A Transformation-based Implementation for CLP with Qualification and Proximity

Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical LP paradigm. However, few of these are designed as extensions of the well-established and powerful CLP scheme for Constraint Logic Programming. In a previous work we have proposed the SQCLP ({\em proximity-based qualified constraint logic programming}) scheme as a quite expressive extension of CLP with support for qualification values and proximity relations as generalizations of uncertainty values and similarity relations, respectively. In this paper we provide a transformation technique for transforming SQCLP programs and goals into semantically equivalent CLP programs and goals, and a practical Prolog-based implementation of some particularly useful instances of the SQCLP scheme. We also illustrate, by showing some simple—and working—examples, how the prototype can be effectively used as a tool for solving problems where qualification values and proximity relations play a key role. Intended use of SQCLP includes flexible information retrieval applications.

💡 Research Summary

The paper addresses the integration of uncertainty handling into the well‑established Constraint Logic Programming (CLP) paradigm by focusing on the SQCLP scheme—“proximity‑based qualified constraint logic programming.” SQCLP enriches classical CLP with two orthogonal extensions: (i) qualification values, which generalize probabilistic or possibilistic measures and are combined using operations such as multiplication or minimum, and (ii) proximity relations, which generalize similarity relations by satisfying a triangular inequality and can be interpreted as distance functions between symbols. These extensions are particularly useful in applications where both the degree of confidence and the “closeness” of terms matter, for instance in flexible information retrieval, natural‑language processing, or image labeling.

Because standard CLP systems do not natively support qualification values or proximity constraints, the authors propose a transformation‑based implementation technique. The transformation proceeds in two systematic steps. First, each clause of an SQCLP program is augmented with an extra argument that carries the qualification value. This argument is computed by applying the appropriate qualification operation to the value inherited from the body and the value introduced by the head. Second, every proximity relation p(a,b) is replaced by a CLP constraint that enforces a distance bound d(a,b) ≤ ε, where ε is a user‑defined tolerance. The distance function d can be instantiated with any metric suitable for the domain (e.g., Euclidean distance on vector embeddings). By encoding proximity as ordinary CLP constraints, the transformed program can be executed by any off‑the‑shelf CLP engine without modification.

The authors formally prove that the transformation is semantics‑preserving. Two theorems are presented: (1) for any original SQCLP clause there exists a transformed CLP clause that yields exactly the same logical consequences together with identical qualification values, and (2) for any goal the set of solutions (including their qualification and proximity information) is unchanged after transformation. The proofs rely on structural induction over program clauses and on the soundness of the underlying constraint solver.

A prototype implementation is built on top of SICStus Prolog and SWI‑Prolog. Qualification values are represented as real numbers in the interval