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Principles of database and knowledge-base systems, Vol. I
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On the declarative semantics of deductive databases and logic programs
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Nonmonotonic Logic II: Nonmonotonic Modal Theories
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Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
Nested expressions in logic programs
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The Magic of Duplicates and Aggregates
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ASSAT: computing answer sets of a logic program by SAT solvers
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Theory and Practice of Logic Programming
A reductive semantics for counting and choice in answer set programming
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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Conflict-driven answer set solving
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ICLP '08 Proceedings of the 24th International Conference on Logic Programming
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Logic programming, knowledge representation, and nonmonotonic reasoning
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Aggregates in answer set optimization
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First-Order encodings for modular nonmonotonic datalog programs
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
The disjunctive datalog system DLV
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Unfounded sets and well-founded semantics of answer set programs with aggregates
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Conflict-driven answer set solving: From theory to practice
Artificial Intelligence
First-order extension of the FLP stable model semantics via modified circumscription
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Look-back Techniques for ASP Programs with Aggregates
Fundamenta Informaticae
Simulating production rules using ACTHEX
Correct Reasoning
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Correct Reasoning
Well-Supported semantics for logic programs with generalized rules
Correct Reasoning
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Exploiting unfounded sets for HEX-Program evaluation
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
Conflict-driven asp solving with external sources
Theory and Practice of Logic Programming
Tableau Calculi for Logic Programs under Answer Set Semantics
ACM Transactions on Computational Logic (TOCL)
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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Annals of Mathematics and Artificial Intelligence
Answer set programming: language, applications and development tools
RR'13 Proceedings of the 7th international conference on Web Reasoning and Rule Systems
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Nested Weight Constraints in ASP
Fundamenta Informaticae - Special Issue on the Italian Conference on Computational Logic: CILC 2011
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The addition of aggregates has been one of the most relevant enhancements to the language of answer set programming (ASP). They strengthen the modelling power of ASP in terms of natural and concise problem representations. Previous semantic definitions typically agree in the case of non-recursive aggregates, but the picture is less clear for aggregates involved in recursion. Some proposals explicitly avoid recursive aggregates, most others differ, and many of them do not satisfy desirable criteria, such as minimality or coincidence with answer sets in the aggregate-free case. In this paper we define a semantics for programs with arbitrary aggregates (including monotone, antimonotone, and nonmonotone aggregates) in the full ASP language allowing also for disjunction in the head (disjunctive logic programming - DLP). This semantics is a genuine generalization of the answer set semantics for DLP, it is defined by a natural variant of the Gelfond-Lifschitz transformation, and treats aggregate and non-aggregate literals in a uniform way. This novel transformation is interesting per se also in the aggregate-free case, since it is simpler than the original transformation and does not need to differentiate between positive and negative literals. We prove that our semantics guarantees the minimality (and therefore the incomparability) of answer sets, and we demonstrate that it coincides with the standard answer set semantics on aggregate-free programs. Moreover, we carry out an in-depth study of the computational complexity of the language. The analysis pays particular attention to the impact of syntactical restrictions on programs in the form of limited use of aggregates, disjunction, and negation. While the addition of aggregates does not affect the complexity of the full DLP language, it turns out that their presence does increase the complexity of normal (i.e., non-disjunctive) ASP programs up to the second level of the polynomial hierarchy. However, we show that there are large classes of aggregates the addition of which does not cause any complexity gap even for normal programs, including the fragment allowing for arbitrary monotone, arbitrary antimonotone, and stratified (i.e., non-recursive) nonmonotone aggregates. The analysis provides some useful indications on the possibility to implement aggregates in existing reasoning engines.