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Extending Fuzzy Linguistic Logic Programming with Negation †

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  • Van Hung Le

    (Faculty of Information Technology, Hanoi University of Mining and Geology, Duc Thang, Bac Tu Liem, Hanoi 100803, Vietnam
    This paper is an extended version of our paper published in the 11th International Conference on Computational Collective Intelligence, ICCCI 2019, Hendaye, France, 4–6 September 2019.)

Abstract

Fuzzy linguistic logic programming (FLLP) is a framework for representation and reasoning with linguistically expressed human knowledge. In this paper, we extend FLLP by allowing negative literals to appear in rule bodies, resulting in normal logic programs. We study the stable model semantics and well-founded semantics of such programs and their relation. The two kinds of semantics are adapted from those of classical ones based on the Gelfond–Lifschitz transformation and van Gelder’s alternating fixpoint approach, respectively. To our knowledge, until now, there has been no work on the well-founded semantics of normal programs in any fuzzy logic programming (FLP) framework based on Vojtáš’s FLP. Moreover, the relation between the two kinds of semantics is usually studied using a bilattice setting of the truth domain. However, our truth domains do not possess a complete knowledge-ordering lattice and, thus, do not have a bilattice structure. The two kinds of semantics possess properties similar to those of the classical case. Every stable model contains the well-founded (partial) model, and the well-founded total model coincides with the unique stable model, but not vice versa. Since the well-founded semantics is closely related to the stable model semantics, it can help compute stable models more efficiently.

Suggested Citation

  • Van Hung Le, 2022. "Extending Fuzzy Linguistic Logic Programming with Negation †," Mathematics, MDPI, vol. 10(17), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3105-:d:901006
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    References listed on IDEAS

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    1. M. Eugenia Cornejo & David Lobo & Jesús Medina, 2020. "Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach," Mathematics, MDPI, vol. 8(6), pages 1-18, June.
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