Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
ACM Transactions on Database Systems (TODS)
Complexity and expressive power of logic programming
ACM Computing Surveys (CSUR)
Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
Representing Knowledge in A-Prolog
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
ASSAT: computing answer sets of a logic program by SAT solvers
Eighteenth national conference on Artificial intelligence
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
A Constructive semantic characterization of aggregates in answer set programming
Theory and Practice of Logic Programming
Well-founded and stable semantics of logic programs with aggregates
Theory and Practice of Logic Programming
A uniform integration of higher-order reasoning and external evaluations in answer-set programming
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Heuristics for hard ASP programs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Answer sets for propositional theories
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
Effective integration of declarative rules with external evaluations for semantic-web reasoning
ESWC'06 Proceedings of the 3rd European conference on The Semantic Web: research and applications
A 25-year perspective on logic programming
Socially constructed trust for distributed authorization
ESORICS'11 Proceedings of the 16th European conference on Research in computer security
RW'13 Proceedings of the 9th international conference on Reasoning Web: semantic technologies for intelligent data access
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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. In this paper, 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 language with negation and disjunction, it turns out that their presence does increase the complexity of non-disjunctive ASP programs up to the second level of the polynomial hierarchy. Interestingly, under cautious reasoning nonmonotone aggregates are even harder than disjunction (Π2p -complete vs co-NP-complete on positive programs). 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. Moreover, we also prove that for positive programs with arbitrary monotone, stratified antimonotone, and stratified nonmonotone aggregates the complexity remains polynomial. This analysis provides some useful indications on the possibility to implement aggregates in existing reasoning engines.