Numerical computation as deduction in constraint logic programming




Lee, Jimmy Ho Man

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Logic programming realizes the ideal of "computation as deduction," except when floating-point arithmetic is involved. In that respect, logic programming languages suffer the same deficiency as conventional algorithmic languages: floating-point operations are only approximate and it is not easy to tell how good the approximation is. This dissertation proposes a framework to extend the benefits of logic programming to computations involving floating-point arithmetic. John Cleary incorporated a relational form of interval arithmetic into Prolog so that variables already bound can be bound again. In this way, the usual logical interpretation of computation no longer holds. Based on Cleary's idea, we develop a technique for narrowing intervals. We present a relaxation algorithm for coordinating the applications of the interval narrowing operations to constraints in a network. We incorporate relational interval arithmetic into two constraint logic programming languages: CHIP and CLP(R). We modify CHIP by allowing domains to be intervals of real numbers. In CLP(R) we represent intervals by inequality constraints. The enhanced languages ICHIP and ICLP(R) preserve the semantics of logic so that numerical computations are deductions, even when floating-point arithmetic is used. We have constructed a prototype of ICLP(R) consisting of a meta-interpreter executed by an existing CLP(R) system. We show that interval narrowing belongs to the class of domain restriction operations in constraint-satisfaction algorithms. To establish a general framework for these operations, we use and generalize Ashby's notions of cylindrical closure and cylindrance. We show that Mackworth's algorithms can be placed in our framework.



Logic programming, Numerical calculations, Computer programs