The Witness Properties and the Semantics of the Prolog Cut

TL;DR

This paper investigates the semantics of the Prolog cut, proposing a restricted system that maintains useful behavior while satisfying desirable logical properties, thus balancing power and internal consistency.

Contribution

It introduces a restricted version of Prolog with cut that preserves key behaviors and satisfies the witness properties, enhancing logical consistency.

Findings

The restricted system preserves first-solution behavior of cut.

It does not have the witness properties in its general form.

The semantics of the restricted system connect more deeply to logic.

Abstract

The semantics of the Prolog ``cut'' construct is explored in the context of some desirable properties of logic programming systems, referred to as the witness properties. The witness properties concern the operational consistency of responses to queries. A generalization of Prolog with negation as failure and cut is described, and shown not to have the witness properties. A restriction of the system is then described, which preserves the choice and first-solution behaviour of cut but allows the system to have the witness properties. The notion of cut in the restricted system is more restricted than the Prolog hard cut, but retains the useful first-solution behaviour of hard cut, not retained by other proposed cuts such as the ``soft cut''. It is argued that the restricted system achieves a good compromise between the power and utility of the Prolog cut and the need for internal consistency in logic programming systems. The restricted system is given an abstract semantics, which depends on the witness properties; this semantics suggests that the restricted system has a deeper connection to logic than simply permitting some computations which are logical. Parts of this paper appeared previously in a different form in the Proceedings of the 1995 International Logic Programming Symposium.