Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
ASSAT: computing answer sets of a logic program by SAT solvers
Artificial Intelligence - Special issue on nonmonotonic reasoning
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
Annals of Mathematics and Artificial Intelligence
Semantical characterizations and complexity of equivalences in answer set programming
ACM Transactions on Computational Logic (TOCL)
Propositional theories are strongly equivalent to logic programs
Theory and Practice of Logic Programming
A common view on strong, uniform, and other notions of equivalence in answer-set programming*
Theory and Practice of Logic Programming
Guarded hybrid knowledge bases12
Theory and Practice of Logic Programming
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Discovering classes of strongly equivalent logic programs
Journal of Artificial Intelligence Research
A new perspective on stable models
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Modularity aspects of disjunctive stable models
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
A characterization of strong equivalence for logic programs with variables
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Clasp: a conflict-driven answer set solver
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Quantified equilibrium logic and hybrid rules
RR'07 Proceedings of the 1st international conference on Web reasoning and rule systems
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Theory and Practice of Logic Programming
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In Answer-Set Programming different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied and characterized by various selections of models in the logic of Here-and-There (HT). For uniform equivalence however, correct characterizations in terms of HT-models can only be obtained for finite theories, respectively programs. In this paper, we show that a selection of countermodels in HT captures uniform equivalence also for infinite theories. This result is turned into coherent characterizations of the different notions of equivalence by countermodels, as well as by a mixture of HT-models and countermodels (so-called equivalence interpretations), which are lifted to first-order theories under a very general semantics given in terms of a quantified version of HT. We show that countermodels exhibit expedient properties like a simplified treatment of extended signatures, and provide further results for non-ground logic programs. In particular, uniform equivalence coincides under open and ordinary answer-set semantics, and for finite non-ground programs under these semantics, also the usual characterization of uniform equivalence in terms of maximal and total HT-models of the grounding is correct, even for infinite domains, when corresponding ground programs are infinite.