Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
Journal of Logic Programming
A logic of knowledge and justified assumptions
Artificial Intelligence
Handbook of logic in artificial intelligence and logic programming (vol. 3)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Reasoning with infinite stable models
Artificial Intelligence
ASSAT: computing answer sets of a logic program by SAT solvers
Artificial Intelligence - Special issue on nonmonotonic reasoning
A generalization of the Lin-Zhao theorem
Annals of Mathematics and Artificial Intelligence
Elementary sets for logic programs
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Loop formulas for logic programs with arbitrary constraint atoms
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Properties and applications of programs with monotone and convex constraints
Journal of Artificial Intelligence Research
A new perspective on stable models
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
A model-theoretic counterpart of loop formulas
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Loop formulas for circumscription
Artificial Intelligence
Circumscriptive event calculus as answer set programming
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A semantical framework for hybrid knowledge bases
Knowledge and Information Systems
Stable models and circumscription
Artificial Intelligence
From answer set logic programming to circumscription via logic of GK
Artificial Intelligence
Loop-separable programs and their first-order definability
Artificial Intelligence
Integrating rules and ontologies in the first-order stable model semantics
LPNMR'11 Proceedings of the 11th international conference on Logic programming and nonmonotonic reasoning
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
On elementary loops of logic programs
Theory and Practice of Logic Programming
Journal of Artificial Intelligence Research
First-order expressibility and boundedness of disjunctive logic programs
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Lin and Zhao's theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the first-order case. We investigate the precise relationship between the first-order stable model semantics and first-order loop formulas, and study conditions under which the former can be represented by the latter. In order to facilitate the comparison, we extend the definition of a first-order loop formula which was limited to a nondisjunctive program, to a disjunctive program and to an arbitrary first-order theory. Based on the studied relationship we extend the syntax of a logic program with explicit quantifiers, which allows us to do reasoning involving non-Herbrand stable models using first-order reasoners. Such programs can be viewed as a special class of first-order theories under the stable model semantics, which yields more succinct loop formulas than the general language due to their restricted syntax.