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 Σ P 2 (=NP NP ). 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, times, or count) on a set or multiset of elements, which satisfy some conditions, cannot be naturally expressed in classic DLP.To overcome this deficiency, we extend DLP by aggregate functions in a conservative way. In particular, we avoid the introduction of constructs with disputed semantics, by requiring aggregates to be stratified. We formally define the semantics of the extended language (called DLP A ), and illustrate how it can be profitably used for representing knowledge. Furthermore, we analyze the computational complexity of DLP A , showing that the addition of aggregates does not bring a higher cost in that respect. Finally, we provide an implementation of DLP A in DLV-a state-of-the-art DLP system -and report on experiments which confirm the usefulness of the proposed extension also for the efficiency of computation. A preliminary version of this work appeared in the Proceedings of IJCAI-03.1. if p occurs in B + (r) and p ′ occurs in H(r), then ||p|| n ≤ ||p ′ || n ; and 2. if p occurs in B − (r) and p ′ occurs in H(r), then ||p|| n < ||p ′ || n ; and 3. if p and p ′ occur in H(r), then ||p|| n = ||p ′ || n . Aggregate-stratification.The idea of aggregate-stratification is that two predicates defined by means of aggregates do not mutually depend on one another.A DLP A program P is aggregate-stratified if there exists a level mapping || || a such that for each pair p and p ′ of predicates of P, and for each rule r ∈ P,

Enterprise/Corporate ontologies are specifications of information of business enterprises. Semantic peculiarities of ASP, like the Closed World Assumption (CWA) and the Unique Name Assumption (UNA), are more appropriate than OWL assumptions for enterprise ontologies, also because these ontologies often are the evolution of relational databases, where both CWA and UNA are adopted. In this paper we present OntoDLV, a system based on Answer Set Programming (ASP) for the specification and reasoning on enterprise ontologies. OntoDLV implements a powerful ontology representation language, called On-toDLP, extending (disjunctive) ASP with all the main ontology constructs including classes, inheritance, relations and axioms. OntoDLP is strongly typed, and includes also complex type constructors, like lists and sets. Importantly, OntoDLV supports a powerful interoperability mechanism with OWL, allowing the user to retrieve information also from OWL Ontologies and to exploit this information in OntoDLP ontologies and queries. The system is already used in a number of realworld applications including agent-based systems, information extraction, and text classification applications. ⋆ Supported by M.I.U.R. within projects "Potenziamento e Applicazioni della Programmazione Logica Disgiuntiva" and "Sistemi basati sulla logica per la rappresentazione di conoscenza: estensioni e tecniche di ottimizzazione."

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