Integrating Interval Constraints into Logic Programming

The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear programs (giving CLP(R)). In this paper we develop a form of CSP for interval constraints. In this way one obtains a logic semantics for the efficient floating-point hardware that is available on most computers. The need for the method arises because in the practice of scheduling and engineering design it is not enough to solve a single CSP. Ideally one should be able to consider thousands of CSPs and efficiently solve them or show them to be unsolvable. This is what CLP/NCSP, the new subscheme of CLP described in this paper is designed to do.

💡 Research Summary

The paper presents a novel extension to the Constraint Logic Programming (CLP) framework by integrating interval constraints, thereby creating a new sub‑scheme called CLP/NCSP (Numerical CSP). Traditional CLP schemes, such as rational‑tree based Prolog and CLP(R), rely on Horn clauses and SLD resolution to generate constraint satisfaction problems (CSPs). While CLP(R) handles linear equations and linear programming using real‑number arithmetic, it does not directly model the inherent approximation of floating‑point hardware. The authors address this gap by introducing interval constraints, which represent each variable’s possible values as a lower and upper bound. Arithmetic operations on intervals produce new intervals, and interval propagation (or narrowing) reduces domains by intersecting constraints. When an empty interval is generated, the system immediately fails, pruning large portions of the search space.

CLP/NCSP retains the declarative syntax of ordinary CLP programs; interval constraints are expressed with simple annotations such as “X in