Tailoring temporal description logics for reasoning over temporal conceptual models

Temporal data models have been used to describe how data can evolve in the context of temporal databases. Both the Extended Entity-Relationship (EER) model and the Unified Modelling Language (UML) have been temporally extended to design temporal databases. To automatically check quality properties of conceptual schemas various encoding to Description Logics (DLs) have been proposed in the literature. On the other hand, reasoning on temporally extended DLs turn out to be too complex for effective reasoning ranging from 2ExpTime up to undecidable languages. We propose here to temporalize the ‘light-weight’ DL-Lite logics obtaining nice computational results while still being able to represent various constraints of temporal conceptual models. In particular, we consider temporal extensions of DL-Lite^N_bool, which was shown to be adequate for capturing non-temporal conceptual models without relationship inclusion, and its fragment DL-Lite^N_core with most primitive concept inclusions, which are nevertheless enough to represent almost all types of atemporal constraints (apart from covering)

A cookbook for temporal conceptual data modelling with description logic

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models

Reasoning about Explanations for Negative Query Answers in DL-Lite

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations

Inconsistency-tolerant Query Answering in Ontology-based Data Access

Ontology-based data access (OBDA) is receiving great attention as a new paradigm for managing information systems through semantic technologies. According to this paradigm, a Description Logic ontology provides an abstract and formal representation of the domain of interest to the information system, and is used as a sophisticated schema for accessing the data and formulating queries over them. In this paper, we address the problem of dealing with inconsistencies in OBDA. Our general goal is both to study DL semantical frameworks that are inconsistency-tolerant, and to devise techniques for answering unions of conjunctive queries under such inconsistency-tolerant semantics. Our work is inspired by the approaches to consistent query answering in databases, which are based on the idea of living with inconsistencies in the database, but trying to obtain only consistent information during query answering, by relying on the notion of database repair. We first adapt the notion of database repair to our context, and show that, according to such a notion, inconsistency-tolerant query answering is intractable, even for very simple DLs. Therefore, we propose a different repair-based semantics, with the goal of reaching a good compromise between the expressive power of the semantics and the computational complexity of inconsistency-tolerant query answering. Indeed, we show that query answering under the new semantics is first-order rewritable in OBDA, even if the ontology is expressed in one of the most expressive members of the DL-Lite family

Ontology-based data access with databases: a short course

Ontology-based data access (OBDA) is regarded as a key ingredient of the new generation of information systems. In the OBDA paradigm, an ontology defines a high-level global schema of (already existing) data sources and provides a vocabulary for user queries. An OBDA system rewrites such queries and ontologies into the vocabulary of the data sources and then delegates the actual query evaluation to a suitable query answering system such as a relational database management system or a datalog engine. In this chapter, we mainly focus on OBDA with the ontology language OWL 2QL, one of the three profiles of the W3C standard Web Ontology Language OWL 2, and relational databases, although other possible languages will also be discussed. We consider different types of conjunctive query rewriting and their succinctness, different architectures of OBDA systems, and give an overview of the OBDA system Ontop

OCL-Lite: a decidable (yet expressive) fragment of OCL

UML has become a de facto standard in conceptual modeling. Class diagrams in UML allow one to model the data in the domain of interest by specifying a set of graphical constraints. However, in most cases one needs to provide the class diagram with additional semantics to completely specify the domain, and this is where OCL comes into play. While reasoning over class diagrams is decidable and has been investigated intensively, it is well known that checking the correctness of OCL constraints is undecidable. Thus, we introduce OCL-Lite, a fragment of the full OCL language and prove that reasoning over UML class diagrams with OCL-Lite constraints is in ExpTime by an encoding in the description logic ALCI. As a side result, DL techniques and tools can be used to reason on UML class diagrams annotated with arbitrary OCL-Lite constraints.Peer ReviewedPostprint (published version

Maintaining Integrity Constraints in Semantic Web

As an expressive knowledge representation language for Semantic Web, Web Ontology Language (OWL) plays an important role in areas like science and commerce. The problem of maintaining integrity constraints arises because OWL employs the Open World Assumption (OWA) as well as the Non-Unique Name Assumption (NUNA). These assumptions are typically suitable for representing knowledge distributed across the Web, where the complete knowledge about a domain cannot be assumed, but make it challenging to use OWL itself for closed world integrity constraint validation. Integrity constraints (ICs) on ontologies have to be enforced; otherwise conflicting results would be derivable from the same knowledge base (KB). The current trends of incorporating ICs into OWL are based on its query language SPARQL, alternative semantics, or logic programming. These methods usually suffer from limited types of constraints they can handle, and/or inherited computational expensiveness. This dissertation presents a comprehensive and efficient approach to maintaining integrity constraints. The design enforces data consistency throughout the OWL life cycle, including the processes of OWL generation, maintenance, and interactions with other ontologies. For OWL generation, the Paraconsistent model is used to maintain integrity constraints during the relational database to OWL translation process. Then a new rule-based language with set extension is introduced as a platform to allow users to specify constraints, along with a demonstration of 18 commonly used constraints written in this language. In addition, a new constraint maintenance system, called Jena2Drools, is proposed and implemented, to show its effectiveness and efficiency. To further handle inconsistencies among multiple distributed ontologies, this work constructs a framework to break down global constraints into several sub-constraints for efficient parallel validation