Order-consistent programs are cautiously monotonic

TL;DR

This paper proves that order-consistent normal logic programs are cautiously monotonic, meaning adding consequences does not change their answer sets, thus ensuring stability and cumulative behavior.

Contribution

It establishes that order-consistent programs are not only consistent but also cautiously monotonic, a property previously unproven for this class.

Findings

Order-consistent programs are cautiously monotonic.

Adding consequences to order-consistent programs does not change their answer sets.

Order-consistent programs are also cumulative.

Abstract

Some normal logic programs under the answer set (stable model) semantics lack the appealing property of "cautious monotonicity." That is, augmenting a program with one of its consequences may cause it to lose another of its consequences. The syntactic condition of "order-consistency" was shown by Fages to guarantee existence of an answer set. This note establishes that order-consistent programs are not only consistent, but cautiously monotonic. From this it follows that they are also "cumulative." That is, augmenting an order-consistent with some of its consequences does not alter its consequences. In fact, as we show, its answer sets remain unchanged.