Declarative and procedural semantics of fuzzy similarity based unification. (English) Zbl 1249.68264

Summary: We argue that for fuzzy unification, we need a procedural and declarative semantics (as opposed to the two-valued case, where the declarative semantics is hidden in the requirement that unified terms are syntactically – letter by letter – identical). We present an extension of the syntactic model of unification to allow near matches, defined using a similarity relation. We work in Hájek’s fuzzy logic in the narrow sense. We base our semantics on a formal model of fuzzy logic programming extended by fuzzy similarities and axioms of predicate calculus with equality. Rules are many valued implications and not Horn clauses. We prove soundness and completeness of the fuzzy similarity based unification.


68T37 Reasoning under uncertainty in the context of artificial intelligence
03B52 Fuzzy logic; logic of vagueness
68Q55 Semantics in the theory of computing
Full Text: EuDML Link


[1] Arcelli F., Formato, F., Gerla G.: Similitude-based unification as a foundation of fuzzy logic programming. Logic Programming and Soft Computing in AI (T. P. Martin and F. Arcelli Fontana, Research Studies Press, Wiley, New York 1998
[2] Baldwin J. F.: Support logic programming. Fuzzy Sets - Theory and Applications (A. Jones, D. Reidel 1986, pp. 133-170 · Zbl 0641.68142 · doi:10.1002/int.4550010202
[3] Dubois D., Lang, J., Prade H.: Fuzzy sets in approximate reasoning, Part 2: Logical approaches. Foundations of Fuzzy Reasoning. Special Memorial Volume; 25 years of fuzzy sets: Attribute to Professor Lotfi Zadeh. First issue (I. B. Turksen, D. Dubois, H. Prade, and R. R. Yager, Fuzzy Sets and Systems 40 (1991), 203-244 · Zbl 0722.03018
[4] Gottwald S.: Fuzzy Sets and Fuzzy Logic. Vieweg, Wiesbaden 1993 · Zbl 1088.03024 · doi:10.1016/j.fss.2005.05.031
[5] Hájek P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht 1998 · Zbl 1007.03022
[6] Kriško P., Marcinčák P., Mihók P., Sabol, J., Vojtáš P.: Low retrieval remote querying dialogue with fuzzy conceptual, syntactical and linguistical unification. Proc. FQAS’98 Flexible Query Answering Systems (T. Andreasen et al, Lecture Notes in Computer Science 1495), Springer Verlag, Berlin 1998, pp. 215-226
[7] Lloyd J. W.: Foundations of Logic Programming. Springer Verlag, Berlin 1987 · Zbl 0807.68001
[8] Martelli A., Montanari U.: An efficient unification algorithm. ACM Trans. Programming Languages and Systems 4 (1982), 258-282 · Zbl 0478.68093 · doi:10.1145/357162.357169
[9] Pedrycz W.: Fuzzy Control and Fuzzy Systems. Report 82/14, Dept. Math., Delft Univ. of Technology · Zbl 0839.93006
[10] Petry F. E.: Fuzzy Databases - Principles and Applications. Kluwer, Dordrecht 1996 · Zbl 0853.68086
[11] Robinson J. A.: A machine-oriented logic based on the resolution principle. J. Assoc. Comp. Mach. 12 (1965), 23-41 · Zbl 0139.12303 · doi:10.1145/321250.321253
[12] Emden E. van: Quantitative deduction and its fixpoint theory. J. Logic Programming 1 (1986), 37-53 · Zbl 0609.68068 · doi:10.1016/0743-1066(86)90003-8
[13] Virtanen H. E.: Linguistic logic programming. Logic Programming and Soft Computing (T. P. Martin and F. Arcelli Fontana, Research Press Studies Lim.), Wiley, New York 1998
[14] Vojtáš P.: Fuzzy reasoning with tunable \(t\)-operators. J. Advanced Comp. Intelligence 2 Fuji Press (1998), 121-127
[15] Vojtáš P.: Fuzzy logic programming. Submitted to Proc. Workshop on Fuzzy Logic at FSTA, for Fuzzy Sets and Systems · Zbl 1015.68036 · doi:10.1016/S0165-0114(01)00106-3
[16] Vojtáš P.: Uncertain reasoning with floating connectives. Proc. AIT’96 Artificial Intelligence Techniques Brno (J. Žižka, Technical University Brno, PC-Dir Publ. 1996, pp. 31-40
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.