Representing Fuzzy Logic Programs by Graded 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 Vojtas 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.

[1]  Peter Vojtás,et al.  Fuzzy logic programming , 2001, Fuzzy Sets Syst..

[2]  Vilém Vychodil,et al.  Query systems in similarity-based databases: logical foundations, expressive power, and completeness , 2010, SAC '10.

[3]  Vilém Vychodil,et al.  Fuzzy attribute logic over complete residuated lattices , 2006, J. Exp. Theor. Artif. Intell..

[4]  Satoko Titani,et al.  Globalization of intui tionistic set theory , 1987, Ann. Pure Appl. Log..

[5]  Vilém Vychodil,et al.  Data Tables with Similarity Relations: Functional Dependencies, Complete Rules and Non-redundant Bases , 2006, DASFAA.

[6]  Luís Moniz Pereira,et al.  Monotonic and Residuated Logic Programs , 2001, ECSQARU.

[7]  Michael Clarke,et al.  Symbolic and Quantitative Approaches to Reasoning and Uncertainty , 1991, Lecture Notes in Computer Science.

[8]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[9]  A. Campbell,et al.  Progress in Artificial Intelligence , 1995, Lecture Notes in Computer Science.

[10]  Elliott Mendelson,et al.  Introduction to Mathematical Logic , 1979 .

[11]  Jan Pavelka,et al.  On Fuzzy Logic I Many-valued rules of inference , 1979, Math. Log. Q..

[12]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[13]  Wolfgang Wechler,et al.  Universal Algebra for Computer Scientists , 1992, EATCS Monographs on Theoretical Computer Science.

[14]  Elliott Mendelson,et al.  Introduction to mathematical logic (3. ed.) , 1987 .

[15]  Radim Bělohlávek,et al.  Fuzzy Relational Systems: Foundations and Principles , 2002 .

[16]  Radko Mesiar,et al.  Generated triangular norms , 2000, Kybernetika.

[17]  Lluis Godo,et al.  Monoidal t-norm based logic: towards a logic for left-continuous t-norms , 2001, Fuzzy Sets Syst..

[18]  Petr Hájek,et al.  On very true , 2001, Fuzzy Sets Syst..

[19]  R. Belohlávek.  Fuzzy Relational Systems: Foundations and Principles , 2002 .

[20]  Anne Lohrli.  Chapman and Hall , 1985 .

[21]  Manuel Ojeda-Aciego,et al.  A Procedural Semantics for Multi-adjoint Logic Programming , 2001, EPIA.

[22]  Ulf Nilsson,et al.  Logic, programming and Prolog , 1990 .

[23]  J. A. Goguen,et al.  The logic of inexact concepts , 1969, Synthese.