Fuzzy logic programming reduced to reasoning with attribute implications

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 FA...

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Veröffentlicht in:Fuzzy sets and systems Jg. 262; S. 1 - 20
Hauptverfasser: Kuhr, Tomas, Vychodil, Vilem
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.03.2015
Schlagworte:
Attribute implications
Functional dependencies
Least model property
Logic programming
Ordinal scales
Residuated lattices
Logic programming
Attribute implications
Residuated lattices
Ordinal scales
Functional dependencies
Least model property
ISSN:0165-0114, 1872-6801
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Zusammenfassung: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. We further show that entailment in FLP is reducible to reasoning with Boolean attribute implications and elaborate on related issues including properties of least models.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2014.04.013