Abstract
We consider logic programming-like systems which are based on solving equations in a given structure as opposed to obtaining unifiers. While such systems are elegant from an operational point of view, a logical interpretation of the programs is not always apparent. In this paper, we restrict ourselves to the class of structures ℜ satisfying the eliminable variable property: we can construct an explicit definition, in the form of one system of equations, of the set of solutions to any ℜ-solvable system of equations. Correspondingly, we consider only the class of equality theories E such that every E-unifiable system of equations has an E-mgu. We then state three properties which provide basic relationships between E and ℜ. We prove that their satisfaction establishes an equivalence between a program considered as an equation solving engine (with respect to a structure) and the program considered as a logic program (with respect to a corresponding equality theory). A logical basis for these programs is thus given.
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6. References
K.L. Clark, "Negation as Failure", in Logic and Databases, H. Gallaire and J. Minker (Eds.), Plenum Press, New York, pp 293–322, 1978.
A. Colmerauer, "PROLOG II — Reference Manual and Theoretical Model", Internal Report, Groupe Intelligence Artificielle, Universite Aix-Marseille II, October 1982.
A. Colmerauer, "Equations and Inequations on Finite and Infinite Trees", Proc. 2nd. Int. Conf. on Fifth Generation Computer Systems, Tokyo, pp 85–99, November 1984.
J. Jaffar, J-L. Lassez and M.J. Maher, "A Logical Foundation for PROLOG II", Technical Report 44, Dept. of Computer Science, Monash University, December 1984. [Revised November 1985]
J. Jaffar, J-L. Lassez and M.J. Maher, "A Logic Programming Language Scheme", in Logic Programming: Relations, Functions and Equations, D. DeGroot and G. Lindstrom (Eds), Prentice-Hall, 1985.
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© 1986 Springer-Verlag Berlin Heidelberg
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Jaffar, J., Stuckey, P.J. (1986). Logic program semantics for programming with equations. In: Shapiro, E. (eds) Third International Conference on Logic Programming. ICLP 1986. Lecture Notes in Computer Science, vol 225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16492-8_84
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DOI: https://doi.org/10.1007/3-540-16492-8_84
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