Aggregate Functions in DLV

Disjunctive Logic Programming (DLP) is a very expressive formalism: it allows for expressing every property of finite structures that is decidable in the complexity class . Despite this high expressiveness, there are some simple properties, often arising in real-world applications, which cannot be encoded in a simple and natural manner. Especially properties that require the use of arithmetic operators (like sum, count, or min) on a set of elements satisfying some conditions, cannot be naturally expressed in classic DLP. To overcome this deficiency, we extend DLP by aggregate functions. In contrast to a previous proposal, we also consider the case of unstratified aggregates. We formally define the semantics of the new language (called DLP ) by means of a generalization of the Gelfond-Lifschitz transformation, and illustrate the use of the new constructs on relevant knowledge-based problems. We analyze the computational complexity of DLP , showing that the addition of aggregates does not bring a higher cost in that respect. And we provide an implementation of DLP in DLV– the state-of-the-art DLP system – and report on experiments which confirm the usefulness of the proposed extension also for the efficiency of the computation.