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 P F|Σ . Applying a general approach based on the probabilistic logic for computing the degree of belief P F|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 P F|Σ is polynomially related to the complexity of solving the #SAT problem for the formula Σ ∧ F . Therefore, some of the above classes in which P F|Σ is computed efficiently establish new polynomial classes given by Σ ∪ F for the #SAT problem and, consequently, for many other related counting problems.
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De Ita Luna, G. (2004). Polynomial Classes of Boolean Formulas for Computing the Degree of Belief. In: Lemaître, C., Reyes, C.A., González, J.A. (eds) Advances in Artificial Intelligence – IBERAMIA 2004. IBERAMIA 2004. Lecture Notes in Computer Science(), vol 3315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30498-2_43
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DOI: https://doi.org/10.1007/978-3-540-30498-2_43
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