Abstract
Various proof methods have been proposed to solve the implication problem, i.e. proving that properties of the form: ∀(P → Q) - where P and Q denote conjunctions of atoms - are logical consequences of logic programs. Nonetheless, it is a commonplace to say that it is still quite a difficult problem. Besides, the advent of the constraint logic programming scheme constitutes not only a major step towards the achievement of efficient declarative logic programming systems but also a new field to explore. By recasting and simplifying the implication problem in the constraint logic programming framework, we define a generic proof method for the implication problem, which we prove sound from the algebraic point of view. We present four examples using CLP(ℕ), CLP(RT), CLP(Σ*) and RISC- CLP(RɛAℒ). The logical point of view of the constraint logic programming scheme enables the automation of the proof method. At last, we prove the unsolvability of the implication problem, we point out the origins of the incompleteness of the proposed proof method and we identify two classes of programs for which we give a decision procedure for the implication problem.
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References
A. Aiba, A. Sakai, Y. Sato, D.J. Hawley, and R. Hasegawa. Constraint logic programming language CAL. Proc. of FGCS’88, pages 263–276, 1988.
K.L. Clark. Predicate logic as a computational formalism. Technical Report Doc 79/59, Logic Programming Group, Imperial College, London, 1979.
A. Colmerauer. Equations and inequations on finite and infinite trees. Proc. of FGCS’84, pages 85–99, 1984.
A. Colmerauer. An introduction to Prolog III. CACM, 33 (7):70–90, July 1990.
L. Colussi and E. Marchiori. Proving correctness of logic programs using axiomatic semantics. In Logic Programming - Proceedings of 8th International Conference, pages 629–642. MIT press, 1991.
Contejean. Solving linear diophantine constraints incrementally. Proc. of ICLP’93, 1993.
P. Deransart. Proof methods of declarative properties of definite programs. Theoretical Computer Science, pages 99–166, 1993.
M. Dincbas, P. Van Hentenrick, H. Simonis, A. Aggoun, T. Graf, and F. Berthier. The constraint logic programming language CHIP. Proc. of FGCS’88, pages 693–702, 1988.
L. Fribourg and M. Veloso Peixoto. Bottom-up evaluation of datalog programs with arithmetic constraints: The case of 3 recursive rules. Technical report, L.I.E.N.S, France, 1994.
R. Giacobazzi, S.K. Debray, and G. Levi. A generalized semantics for constraint logic programs. Proc. of FGCS’92, pages 581–591, 1992.
S. Grigorieif. Décidabilité et complexité des théories logiques. Logique et Informatique: une introduction, Collection Didactique, INRIA, pages 7–97, 1989.
D. Hofstadter. Godel, Escher, Bach: an Eternal Golden Braid. Basic Books, Inc., 1979.
H. Hong. Non-linear real constraints in constraint logic programming. In LNCS 632, pages 201–212. Springer Verlag, 1992.
J. Jaffar and J.L. Lassez. Constraint logic programming. Technical Report 74, Monach University, Australia, 1986.
J. Jaffar and M.J. Maher. Constraint logic programming: asurvev. J. Logic Programming, pages 503–581, 1994.
J. Jaffar, S. Michaylov, P.J. Stuckey, and R.H.C. Yap. The CLP(R) language and system. Proc. of the 4th ICLP, 1987.
P.T. Johnstone. Notes on logic and set theory. Cambridge mathematical textbooks. Cambridge University Press, 1986.
T. Kanamori and H. Fujita. Formulation of induction formulas in verification of prolog programs. Proc. of the 8th CADE, pages 281–299, 1986.
J.M. Lever. Proving program properties by means of SLS-resolution. Proc. of the 8th ICLP, pages 614–628, 1991.
J.W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 1987.
Z. Manna. Mathematical theory of computation. McGraw-Hill, 1974.
F. Mesnard et al. CLP(Q) for proving interargument relations. In LNCS 649, pages 308–320. Springer Verlag, 1992.
M.L. Minsky. Recursive unsolvability of post’s problem of ‘tag’ and other topics in the theory of Turing machines. Ann. of Math., 74:437–455, 1961.
S. Renault. Generalized extended execution for normal programs. In LNCS 883. Springer Verlag, 1994.
J.C. Shepherdson. Unsolvable problems for SLDNF resolution. J. Logic Programming, pages 19–22, 1991.
C. Walinsky. CLP(Σ*): Constraint logic programming with regular sets. Proc. of the 6th ICLP, pages 181–196,1989.
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Mesnard, F., Horau, S., Maillard, A. (1996). CLP(x) for Proving Program Properties. In: Baader, F., Schulz, K.U. (eds) Frontiers of Combining Systems. Applied Logic Series, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0349-4_17
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DOI: https://doi.org/10.1007/978-94-009-0349-4_17
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