Rfuzzy framework

Fuzzy reasoning is a very productive research field that during the last years has provided a number of theoretical approaches and practical implementation prototypes. Nevertheless, the classical implementations, like Fril, are not adapted to the latest formal approaches, like multi-adjoint logic semantics. Some promising implementations, like Fuzzy Prolog, are so general that the regular user/programmer does not feel comfortable because either representation of fuzzy concepts is complex or the results difficult to interpret. In this paper we present a modern framework, Rfuzzy, that is modelling multi-adjoint logic. It provides some extensions as default values (to represent missing information, even partial default values) and typed variables. Rfuzzy represents the truth value of predicates through facts, rules and functions. Rfuzzy answers queries with direct results (instead of constraints) and it is easy to use for any person that wants to represent a problem using fuzzy reasoning in a simple way (by using the classical representation with real numbers).

[1]  Tru H. Cao,et al.  Annotated fuzzy logic programs , 2000, Fuzzy Sets Syst..

[2]  Ehud Y. Shapiro,et al.  Logic Programs With Uncertainties: A Tool for Implementing Rule-Based Systems , 1983, IJCAI.

[3]  Manuel Ojeda-Aciego,et al.  A completeness theorem for multi-adjoint logic programming , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[4]  Norbert Fuhr Probabilistic Datalog: implementing logical information retrieval for advanced applications , 2000 .

[5]  Ginés Moreno,et al.  Designing a Software Tool for Fuzzy Logic Programming , 2008 .

[6]  Enric Trillas,et al.  A general class of triangular norm-based aggregation operators: quasi-linear T-S operators , 2002, Int. J. Approx. Reason..

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

[8]  Deyi Li,et al.  A Fuzzy Prolog Database System , 1990 .

[9]  M. Mukaidono,et al.  Fuzzy resolution principle , 1988, [1988] Proceedings. The Eighteenth International Symposium on Multiple-Valued Logic.

[10]  Gerd Wagner,et al.  A Logical Reconstruction of Fuzzy Inference in Databases and Logic Programs , 1997 .

[11]  Susana Muñoz-Hernández,et al.  Fuzzy Prolog: A Simple General Implementation Using CLP(R) , 2002, ICLP.

[12]  V. S. Subrahmanian,et al.  Theory of Generalized Annotated Logic Programming and its Applications , 1992, J. Log. Program..

[13]  V. S. Subrahmanian,et al.  Probabilistic Logic Programming , 1992, Inf. Comput..

[14]  Susana Muñoz-Hernández,et al.  Combining Crisp and Fuzzy Logic in a Prolog Compiler , 2002, APPIA-GULP-PRODE.

[15]  Laks V. S. Lakshmanan,et al.  A Parametric Approach to Deductive Databases with Uncertainty , 1996, Logic in Databases.

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

[17]  Frank Klawonn,et al.  Lukasiewicz logic based Prolog , 1994 .

[18]  Mitsuru Ishizuka,et al.  Prolog-ELF incorporating fuzzy logic , 2009, New Generation Computing.

[19]  Thomas Lukasiewicz,et al.  Fixpoint Characterizations for Many-Valued Disjunctive Logic Programs with Probabilistic Semantics , 2001, LPNMR.

[20]  Richard C. T. Lee Fuzzy Logic and the Resolution Principle , 1971, JACM.

[21]  Susana Muñoz-Hernández,et al.  Fuzzy Prolog: a new approach using soft constraints propagation , 2004, Fuzzy Sets Syst..

[22]  M. H. van Emden,et al.  Quantitative Deduction and its Fixpoint Theory , 1986, J. Log. Program..

[23]  Nikola Kasabov Fril—fuzzy and evidential reasoning in artificial intelligence , 1996 .

[24]  E. Trillas,et al.  Conjunction and disjunction on ([0,1], ≤) , 1995 .

[25]  V. S. Subrahmanian On the Semantics of Quantitative Logic Programs , 1987, SLP.

[26]  Manuel Ojeda-Aciego,et al.  Multi-adjoint Logic Programming with Continuous Semantics , 2001, LPNMR.

[27]  Laks V. S. Lakshmanan,et al.  Probabilistic Deductive Databases , 1994, ILPS.

[28]  Gerd Wagner Negation in Fuzzy and Possibilistic Logic Programs , 1998 .

[29]  Francesca Rossi,et al.  Semiring-based constraint logic programming: syntax and semantics , 2001, TOPL.

[30]  Melvin Fitting,et al.  Bilattices and the Semantics of Logic Programming , 1991, J. Log. Program..

[31]  Didier Dubois,et al.  Towards Possibilistic Logic Programming , 1991, ICLP.

[32]  Laks V. S. Lakshmanan,et al.  An Epistemic Foundation for Logic Programming with Uncertainty , 1994, FSTTCS.

[33]  V. S. Subrahmanian,et al.  Stable Model Semantics for Probabilistic Deductive Databases , 1990, ISMIS.