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Similarity-based unification: A multi-adjoint approach. (English) Zbl 1073.68026

Summary: The aim of this paper is to build a formal model for similarity-based fuzzy unification in multi-adjoint logic programs. Specifically, a general framework of logic programming which allows the simultaneous use of different implications in the rules and rather general connectives in the bodies is introduced, then a procedural semantics for this framework is presented, and an approximative-completeness theorem proved. On this computational model, a similarity-based unification approach is constructed by simply adding axioms of fuzzy similarities and using classical crisp unification which provides a semantic framework for logic programming with different notions of similarity.

MSC:

68N17 Logic programming
03B52 Fuzzy logic; logic of vagueness

Software:

Likelog; FRIL
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References:

[1] T. Alsinet, L. Godo, A complete calculus for possibilistic logic programming with fuzzy propositional variables, in: Proc. of UAI2000 Conf., Stanfard, CA, 2000, pp. 1-10.
[2] T. Alsinet, L. Godo, A complete proof method for possibilistic logic programming with semantical unication of fuzzy constants, in: Proc. of ESTYLF2000 Conf., Sevilla, Spain, 2000, pp. 279-284.
[3] F. Arcelli, F. Formato, Likelog: a logic programming language for flexible data retrieval, in: ACM Symp. on Applied Computing, San antonio, TX, 1999, pp. 260-267.
[4] Baldwin, J.F.; Martin, T.P.; Pilsworth, B.W., FRIL-fuzzy and evidential reasoning in AI, (1995), Research Studies Press, Wiley New York
[5] C.V. Damásio, L. Moniz Pereira, Monotonic and residuated logic programs, in: S. Benferhat, P. Besnard (Eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU’01, Lecture Notes in Artificial Intelligence, Vol. 2143, Springer, Heidelberg, 2001, pp. 748-759. · Zbl 1001.68545
[6] Decker, S.; Melnik, S.; van Harmelen, F.; Fensel, D.; Klein, M.; Broekstra, J.; Erdmann, M.; Horrocks, I., The semantic webthe roles of XML and RDF, IEEE Internet comput., 43, 2-13, (2000)
[7] Dilworth, R.P.; Ward, M., Residuated lattices, Trans. amer. math. soc., 45, 335-354, (1939) · Zbl 0021.10801
[8] D. Dubois, H. Prade, S. Sandri, Possibilistic logic with fuzzy constants and fuzzily restricted quantiers, in: F. Arcelli, T.P. Martin (Eds.), Logic Programming and Soft Computing, Research Studies Press, Hertfordshire, UK, 1998.
[9] Fagin, R.; Wimmers, E.L., A formula for incorporating weights into scoring rules, Theoret. comput. sci., 239, 309-338, (2000) · Zbl 0945.68044
[10] Formato, F.; Gerla, G.; Sessa, M.I., Similarity-based unification, Fund. inform., 41, 4, 393-414, (2000) · Zbl 0954.68032
[11] Jeffery, K.G., What’s next in database, ERCIM news, 39, 24-26, (1999)
[12] Kifer, M.; Subrahmanian, V.S., Theory of generalized annotated logic programming and its applications, J. logic programming, 12, 335-367, (1992)
[13] Klawonn, F., Should fuzzy equality and similarity satisfy transitivity?, Fuzzy sets and systems, 133, 2, 175-180, (2003) · Zbl 1020.03053
[14] S. Krajči, R. Lencses, J. Medina, M. Ojeda-Aciego, P. Vojtáš, A similarity-based unification model for flexible querying, in: T. Andreasen, A. Motro, H. Christiansen, H.L. Larsen (Eds.), Flexible Querying and Answering Systems, FQAS’02, Lecture Notes in Artificial Intelligence, Vol. 2522, Springer, Heidelberg, 2002, pp. 263-273.
[15] P. Kriško, P. Marcinšák, P. Mihók, J. Sabol, P. Vojtáš, Low retrieval remote querying dialogue with fuzzy conceptual, syntactical and linguistical unification, in: T. Andreasen, H. Christiansen, H.L. Larsen (Eds.), Flexible Query Answering Systems, FQAS’98, Lecture Notes in Computer Science, Vol. 1495, Springer, Berlin, 1998, pp. 215-226.
[16] R. Lencses, Algoritmy v oblasti zı́skavania informácii, in: Proc. Information Technologies—Applications and Theory, Faculty of Science, UPJS, Košice, Slovakia, 2001, pp. 53-64.
[17] J. Medina, E. Mérida-Casermeiro, M. Ojeda-Aciego, A neural approach to extended logic programs, in: J. Mira, J.R. Alvarez (Eds.), Seventh Internat. Work Conf. on Artificial and Natural Neural Networks, IWANN’03, Lecture Notes in Computer Science, Vol. 2686, Springer, Berlin, 2003, pp. 654-661.
[18] J. Medina, M. Ojeda-Aciego, P. Vojtáš, Multi-adjoint logic programming with continuous semantics, in: T. Eiter, W. Faber, M. Truszczynski (Eds.), Logic Programming and Non-Monotonic Reasoning, LPNMR’01, Lecture Notes in Artificial Intelligence, Vol. 2173, Springer, Heidelberg, 2001, pp. 351-364. · Zbl 1007.68023
[19] J. Medina, M. Ojeda-Aciego, P. Vojtáš, A procedural semantics for multi-adjoint logic programming, in: Progress in Artificial Intelligence, EPIA’01, Lecture Notes in Artificial Intelligence, Vol. 2258, 2001, pp. 290-297. · Zbl 1053.68540
[20] J. Pavelka, On fuzzy logic I, II, III, Z. Math. Logik Grundlag Math. 25 (1979) 45-52, 119-134, 447-464. · Zbl 0435.03020
[21] Sessa, M.I., Approximate reasoning by similarity-based SLD resolution, Theoret. comput. sci., 275, 1-2, 389-426, (2002) · Zbl 1051.68045
[22] H. Virtanen, Łukasiewicz logic programming based on fuzzy equality, in: Intelligent Techniques and Soft Computing Proc. EUFIT’96, aachen, Germany, 1996, pp. 646-650.
[23] Vojtáš, P., Fuzzy logic programming, Fuzzy sets and systems, 124, 3, 361-370, (2001) · Zbl 1015.68036
[24] P. Vojtáš, L. Paulı́k, Soundness and completeness of non-classical extended SLD-resolution, in: Extensions of Logic Programming, ELP’96, Lecture Notes in Computer Science, Vol. 1050, Springer, Berlin, 1996, pp. 289-301.
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