×

zbMATH — the first resource for mathematics

A comparison of fuzzy and annotated logic programming. (English) Zbl 1065.68024
Summary: The aim of this paper is to contribute to the study of relationships between different formalism for handling uncertainty in logic programming, knowledge-based systems and deductive databases. Generalized annotated programs with restricted semantics (RGA-programs) are well suited to fit real-world data. We show that RGA-programs with constant annotations in body are equivalent to programs with left discontinuous annotation and with possibly non-computable semantics. Our model of Fuzzy Logic Programming (FLP) can well handle recursive programs. We show that FLP has the same expressive power as RGA-programs without constant annotations in body of rules. We introduce several syntactical transformations of programs and study their models and production operators. We introduce a new efficient procedural semantics for RGA-programs and show connections between different sorts of computed answers.

MSC:
68N17 Logic programming
68T37 Reasoning under uncertainty in the context of artificial intelligence
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arenas, M.; Bertossi, L.; Kifer, M., Applications of annotated predicate calculus to querying inconsistent databases, (), 926-941 · Zbl 0983.68054
[2] Baldwin, J.F., Evidential support logic programming, Fuzzy sets and systems, 24, 1-26, (1987) · Zbl 0639.68105
[3] L. Bertossi, J. Chomicki, Query answering in inconsistent databases, in: J. Chomicki, R. van der Meyden, G. Saake (Eds.), Logics for Emerging Applications of Databases, Springer Verlag, Berlin, 2004, pp. 43-84. · Zbl 1079.68026
[4] Damasio, C.V.; Pereira, L.M., Hybrid probabilistic logic programs as residuated logic programs, (), 57-72 · Zbl 0998.68030
[5] A. Dekhtyar, V.S. Subrahmanian, Hybrid probabilistic programs, in: ICLP 1997, MIT Press, Cambridge, 1997, pp. 391-405. · Zbl 0955.68020
[6] D. Dubois, J. Lang, H. Prade, Possibilistic logic, in: D.M. Gabbay, et al. (Eds.), Handbook of Logic in AI and LP, vol. 3, Oxford University Press, Oxford, 1994, pp. 439-513.
[7] Dubois, D.; Lang, J.; Prade, H., Fuzzy sets in approximate reasoning, part 2logical approaches, Fuzzy sets and systems, 40, 203-244, (1991) · Zbl 0722.03018
[8] Eiter, T.; Mascardi, V.; Subrahmanian, V.S., Error-tolerant agents, (), 586-625 · Zbl 1012.68541
[9] Fitting, M., Fixpoint semantics for logic programming, a survey, Theoret. comput. sci., 278, 25-51, (2002) · Zbl 1002.68023
[10] Gerla, G., Fuzzy logic: mathematical tools for approximate reasoning, (2000), Kluwer Dordrecht
[11] Gottwald, S., A treatise on many-valued logics, (2001), Research Studies Press Baldock · Zbl 1048.03002
[12] R. Haehnle, Uniform notation of tableau rules for multiple-valued logics, in: Proc. Internat. Symp. on Multiple Valued Logic, Computer Society Press, Los Alamitos, CA, 1991, pp. 26-29.
[13] Hájek, P., Metamathematics of fuzzy logic, (1999), Kluwer Dordrecht · Zbl 0937.03030
[14] Kifer, M.; Subrahmanian, V.S., Theory of generalized annotated logic programming and its applications, J. logic programing, 12, 335-367, (1992)
[15] Krajči, S.; Lencses, R.; Vojtáš, P., A data model for annotated programs, (), 141-154
[16] P. Kullmann, S. Sandri, An annotated logic theorem prover for an extended possibilistic logic, Fuzzy Sets and Systems, this issue. · Zbl 1076.68087
[17] Lu, J.J., Programming with signs and annotations, J. logic comput., 6, 755-778, (1996) · Zbl 0874.68062
[18] T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming, in: Proc. ISMVL 1999, IEEE Computer Society, Freiburg im Breisgau, Germany, 1999, pp. 235-240.
[19] Pokorný, J.; Vojtáš, P., A data model for flexible querying, (), 280-293 · Zbl 1005.68515
[20] Sessa, M.I., Approximate reasoning by similarity-based SLD resolution, Theoret. comput. sci., 275, 389-426, (2002) · Zbl 1051.68045
[21] Subrahmanian, V.S.; Bonatti, P.A.; Dix, J.; Eiter, T.; Kraus, S.; Ozcan, F.; Ross, R., Heterogenous active agents, (2000), MIT Press Cambridge
[22] Vojtáš, P., Fuzzy logic programming, Fuzzy sets and systems, 124, 361-370, (2001) · Zbl 1015.68036
[23] P. Vojtáš, T. Alsinet, L. Godo, Different models of fuzzy logic programming with fuzzy unification (towards revision of fuzzy databases), in: Proc. Joint 9th IFSA World Congr. and 20th NAFIPS Internat. Conf. (IFSA-NAFIPS 2001) Vancouver, IEEE, 2001, pp. 1541-1546, available on CD, ISBN 0-7803-7079-1, IEEE Catalogue number 01TH8569C.
[24] Vojtáš, P.; Paulı́k, L., Soundness and completeness of non-classical extended SLD resolution, (), 289-301
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.