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In this paper we study Graphol, a fully graphical language inspired by standard formalisms for conceptual modeling, similar to the UML class diagram and the ER model, but equipped with formal semantics. We formally prove that Graphol is equivalent to OWL 2, i.e., it can capture every OWL 2 ontology and vice versa. We also present some usability studies indicating that Graphol is suitable for quick adoption by conceptual modelers that are familiar with UML and ER. This is further testified by the adoption of Graphol for ontology representation in several industrial projects. [ABSTRACT FROM AUTHOR]

Finite model reasoning in UML class diagrams is an important task for assessing the quality of the analysis phase in the development of software applications in which it is assumed that the number of objects of the domain is finite. In this paper, we show how to encode finite model reasoning in UML class diagrams as a constraint satisfaction problem (CSP), exploiting techniques developed in description logics. In doing so we set up and solve an intermediate CSP problem to deal with the explosion of 'class combinations' arising in the encoding. To solve the resulting CSP problems we rely on the use of off-the-shelf tools for constraint modeling and programming. As a result, we obtain, to the best of our knowledge, the first implemented system that performs finite model reasoning on UML class diagrams. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study data complexity of answering conjunctive queries over description logic (DL) knowledge bases constituted by a TBox and an ABox. In particular, we are interested in characterizing the FOL-rewritability and the polynomial tractability boundaries of conjunctive query answering, depending on the expressive power of the DL used to express the knowledge base. FOL-rewritability means that query answering can be reduced to evaluating queries over the database corresponding to the ABox. Since first-order queries can be expressed in SQL, the importance of FOL-rewritability is that, when query answering enjoys this property, we can take advantage of Relational Data Base Management System (RDBMS) techniques for both representing data, i.e., ABox assertions, and answering queries via reformulation into SQL. What emerges from our complexity analysis is that the description logics of the DL-Lite family are essentially the maximal logics allowing for conjunctive query answering through standard database technology. In this sense, they are the first description logics specifically tailored for effective query answering over very large ABoxes. [Copyright &y& Elsevier]

Description logic Knowledge and Action Bases (KAB) are a mechanism for providing both a semantically rich representation of the information on the domain of interest in terms of a description logic knowledge base and actions to change such information over time, possibly introducing new objects. We resort to a variant of DL-Lite where the unique name assumption is not enforced and where equality between objects may be asserted and inferred. Actions are specified as sets of conditional effects, where conditions are based on epistemic queries over the knowledge base (TBox and ABox), and effects are expressed in terms of new ABoxes. In this setting, we address verification of temporal properties expressed in a variant of first-order μ-calculus with quantification across states. Notably, we show decidability of verification, under a suitable restriction inspired by the notion of weak acyclicity in data exchange. [ABSTRACT FROM AUTHOR]

Abstract: View-based query answering is the problem of answering a query based only on the precomputed answers to a set of views. While this problem has been widely investigated in databases, it is largely unexplored in the context of Description Logic ontologies. Differently from traditional databases, Description Logics may express several forms of incomplete information, and this poses challenging problems in characterizing the semantics of views. In this paper, we first present a general framework for view-based query answering, where we address the above semantical problems by providing two notions of view-based query answering over ontologies, all based on the idea that the precomputed answers to views are the certain answers to the corresponding queries. We also relate such notions to privacy-aware access to ontologies. Then, we provide decidability results, algorithms, and data complexity characterizations for view-based query answering in several Description Logics, ranging from those with limited modeling capability to highly expressive ones. [Copyright &y& Elsevier]

A Description Logic (DL) ontology is constituted by two components, a TBox that expresses general knowledge about the concepts and their relationships, and an ABox that describes the properties of individuals that are instances of concepts. We address the problem of how to deal with changes to a DL ontology, when these changes affect only the ABox, i.e. when the TBox is considered invariant. We consider two basic changes, namely instance-level update and instance-level erasure, roughly corresponding to the addition and the deletion of a set of facts involving individuals. We characterize the semantics of instance-level update and erasure on the basis of the approaches proposed by Winslett and by Katsuno and Mendelzon. Interestingly, DLs are typically not closed with respect to instance-level update and erasure, in the sense that the set of models corresponding to the application of any of these operations to a knowledge base in a DL L may not be expressible by ABoxes in L. In particular, we show that this is true for DL-LiteF, a tractable DL that is oriented towards data-intensive applications. To deal with this problem, we first introduce DL-LiteFS, a DL that minimally extends DL-LiteF and is closed with respect to instance-level update, and present a polynomial algorithm for computing instance-level update in this logic. Then, we provide a principled notion of best approximation with respect to a fixed language L of instance-level update and erasure, and exploit the algorithm for instance-level update for DL-LiteFS to get polynomial algorithms for approximated instance-level update and erasure for DL-LiteF. These results confirm the nice computational properties of DL-LiteF for data intensive applications, even where information about instances is not only read, but also written. [ABSTRACT FROM PUBLISHER]

