says: choose arbitrarily which of the atoms <math>p,q,r</math> to include in the stable model. The lparseLparse program that contains this choice rule and no other rules has 8 stable models—arbitrary subsets of <math>\{p,q,r\}</math>. The definition of a stable model was generalized to programs with choice rules.<ref>{{cite book |first1=I. |last1=Niemelä |first2=P. |last2=Simons |first3=T. |last3=Soinenen |chapter=Stable model semantics of weight constraint rules |editor1-first=Michael |editor1-last=Gelfond |editor2-first=Nicole |editor2-last=Leone |editor3-first=Gerald |editor3-last=Pfeifer |title=Logic Programming and Nonmonotonic Reasoning: 5th International Conference, LPNMR '99, El Paso, Texas, USA, December 2–4, 1999 Proceedings |chapter-url=https://books.google.com/books?id=Abj-OpFeDjQC&pg=PA317 |year=2000 |publisher=Springer |isbn=978-3-540-66749-0 |pages=317–331 |series=Lecture Notes in Computer Science: Lecture Notes in Artificial Intelligence |volume=1730}} [http://www.tcs.hut.fi/~ini/papers/nss-lpnmr99-www.ps.gz as Postscript]</ref> Choice rules can be treated also as abbreviations for [[Stable model semantics#Stable models of a set of propositional formulas|propositional formulas under the stable model semantics]].<ref>{{cite journal |first1=P. |last1=Ferraris |first2=V. |last2=Lifschitz |title=Weight constraints as nested expressions |journal=Theory and Practice of Logic Programming |volume=5 |issue=1–2 |pages=45–74 |date=January 2005 |doi=10.1017/S1471068403001923 |arxiv=cs/0312045 }} [http://www.cs.utexas.edu/users/vl/papers/weight.ps as Postscript]</ref> For instance, the choice rule above can be viewed as shorthand for the conjunction of three "[[excluded middle]]" formulas:
The language of lparseLparse allows us also to write "constrained" choice rules, such as
<syntaxhighlight lang="prolog">
Line 187:
===Large clique===
A [[Clique (graph theory)|clique]] in a graph is a set of pairwise adjacent vertices. The following lparseLparse program finds a clique of size <math>\geq n</math> in a given graph, or determines that it does not exist:
