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

Assuming a Knowledge Base Σ expressed by a two Conjunctive Form (2-CF), we show that if the constrained graph of Σ is acyclic or if its cyles are independent one to the other, then it is possible to count efficiently the number of models of Σ. We determine a set of recurrence equations which allow us to design an incremental technique for counting models by a simple traversal of the constrained graph. One of the advantages of such technique, furthermore that it has linear time complexity, is that applying it backwards allows us to determine the exact number of the logical values (the charge) that each variable has in the set of models. The charge of each variable allow us to design an efficient scheme of reasoning, even in the case where the formula-based representation does not allow to do it. Indeed, we can compute the degree of belief for new information (a literal or a binary clause) efficiently.