Abstract
The aim of our work is the definition of a model-theoretic semantics of normal logic programs with embedded implications. We first propose a quite simple operational semantics for this class of programs whose negation mechanism is the constructive negation. This semantics is used to prove the adequacy of the model-theoretic semantics. Then we define a declarative semantics for this class of programs in terms of Beth models and show that in the model class associated to every program there is a least model that can be seen as the semantics of the program, which may be built upwards as the least fixpoint of a continuous immediate consequence operator. Finally, it is proved that the operational semantics is sound and complete with respect to the least fixpoint semantics.
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References
A. J. Bonner and L. T. McCarty. Adding negation-as-failure to intuitionistic logic programming. In Proc. of the North American Conf. on Logic Programming, 681–703, 1990.
M. Bugliesi, E. Lamma, and Mello Paola. Modularity in logic programming. Journal of Logic Programming, 19,20:443–502, 1994.
W. Drabent. What is a failure? An approach to constructive negation. Acta Informática, 32:27–59, 1995.
S. Etalle and F. Teusink. A compositional semantics for normal open programs. In Proc. Int. Conf. and Symp. on Logic Programming’96. The MIT Press, 1996.
F. Fages. Constructive negation by pruning. J. of Logic Programming, 32:85–118, 1997.
G. Ferrand and A. Lallouet. A compositional proof method of partial correctness for normal logic programs. In Int. Logic Programming Symp., pages 209–223. J. Lloyd, ed., 1995.
L. Giordano and N. Olivi. Combining negation as failure and embedded implication in logic programs. Journal of Logic Programming, (36):91–147, 1998.
P. Lucio, F. Orejas, and E. Pino. An algebraic framework for the definition of compositional semantics of normal logic programs. Journal of Logic Programming, 40:89–123, 1999.
D. Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, 6:79–108, 1989.
F. Orejas, E. Pino, and H. Ehrig. Institutions for logic programming. Theoretical Computer Science, 173:485–511, 1997.
E. Pasarella, E. Pino, and F. Orejas. Constructive negation without subsidiary trees. In Alpuente M., editor, Proceedings of the 9th International Workshop on Functional and Logic Programming, WFLP’2000., pages 195–209, 2000.
J.C. Shepherson. Negation in logic programming. In J. Minker, editor, Foundations on Deductive Databases and Logic Programs, pages 19–88. Morgan Kaufmann, 1988.
P. J. Stuckey. Negation and constraint logic programmming. Information and Computation, 118:12–23, 1995.
D. van Dalen. Intuitionistic logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic-Vol III, 1986.
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Orejas, F., Pasarella, E., Pino, E. (2001). Semantics of Normal Logic Programs with Embedded Implications. In: Codognet, P. (eds) Logic Programming. ICLP 2001. Lecture Notes in Computer Science, vol 2237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45635-X_25
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DOI: https://doi.org/10.1007/3-540-45635-X_25
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