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.
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