Representing Fuzzy Logic Programs by Graded Attribute Implications

  • Tomas Kuhr
  • Vilem Vychodil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7647)


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.


logic programming attribute implications functional dependencies ordinal scales residuated lattices 


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tomas Kuhr
    • 1
  • Vilem Vychodil
    • 1
  1. 1.DAMOL (Data Analysis and Modeling Laboratory) Dept. Computer SciencePalacky UniversityOlomoucCzech Republic

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