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semantic properties

Theory and Practice of Logic Programming (1)

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Order-consistent programs are cautiously monotonic
HUDSON TURNER
Journal:

Theory and Practice of Logic Programming / Volume 1 / Issue 4 / July 2001

Published online by Cambridge University Press:

25 June 2001, pp. 487-495
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Some normal logic programs under the answer set (or 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 program with some of its consequences does not alter its consequences. In fact, as we show, its answer sets remain unchanged.