Programs with Negation

Our next goal is to extend the definition of a stable model from Sect. 4.4 to propositional programs that contain negation, and to apply this generalization to clingo programs with negation and choice. We begin with an informal discussion of a few examples.

[1]  Vladimir Lifschitz,et al.  Thirteen Definitions of a Stable Model , 2010, Fields of Logic and Computation.

[2]  Alfred Tarski,et al.  The Sentential Calculus with Infinitely Long Expressions , 1958 .

[3]  Miroslaw Truszczynski,et al.  Connecting First-Order ASP and the Logic FO(ID) through Reducts , 2012, Correct Reasoning.

[4]  Michael Gelfond,et al.  Classical negation in logic programs and disjunctive databases , 1991, New Generation Computing.

[5]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[6]  Robert C. Moore Semantical Considerations on Nonmonotonic Logic , 1985, IJCAI.

[7]  Michael Gelfond,et al.  On Stratified Autoepistemic Theories , 1987, AAAI.

[8]  Christine Froidevaux,et al.  Minimalism subsumes Default Logic and Circumscription in Stratified Logic Programming , 1987, LICS.

[9]  Vladimir Lifschitz,et al.  Splitting a Logic Program , 1994, ICLP.

[10]  Martin Gebser,et al.  Abstract gringo , 2015, Theory Pract. Log. Program..

[11]  K. Fine The Justification of Negation as Failure , 1989 .

[12]  Vladimir Lifschitz,et al.  Weight constraints as nested expressions , 2003, Theory and Practice of Logic Programming.

[13]  Erwin Engeler,et al.  Languages with expressions of infinite length , 1966 .

[14]  I. Niemelä,et al.  Extending the Smodels system with cardinality and weight constraints , 2001 .

[15]  Vladimir Lifschitz,et al.  Nested expressions in logic programs , 1999, Annals of Mathematics and Artificial Intelligence.