Is there an Axiomatic Semantics for Standard Pure Prolog

Abstract Many studies [1, 7, 20, 21, 26, 28] have shown the soundness and completeness of SLD-resolution and of the finite failure rule for a definite program. This semantics corresponds to the operational semantics of an (ideal) Prolog system, i.e. which only generates fair SLD-trees and employs a breadth-first search rule. Unfortunately, the Prolog systems currently used may generate non-fair SLD-trees and employ a depth-first-left-right strategy which is no longer complete. For these standard Prolog implementations, the operational semantics of a program depends not only on its logic content but also on the way it is written. In this work, we introduce two systems of axioms associated to a definite program P : • the finite standard translation Ax fst which provides a logic characterization of the finite operational semantics of a definite program P computed by a Standard Prolog System and does not depend on the ordering given to the clauses in the program P . • the finite invariant translation Ax f which gives a logic characterization of the success and the failures of P , all SLD-trees of which are finite. This translation does not depend on the ordering given to the clauses in the program and to the atoms in each clause.