Representing fuzzy logic programs by graded attribute implications

Authors:
Tomas Kuhr;Vilem Vychodil
Affiliations:
DAMOL (Data Analysis and Modeling Laboratory) Dept. Computer Science, Palacky University, Olomouc, Czech Republic;DAMOL (Data Analysis and Modeling Laboratory) Dept. Computer Science, Palacky University, Olomouc, Czech Republic
Venue:
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
Year:
2012

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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.