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Representing Fuzzy Logic Programs by Graded Attribute Implications

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7647))

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Abstract

We present a link between two types of logic systems for reasoning with graded if-then rules: the system of fuzzy logic programming (FLP) in sense of Vojtáš and the system of fuzzy attribute logic (FAL) in sense of Belohlavek and Vychodil. We show that each finite theory consisting of formulas of FAL can be represented by a definite program so that the semantic entailment in FAL can be characterized by correct answers for the program. Conversely, we show that for each definite program there is a collection of formulas of FAL so that the correct answers can be represented by the entailment in FAL. Using the link, we can transport results from FAL to FLP and vice versa which gives us, e.g., a syntactic characterization of correct answers based on Pavelka-style Armstrong-like axiomatization of FAL.

Supported by grant no. P103/11/1456 of the Czech Science Foundation and internal grant of Palacky University no. PrF_2012_029. DAMOL is supported by project reg. no. CZ.1.07/2.3.00/20.0059 of the European Social Fund in the Czech Republic.

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Authors and Affiliations

  1. DAMOL (Data Analysis and Modeling Laboratory) Dept. Computer Science, Palacky University, 17. listopadu 12, CZ–77146, Olomouc, Czech Republic

    Tomas Kuhr & Vilem Vychodil

Authors
  1. Tomas Kuhr
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  2. Vilem Vychodil
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Editors and Affiliations

  1. IIIA-CSIC, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10, Naka, 186-0004, Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. Universitat de Girona, Campus Montilivi, building EPS-4, 17071, Girona, Spain

    Beatriz López  & Mateu Villaret  & 

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Kuhr, T., Vychodil, V. (2012). Representing Fuzzy Logic Programs by Graded Attribute Implications. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_23

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  • DOI: https://doi.org/10.1007/978-3-642-34620-0_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34619-4

  • Online ISBN: 978-3-642-34620-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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