A geometric interpretation of LD-resolution

Authors:
R. N. Banerjee;A. Bujosa
Affiliations:
Applied Mathematics Department, Escuela Técnica Superior de Ingenieros de Telecomunicación, Ciudad Universitaria s/n, 28040 Madrid, Spain;Applied Mathematics Department, Escuela Técnica Superior de Ingenieros de Telecomunicación, Ciudad Universitaria s/n, 28040 Madrid, Spain
Venue:
Theoretical Computer Science - Logic, semantics and theory of programming
Year:
2004

Citing 14
Cited 0

Foundations of logic programming; (2nd extended ed.)

Foundations of logic programming; (2nd extended ed.)
Fractals everywhere

Fractals everywhere
Unification revisited

Foundations of deductive databases and logic programming
Dynamical systems, measures, and fractals via domain theory

Information and Computation
Syntactic elements of declarative programming: symbolic linear equations

Fundamenta Informaticae
Unification: nothing but the solution of a system of linear equations

Fundamenta Informaticae
Continuation-Based Program Transformation Strategies

Journal of the ACM (JACM)
Universal Algebra, Algebraic Logic, and Databases

Universal Algebra, Algebraic Logic, and Databases
Programming in PROLOG

Programming in PROLOG
Vectorial Equations Solving for Mechanical Geometry Theorem Proving

Journal of Automated Reasoning
Elementary Logic Programs

PLILP '90 Proceedings of the 2nd International Workshop on Programming Language Implementation and Logic Programming
Implementing Term Algebra Syntactic Unification in Free Modules over Certain Rings

FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
Generalized metrics and uniquely determined logic programs

Theoretical Computer Science - Topology in computer science
Strictly level-decreasing logic programs

IW-FM'98 Proceedings of the 2nd Irish conference on Formal Methods

Quantified Score

Hi-index	0.00

Visualization

Abstract

We devise an interpretation of a binarised definite logic program in a geometric framework which is closer to Dynamical Systems than to Logic. The building blocks of our framework are a family of affine sub-modules in a free finitely generated module over a special kind of ring. We describe SLD-resolution of definite binary programs as the iterated action of a finite union of affine graphs, associated to the program clauses, on a certain set of affine varieties associated to the original syntactic terms. This action is shown to faithfully represent the running of the corresponding program on a given goal, since all answers and only those answers the program would output are obtained. Hence, a programming language such as pure Prolog completely falls within our description.