Order-consistent programs are cautiously monotonic
<|reference_start|>Order-consistent programs are cautiously monotonic: 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.<|reference_end|>
@article{turner2000order-consistent,
    title={Order-consistent programs are cautiously monotonic},
    author={Hudson Turner},
    journal={arXiv preprint arXiv:cs/0011042},
    year={2000},
    archivePrefix={arXiv},
    eprint={cs/0011042},
    primaryClass={cs.LO cs.AI}
}