Abstract
It is clearly desirable that logical specifications and the programs that implement them should be as close as possible. Such a claim is often made in support of the logic programming paradigm. However, SLD-resolution, the basic procedural semantics for logic programming, is only defined for programs whose statements are Horn clauses. Most research for extending the Horn clause framework has been concerned with allowing negative literals in the bodies of the statements where SLD-resolution is extended with negation-as-failure. However, one of the main components of first order logic not allowed in clauses is (explicit) quantification. This paper addresses this problem by showing how SLD-resolution can be extended to allow for universally quantified implication formulas as conjuncts in the body of the statements. It will be shown that this technique includes negation-as-failure as a degenerate case.
P.M. Hill and F. Ibañez were supported by EPSRC grant GR/H/79862
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References
K.R. Apt. Arrays, bounded quantification and iteration in logic and constraint programming. In Proc. of GULP-PRODE'95 Salerno, Italy, 1995.
K.R. Apt and H.C. Doets. A new definition of SLDNF-resolution. Journal of Logic Programming, 18(2):177–190, 1992.
H. Arro, J. Barklund, and J. Bevemyr. Parallel bounded quantification-preliminary results. ACM SIGPLAN Notices, 28(5):117–124, August 1993.
J. Barklund. Bounded quantifications for iterations and concurrency in logic programming. New Generation Computing, 12(2), 1994.
J. Barklund and J. Bevemyr. Prolog with arrays and bounded quantification. In Logic Programming and Automated Reasoning (LPAR'93). Springer-Verlag, 1993.
J. Barklund and J. Bevemyr. Executing bounded quantifications on shared memory multiprocessors. PLILP, LNCS 714, pages 302–317, 1993. Springer-Verlag.
M. Carlsson and J. Widén. SICStus Prolog user's manual. Technical Report 6R88007C, Swedish Institute of Computer Science, 1991.
K.L. Clark. Negation as failure. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 293–322. Plenum Press, 1978.
P.M. Hill and J.W. Lloyd. The Gödel Programming Language. MIT Press, 1994.
J.W. Lloyd and R.W. Topor. Making Prolog more expressive. Journal of Logic Programming, 1(3):225–240, 1984.
J.W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 2nd ed., 1987.
J.W. Lloyd and J.C. Shepherdson. Partial evaluation in logic programming. The Journal of Logic Programming, 11(3&4):217–242, 1991.
J.W. Lloyd. Programming in an integrated functional and logic language. Journal of Functional and Logic Programming, 1997. To appear.
G. Nadathur. A proof procedure for the logic of hereditary harrop formulas. Journal of Automated Reasoning, 11:115–145, 1993.
T. Sato and H. Tamaki. First order compiler: A deterministic logic program synthesis algorithm. Journal of Symbolic Computation, 8:605–627, 1988.
R. D. Tennent. Semantics of Programming Languages. Prentice-Hall, 1991.
A. Voronkov. Logic programming with bounded quantifiers. In A. Voronkov, editor, Logic Programming — 2nd Russian Conf. on Logic Programming, pages 486–514. Springer-Verlag, 1992.
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Bowers, A.F., Hill, P.M., Ibañez, F. (1997). Resolution for logic programming with universal quantifiers. In: Glaser, H., Hartel, P., Kuchen, H. (eds) Programming Languages: Implementations, Logics, and Programs. PLILP 1997. Lecture Notes in Computer Science, vol 1292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033837
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DOI: https://doi.org/10.1007/BFb0033837
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