Abstract
The addition of aggregates has been one of the most relevant enhancements to the language of answer set programming (ASP). They strengthen the modeling power of ASP, in terms of concise problem representations. While many important problems can be encoded using nonrecursive aggregates, some relevant examples lend themselves for the use of recursive aggregates. Previous semantic definitions typically agree in the nonrecursive case, but the picture is less clear for 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 disjunctive programs with arbitrary aggregates (including monotone, antimonotone, and nonmonotone aggregates). This semantics is a fully declarative, genuine generalization of the answer set semantics for disjunctive logic programming (DLP). It is defined by a natural variant of the Gelfond-Lifschitz transformation, and treats aggregate and non-aggregate literals in a uniform way. We prove that our semantics guarantees the minimality (and therefore the incomparability) of answer sets, and demonstrate that it coincides with the standard answer set semantics on aggregate-free programs. Finally we analyze the computational complexity of this language, paying particular attention to the impact of syntactical restrictions on programs.
This work was supported by the European Commission under projects IST-2002-33570 INFOMIX, IST-2001-37004 WASP, and IST-2001-33570 COLOGNET.
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Faber, W., Leone, N., Pfeifer, G. (2004). Recursive Aggregates in Disjunctive Logic Programs: Semantics and Complexity. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_19
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DOI: https://doi.org/10.1007/978-3-540-30227-8_19
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