expressed by a two Conjunctive Form (2-CF), we determine a set of recurrence equations which allow us to design an incremental technique for counting models of Σ by a simple traversal of its constraint graph GΣ. We show that if the constraint graph of Σ has no intersecting cycles then it is possible to count efficiently the number of models of Σ. One of the advantages of our technique, furthermore that it has a polynomial time complexity, is that applying it backwards, we can determine the charge (the number of true and false logical values) that each variable has into the set of models of the input 2-CF. The charge of the variables allow us to design an efficient scheme of reasoning. Given the KB Σ such that GΣ has no intersecting cycles, and new information F (a literal or a binary clause), the degree of belief in F with respect to Σ, denoted as PF |Σ, is computed efficiently even in the case Σ F .