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Fuzzy logic programming. (English) Zbl 1015.68036
Summary: We consider the theory of fuzzy logic programming without negation. Our results cover logical systems with a wide variety of connectives ranging from t-norm and conorms, through conjunctors and disjunctors and their residuals to aggregation operators. Rules of our programs are many valued implications. We emphasize, that in contrast to other approaches, our logic is truth functional, i.e. according to P. Hájek, we work in fuzzy logic in narrow sense. We prove the soundness and the completeness of our formal model. We deal with applications to threshold computation, abduction, fuzzy unification based on similarity. We show that fuzzy unification based on similarities has applications to fuzzy databases and flexible querying.

68N17 Logic programming
03B52 Fuzzy logic; logic of vagueness
Full Text: DOI
[1] D. Dubois, J. Lang, H. Prade, Fuzzy sets in approximate reasoning, Part 2: Logical approaches, in: I.B. Turksen, D. Dubois, H. Prade, R.R. Yager (Eds.), Foundations of Fuzzy Reasoning. Special Memorial Volume; 25 years of fuzzy sets: A tribute to Professor Lotfi Zadeh, First issue; Fuzzy Sets and Systems 40 (1991) 203-244. · Zbl 0722.03018
[2] van Emden, M.H., Quantitative deduction and its fixpoint theory, J. logic programming, 1, 37-53, (1986) · Zbl 0609.68068
[3] K. Goedel, Zum intuitionistischen Aussagenkalkuel. Anzeiger Akademie der Wissenschaften Wien, Math.- Naturwissensch. Klasse 69 (1932) 65-66; also in Ergebnisse eines mathematischen Kolloquiums 4 (1933) 40. · JFM 58.1001.03
[4] Gottwald, S., Mehrwertige logik, (1988), Akademie Verlag Berlin
[5] Gottwald, S., Fuzzy sets and fuzzy logic, (1993), Vieweg Braunschweig
[6] M.M. Gupta, J. Qi, Theory of T-norms and fuzzy inference methods, in: M.M. Gupta (Ed.), Fuzzy Logic and Uncertainty Modeling, Special Memorial Volume; 25 years of fuzzy sets: A tribute to Proffesor Lotfi Zadeh, Third issue, Fuzzy Sets and Systems 40 (1991) 431-450.
[7] Hájek, P., Metamathematics of fuzzy logic, (1998), Kluwer Dordrecht · Zbl 0937.03030
[8] Klawonn, K.; Kruse, K.; Łukasiewicz, A., Logic based prolog, Mathware soft comput., 1, 5-29, (1994)
[9] Li, D.Y.; Liu, D.B., A fuzzy prolog database system, (1990), Research Studies Press and Wiley New York
[10] Lloyd, J.W., Foundation of logic programming, (1987), Springer Berlin
[11] Łukasiewicz, J., Selected works, (1970), North-Holland Amsterdam · Zbl 0212.00902
[12] M. Mukaidono, H. Kikuchi, Foundations of fuzzy logic programming, in: P.-Z. Wang, K.-F. Loe (Eds.), Between Mind and Computer, Advances in Fuzzy Systems—Applications and Theory, vol. 1, World Scientific Publ., Singapore, pp. 225-244.
[13] Naito, E.; Ozawa, J.; Hayashi, I.; Wakami, N., A proposal of a fuzzy connective with learning function, (), 345-364
[14] V. Novák, On the syntactico-semantical completeness of first-order fuzzy logic I, II. Kybernetika 26 (1990) 26-47, 134-152.
[15] J. Pavelka, On fuzzy logic I, II, III, Zeitschr. Math. Logik und Grundl. Math. 25 (1979) 45-52, 119-134, 447-464. · Zbl 0435.03020
[16] W. Pedrycz, Fuzzy control and fuzzy systems, Report 82/14, Dept. Math., Delft Univ. of Technology. · Zbl 0839.93006
[17] Shapiro, E.Y., Programs with uncertainties, (), 529-532
[18] Shortliffe, E.H.; Buchanan, B.G., A model of inexact reasoning in medicine, Math. biosci., 23, 351-379, (1975)
[19] D. Smutná, P. Vojtáš, Fuzzy resolution with residuation of material implication, EUROFUSE-SIC’99, Budapest 1999, pp. 472-476.
[20] Smutná, D.; Vojtáš, P., New connectives for (full) fuzzy resolution, (), 146-151 · Zbl 0986.03021
[21] Vojtáš, P., Fuzzy reasoning with tunable t-operators, J. adv. comput. intelligence, 2, 121-127, (1998)
[22] P. Vojtáš, Fuzzy logic abduction, Proc. Workshop 17 at ECAI’98, Brighton, 1998.
[23] Vojtáš, P., Declarative and procedural model of fuzzy unification, Kybernetika, 36, 707-720, (2000) · Zbl 1249.68264
[24] Vojtáš, P.; Paulı́k, L., Soundness and completeness of non-classical extended SLD resolution, (), 289-301
[25] Vojtáš, P.; Fabián, Z., Aggregating similar witness for flexible query answering, (), 220-229
[26] Vinař, J.; Vojtáš, P., A formal model for fuzzy knowledge based systems with similarities, Neural network world, 10, 891-905, (2000)
[27] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
[28] Zadeh, L.A., Fuzzy logic and approximate reasoning (in memory of grigore moisil), Synthese, 30, 407-428, (1975) · Zbl 0319.02016
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