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Reasoning with Propositional Logic: From SAT Solvers to Knowledge Compilation

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Abstract

The Propositional Logic plays a central role in Artificial Intelligence. Extremely simple, this logic already addresses some of the most important problems in computer theory. It allows an incredible panel of pragmatic solutions to be successfully applied on a large number of (theoretically) hard problems. Its apparent simplicity allows one to design very efficient and compact algorithms to tackle, in practice, problems lying at the first levels of the complexity classes. In this chapter, we first present the kind of A.I. problems that can typically be addressed by this formalism. Then, we present an historical view of the impressive progresses observed in the practical solving of the Satisfiability (SAT) problem. Then, we introduce the concept of Knowledge Compilation, another important field of A.I. often build upon Propositional Logic. We also introduce Quantified Boolean Formula (QBF), a natural extension of SAT to quantifiers.

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Notes

  1. 1.

    See www.cs.utexas.edu/users/hunt/FMCAD/.

  2. 2.

    A Horn clause is a clause containing at most one positive literal. A Horn formula is a formula under CNF containing only Horn clauses.

  3. 3.

    See evaluation site Maxsat, maxsat.ia.udl.cat.

  4. 4.

    This time is often much longer than the time of a single request.

  5. 5.

    Note that any theory can still be compiled into a complete theory for unit resolution (del Val 1994).

  6. 6.

    An important development effort has been carried out for providing a very simple and useful SDD package: http://reasoning.cs.ucla.edu/sdd/.

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Authors and Affiliations

  1. LaBRI-CNRS, Bordeaux INP, Université Bordeaux, Bordeaux, France

    Laurent Simon

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Correspondence to Laurent Simon .

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  1. CRIL-CNRS, Université d’Artois and Institut Universitaire de France, Lens, France

    Pierre Marquis

  2. Aix Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France

    Odile Papini

  3. IRIT, CNRS and Université Paul Sabatier, Toulouse, France

    Henri Prade

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Simon, L. (2020). Reasoning with Propositional Logic: From SAT Solvers to Knowledge Compilation. In: Marquis, P., Papini, O., Prade, H. (eds) A Guided Tour of Artificial Intelligence Research. Springer, Cham. https://doi.org/10.1007/978-3-030-06167-8_5

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