Abstract
A strong (L) logic programming language ([14], [15]) is given by two sub-classes of formulas (programs and goals) of the underlying logic L, provided that: firstly, any program P (viewed as a L-theory) has a canonical model M P which is initial in the category of all its L-models; secondly, the L-satisfaction of a goal G in M P is equivalent to the L-derivability of G from P, and finally, there exists an effective (computable) proof-subcalculus of the L-calculus which works out for derivation of goals from programs. In this sense, Horn clauses constitute a strong (first-order) logic programming language. Following the methodology suggested in [15] for designing logic programming languages, an extension of Horn clauses should be made by extending its underlying first-order logic to a richer logic which supports a strong axiomatization of the extended logic programming language. A well-known approach for extending Horn clauses with embedded implications is the static scope programming language presented in [8]. In this paper we show that such language can be seen as a strong FO⊃ logic programming language, where FO⊃ is a very natural extension of first-order logic with intuitionistic implication. That is, we present a new characterization of the language in [8] which shows that Horn clauses extended with embedded implications, viewed as FO⊃-theories, preserves all the attractive mathematical and computational properties that Horn clauses satisfy as first-order-theories.
This work has been partially supported by the CICYT-project TIC95-1016-C02-02.
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References
Arruabarrena, R. and Navarro, M. On Extended Logic Languages Supporting Program Structuring, In: Proc. of APPIA-GULP-PRODE’96, 191–203, (1996).
Bugliesi, M., Lamma, E. and Mello, P., Modularity in Logic Programming, Journal of Logic Programming, (19-20): 443–502, (1994).
Bonner, A. J., and McCarty, L. T., Adding Negation-as-Failure to Intuitionistic Logic Programming, In: Proc. of the North American Conf. on Logic Programming, MIT Press, 681–703, (1990).
Bonner, A. J., McCarty, L. T., and Vadaparty, K., Expresing Database Queries with Intuitionistic Logic. In: Proc. of the North American Conf. on Logic Programming, MIT Press, 831–850, (1989).
Gabbay, D. M., N-Prolog: An Extension of Prolog with Hypothetical Implications. II. Logical Foundations and Negation as Failure, Journal of Logic Programming 2(4):251–283 (1985).
Gabbay, D. M. and Reyle, U., N-Prolog: An Extension of Prolog with Hypothetical Implications. I., Journal of Logic Programming 1(4):319–355 (1984).
Giordano, L., and Martelli, A.; Structuring Logic Programs: A Modal Approach, Journal of Logic Programming 21:59–94 (1994).
Giordano, L., Martelli, A., and Rossi, G., Extending Horn Clause Logic with Implication Goals, Theoretical Computer Sscience, 95:43–74, (1992).
Giordano, L., and Olivetti, N.; Combining Negation as Failure and Embedded Implications in Logic Programs, Journal of Logic Programming 36:91–147 (1998).
Harland., J. Succecs and Failure for Hereditary Harrop Formulae, Journal of Logic Programming, 17:1–29, (1993).
Lucio, P. \( \mathcal{F}\mathcal{O}^ \supset \): A Complete Extension of First-order Logic with Intuitionistic Implication, Technical Research Report UPV-EHU/LSI/TR-6-98, URL address: http://www.sc.ehu.es/paqui, Submitted to a journal for publication.
McCarty, L. T., Clausal Intuitionistic Logic I. Fixed-Point Semantics, Journal of Logic Programming, 5:1–31, (1988).
McCarty, L. T., Clausal Intuitionistic Logic II. Tableau Proof Procedures, Journal of Logic Programming, 5:93–132, (1988).
Meseguer, J., General Logics, In: Ebbinghaus H.-D. et al. (eds), Logic Colloquium’87, North-Holland, 275–329, (1989).
Meseguer, J., Multiparadigm Logic Programming, In: Proccedings of ALP’92, L.N.C.S. 632. Springer-Verlag, 158–200, (1992).
Miller, D., A Logical Analysis of Modules in Logic Programming, In: Journal of Logic Programming, 6:79–108, (1989).
Miller, D., Abstraction in Logic Programs. In: Odifreddi, P. (ed), Logic and Computer Science, Academic Press, 329–359, (1990).
Miller, D., Nadathur, G., Pfenning, F. and Scedrov, A., Uniform Proofs as a Foundation for Logic Programming, Annals of Pure and App. Logic, 51:125–157, (1991).
Monteiro, L., Porto, A., Contextual Logic Programmming, In: Proc. 6th International Conf. on Logic Programming, 284–299, (1989).
Moscowitz, Y., and Shapiro, E., Lexical logic programs, In: Proc. 8th International Conf. on Logic Programming, 349–363, (1991).
van Dalen, D., and Troelstra, Constructivism in Mathematics: An Introduction Vol.1 and Vol.2, Elsevier Science, North-Holland, (1988).
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Arruabarrena, R., Lucio, P., Navarro, M. (1999). A Strong Logic Programming View for Static Embedded Implications. In: Thomas, W. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 1999. Lecture Notes in Computer Science, vol 1578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49019-1_5
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