Query containment and query answering are two important computational tasks in databases. While query answering amounts to computing the result of a query over a database, query containment is the problem of checking whether, for every database, the result of one query is a subset of the result of another query. In this article, we deal with unions of conjunctive queries, and we address query containment and query answering under description logic constraints. Every such constraint is essentially an inclusion dependency between concepts and relations, and their expressive power is due to the possibility of using complex expressions in the specification of the dependencies, for example, intersection and difference of relations, special forms of quantification, regular expressions over binary relations. These types of constraints capture a great variety of data models, including the relational, the entity-relationship, and the object-oriented model, all extended with various forms of constraints. They also capture the basic features of the ontology languages used in the context of the Semantic Web. We present the following results on both query containment and query answering. We provide a method for query containment under description logic constraints, thus showing that the problem is decidable, and analyze its computational complexity. We prove that query containment is undecidable in the case where we allow inequalities in the right-hand-side query, even for very simple constraints and queries. We show that query answering under description logic constraints can be reduced to query containment, and illustrate how such a reduction provides upper-bound results with respect to both combined and data complexity. [ABSTRACT FROM AUTHOR]

Although current languages used in ontology-based data access (OBDA) systems allow for mapping source data to instances of concepts and relations in the ontology, several application domains need more flexible tools for inferring knowledge from data, which are able to dynamically acquire axioms about new concepts and relations directly from the data. In this paper we introduce the notion of mapping-based knowledge base (MKB) to formalize the situation where both the extensional and the intensional level of the ontology are determined by suitable mappings to a set of data sources. This allows for making the intensional level of the ontology as dynamic as the extensional level traditionally is. To do so, we resort to the meta-modeling capabilities of higher-order description logics, in particular the description logic Hi (DL-Lite R) , which allows seeing concepts and relations as individuals, and vice versa. The challenge in this setting is to design efficient algorithms for answering queries posed to MKBs. Besides the definition of MKBs, our main contribution is to prove that answering instance queries posed to MKBs expressed in Hi (DL-Lite R) can be done efficiently. [ABSTRACT FROM AUTHOR]

Abstract: UML is the de-facto standard formalism for software design and analysis. To support the design of large-scale industrial applications, sophisticated CASE tools are available on the market, that provide a user-friendly environment for editing, storing, and accessing multiple UML diagrams. It would be highly desirable to equip such CASE tools with automated reasoning capabilities, such as those studied in Artificial Intelligence and, in particular, in Knowledge Representation and Reasoning. Such capabilities would allow to automatically detect relevant formal properties of UML diagrams, such as inconsistencies or redundancies. With regard to this issue, we consider UML class diagrams, which are one of the most important components of UML, and we address the problem of reasoning on such diagrams. We resort to several results developed in the field of Knowledge Representation and Reasoning, regarding Description Logics (DLs), a family of logics that admit decidable reasoning procedures. Our first contribution is to show that reasoning on UML class diagrams is EXPTIME-hard, even under restrictive assumptions; we prove this result by showing a polynomial reduction from reasoning in DLs. The second contribution consists in establishing EXPTIME-membership of reasoning on UML class diagrams, provided that the use of arbitrary OCL (first-order) constraints is disallowed. We get this result by using , a very expressive EXPTIME-decidable DL that has been developed to capture typical features of conceptual and object-oriented data models. The last contribution has a more practical flavor, and consists in a polynomial encoding of UML class diagrams in the DL , which essentially is the most expressive DL supported by current state-of-the-art DL-based reasoning systems. Though less expressive than , the DL preserves enough semantics to keep reasoning about UML class diagrams sound and complete. Exploiting such an encoding, one can use current DL-based reasoning systems as core reasoning engines for a next generation of CASE tools, that are equipped with reasoning capabilities on UML class diagrams. [Copyright &y& Elsevier]