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Foundations of a DPLL-Based Solver for Fuzzy Answer Set Programs

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Computational Intelligence (IJCCI 2017)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 829))

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Abstract

Recent years have witnessed the effort to extend answer set programming (ASP) with properties of fuzzy logic. The result of this combination is fuzzy answer set programming (FASP), a powerful framework for knowledge representation and non-monotonic reasoning with graded levels of truth. The various results in solving FASP make use of transformations into fuzzy satisfiability (SAT) problems, optimization programs, satisfiability modulo theories (SMT), or classical ASP, each of which comes with limitations or scaling problems. Moreover, most of the research revolves around Gödel and Łukasiewicz semantics. The former approach is elegant in its attempt to generalize well-known methods in classical ASP to the fuzzy case. In our work we seek to extend this approach under the product semantics, utilizing the fuzzy generalization of the DPLL algorithm. As such, we design the inner works of a DPLL-based fuzzy SAT solver for propositional product logic, which should provide foundations for the technical implementation of the solver.

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Notes

  1. 1.

    We do not explicitly refer to the properties and neutral elements of \({\pmb {\vee }}\), \({\pmb {\wedge }}\).

  2. 2.

    This is because we can regard rules as residual implicators.

  3. 3.

    Constants in the open interval (0, 1).

  4. 4.

    With the decreasing connective precedence: \(\lnot \), \({\Delta }\), \( { \& \ }\), \(\eqcirc \), \(\prec \), \(\wedge \), \(\vee \), \(\rightarrow \), \(\leftrightarrow \).

  5. 5.

    With the decreasing operator precedence: \(\pmb \sim \), \({\pmb {\Delta }}\), \({\cdot }\), \({\pmb {\eqcirc }}\), \({\pmb {\prec }}\), \({\pmb {\wedge }}\), \({\pmb {\vee }}\), \({\pmb {\Rightarrow }}\).

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Acknowledgements

The research reported in this paper was supported by the grant UK/244/2018.

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Authors and Affiliations

  1. Department of Applied Informatics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovak Republic

    Ivor Uhliarik

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  1. Ivor Uhliarik
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Correspondence to Ivor Uhliarik .

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Editors and Affiliations

  1. IUT Sénart, Université Paris-Est Créteil (UPEC), Créteil, France

    Christophe Sabourin

  2. Department of Computer Architecture and Technology, University of Granada, Granada, Spain

    Juan Julian Merelo

  3. Université Paris-Est Créteil (UPEC), Créteil, France

    Kurosh Madani

  4. University of Reading, Reading, UK

    Kevin Warwick

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Uhliarik, I. (2019). Foundations of a DPLL-Based Solver for Fuzzy Answer Set Programs. In: Sabourin, C., Merelo, J.J., Madani, K., Warwick, K. (eds) Computational Intelligence. IJCCI 2017. Studies in Computational Intelligence, vol 829. Springer, Cham. https://doi.org/10.1007/978-3-030-16469-0_6

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