Integrating Interval Constraints into Logic Programming

TL;DR

This paper introduces CLP/NCSP, a new logic programming scheme that integrates interval constraints to efficiently handle and solve large sets of constraint satisfaction problems, especially useful in scheduling and engineering design.

Contribution

It develops a form of CSP for interval constraints within logic programming, enabling efficient handling of multiple CSPs for practical applications.

Findings

Developed a logic semantics for interval constraints.

Enabled efficient solving of thousands of CSPs.

Applicable to scheduling and engineering design problems.

Abstract

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.