Polynomial classes of boolean formulas for computing the degree of belief

Abstract

Given a knowledge base σ and a formula F both in propositional Conjunctive Form, we address the problem of designing efficient procedures to compute the degree of belief in F with respect to σ as the conditional probability PF|σ- Applying a general approach based on the probabilistic logic for computing the degree of belief PF|σ, we can determine classes of conjunctive formulas for σ and F in which P F|σ can be computed efficiently. It is known that the complexity of computing PF|σ is polynomially related to the complexity of solving the #SAT problem for the formula σ Λ F. Therefore, some of the above classes in which PF|Σ is computed efficiently establish new polynomial classes given by σ ∪ F for the #SAT problem and, consequently, for many other related counting problems. © Springer-Verlag Berlin Heidelberg 2004.