Abstract
We consider theoretical (mathematical) model of extended logic programming in many valued logic with arbitrary triple of connectives (seq, et1, et2), where et1 evaluates modus ponens containing the implication seq and et2 is the conjunction from bodies of clauses. Our motivation comes from MYCIN-like expert systems written in Prolog with uncertainty reasoning mechanism. Our declarative semantics is based on generalization of P. Hájek's RPL and RQL logic. We introduce a procedural semantics and prove soundness and completeness of this semantics for definite programs with confidence factors.
This work was supported by the grant 2/1224/95 of the Slovak Grant Agency for Science.
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References
Apt, K. R.: Logic programming. In: van Leeuwen, J.(Ed.): Handbook of Theoretical Computer Science, Vol. B, Formal methods and semantics, 493–574, Elsevier, 1990
The Arity/Expert language. Arity Corp., Concord MA, 1986
Ding L., Shen Z. L., Mukaidono M.: Fuzzy linear resolution as the inference engine of intelligent systems. In: Ras Z. W. (Ed.): Methodologies for Intelligent Systems, Volume 4, Elsevier Science Publ., Amsterdam, 1989, 1–8
Dubois D., Lang J., Prade H.: Fuzzy sets in approximate reasoning, Part 2: Logical approaches. Fuzzy Sets and Systems 40 (1991) 203–244
Gottwald, S.: Mehrwertige Logik. Akademie Verlag, Berlin, 1988
Hájek, P.: Fuzzy logic and arithmetical hierarchy I. Fuzzy Sets and Systems (to appear)
Hájek, P.: Fuzzy logic and arithmetical hierarchy II. Preprint, 1995
Hájek, P.: Fuzzy logic from the logical point of view. In: Bartošek, M., Staudek, J., Wiedermann, J. (Eds.): SOFSEM'95: Theory and Practice of Informatics, 31–49, Lecture Notes in Comp. Sci., 1012, Springer, Berlin, 1995
Klawonn, K., Kruse, K.: A Lukasiewicz logic based Prolog. Mathware Soft Comput. 1 (1994) 5–29
Lloyd, J.W.: Foundation of Logic Programming. Springer Verlag, Berlin, 1987
Meritt, D.: Building Expert Systems in Prolog. Springer Verlag, Berlin, 1989
Mukaidono, M., Kikuchi, H.: Foundations of fuzzy logic programming. In: Wang, P-Z., Loe, K-F.(Eds.): Between Mind and Computer, 225–244, Advances in Fuzzy Systems — Applications and Theory, Vol.1, World Scientific Publ., Singapore
Novák, V.: On the syntactico-semantical completeness of first-order fuzzy logic I, II. Kybernetika 26 (1990) 47–26, 134–152
Pavelka, J.: On fuzzy logic I, II, III. Zeitschr. f. Math. Logik und Grundl. der Math. 25 (1979) 45–52, 119–134, 447–464
Shortliffe, E. H., Buchanan, B. G.: A model of inexact reasoning in medicine. Math. Biosci. 23 (1975) 351–379
Sterling, L., Shapiro, E.: The Art of Prolog. MIT Press, Cambridge MA, 1986
Vojtáš, P., Paulík, L., Lieskovský, M.: Expert systems and different logic systems. In: Žižka, J., Brazdil, P. (Eds.): Artificial Intelligence Techniques AIT'95, 233–239, Published by Tech. Univ., Brno, 1995
Vojtáš P., Paulík, L.: Logical Programming in RPL and RQL. In: Bartosek, M., Staudek, J., Wiedermann, J. (Eds.): SOFSEM'95: Theory and Practice of Informatics, 487–492, Lecture Notes in Comp. Sci., 1012, Springer, Berlin, 1995
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Vojtás, P., Paulík, L. (1996). Soundness and completeness of non-classical extended SLD-resolution. In: Dyckhoff, R., Herre, H., Schroeder-Heister, P. (eds) Extensions of Logic Programming. ELP 1996. Lecture Notes in Computer Science, vol 1050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60983-0_20
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DOI: https://doi.org/10.1007/3-540-60983-0_20
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