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A Deletion Algorithm for the Marginal Problem in Propositional Logic Based on Boolean Arrays

Author

Listed:
  • Efraín Díaz-Macías

    (Faculty of Engineering Sciences, State Technical University of Quevedo, Quevedo 120301, Ecuador
    These authors contributed equally to this work.)

  • Serafín Moral

    (Department of Computer Science and Artificial Intelligence, University of Granada, 18071 Granada, Spain
    These authors contributed equally to this work.)

Abstract

This paper proposes a deletion algorithm for the marginal problem in propositional logic. The algorithm is based on the general Davis and Putnam deletion algorithm DP, expressed as a bucket elimination algorithm, representing sets of clauses with the same set of variables employing a Boolean array. The main contribution is the development of alternative procedures when deleting a variable which allow more efficient computations. In particular, it takes advantage of the case in which the variable to delete is determined by a subset of the rest of the variables. It also provides a set of useful results and tools for reasoning with Boolean tables. The algorithms are implemented using Python and the NumPy library. Experiments show that this procedure is feasible for intermediate problems and for difficult problems from hard Bayesian networks cases

Suggested Citation

  • Efraín Díaz-Macías & Serafín Moral, 2023. "A Deletion Algorithm for the Marginal Problem in Propositional Logic Based on Boolean Arrays," Mathematics, MDPI, vol. 11(12), pages 1-28, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2748-:d:1173469
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    References listed on IDEAS

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    1. Charles R. Harris & K. Jarrod Millman & Stéfan J. Walt & Ralf Gommers & Pauli Virtanen & David Cournapeau & Eric Wieser & Julian Taylor & Sebastian Berg & Nathaniel J. Smith & Robert Kern & Matti Picu, 2020. "Array programming with NumPy," Nature, Nature, vol. 585(7825), pages 357-362, September.
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