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Polynomial Classes of Boolean Formulas for Computing the Degree of Belief

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Advances in Artificial Intelligence – IBERAMIA 2004 (IBERAMIA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3315))

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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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Authors and Affiliations

  1. Institute in Astrophysics, Optics and Electronics,  

    Guillermo De Ita Luna

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  1. Guillermo De Ita Luna
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Editors and Affiliations

  1. Laboratorio Nacional de Informatica Avanzada, A.C. Lania, Rebsamen 80, Col. Centro, 91000, Xalapa, Veracruz, Mexico

    Christian Lemaître

  2. Department of Computer Science, National Institute of Astrophysics, Optics and Electronics (INAOE), Luis E. Erro 1, 72840, Sta. Maria Tonantzintla, Puebla, Mexico

    Carlos A. Reyes

  3. Computer Science Department, National Institute of Astrophysics, Optics and Electronics, Luis Enrique Erro 1, 72840, Tonantzintla, México

    Jesús A. González

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© 2004 Springer-Verlag Berlin Heidelberg

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23806-5

  • Online ISBN: 978-3-540-30498-2

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