Interval computation as deduction in chip

Abstract

Logic programming realizes the ideal of “computation is deduction,” but not when floating-point numbers are involved. In that respect logic programming languages are as careless as conventional computation: they ignore the fact that floating-point operations are only approximate and that it is not easy to tell how good the approximation is. It is our aim to extend the benefits of logic programming to computation involving floating-point arithmetic. Our starting points are the ideas of Cleary and the CHIP programming language. Cleary proposed a relational form of interval arithmetic that was incorporated in BNR Prolog in such a way that variables already bound can be bound again. In this way the usual logical interpretation of computation no longer holds. In this paper we develop a technique for narrowing intervals that we relate both to Cleary's work and to the constraint-satisfaction techniques of artificial intelligence. We then modify CHIP by allowing domains to be intervals of real numbers. To reduce arithmetic primitives with interval domains, we use our interval narrowing technique as an implementation of the looking-ahead inference rule. We show that the result is a system where answers are logical consequences of a declarative logic program, even when floating-point computations have been used. We believe ours is the first system with this property.