Abstract
An ontology specifies an abstract model of a domain of interest via a formal language that is typically based on logic. Although description logics are popular formalisms for modeling ontologies, tuple-generating dependencies (tgds), originally introduced as a unifying framework for database integrity constraints, and later on used in data exchange and integration, are also well suited for modeling ontologies that are intended for data-intensive tasks. The reason is that, unlike description logics, tgds can easily handle higher-arity relations that naturally occur in relational databases. In recent years, there has been an extensive study of tgd-ontologies and of their applications to several different data-intensive tasks. However, the fundamental question of whether the expressive power of tgd-ontologies can be characterized in terms of model-theoretic properties remains largely unexplored. We establish several characterizations of tgd-ontologies, including characterizations of ontologies specified by such central classes of tgds as full, linear, guarded, and frontier-guarded tgds. Our characterizations use the well-known notions of critical instance and direct product, as well as a novel locality property for tgd-ontologies. We further use this locality property to decide whether an ontology expressed by frontier-guarded (respectively, guarded) tgds can be expressed by tgds in the weaker class of guarded (respectively, linear) tgds, and effectively construct such an equivalent ontology if one exists.
Highlights
Model theory is the study of the interaction between formulas in some logical formalism and their models, that is, structures that satisfy the formulas
The first two properties rely on the well-known notions of critical instance and direct product, which have been used in several different contexts, whereas the third one relies on a novel locality property, which we consider as one of the main conceptual contributions of the present work
We have established model-theoretic characterizations of TGD-ontologies, including characterizations of ontologies specified by central classes of tgds, such as full, linear, guarded, and frontier-guarded tgds
Summary
Model theory is the study of the interaction between formulas in some logical formalism and their models, that is, structures that satisfy the formulas. Makowsky and Vardi [14] were the first to obtain model-theoretic characterizations of classes of database dependencies expressed in suitable fragments of first-order logic. They classified the work on model-theoretic characterizations into two distinct approaches, which they called the preservation approach and the axiomatizability approach: Preservation Approach In this approach, one considers two logical formalisms L and L′, where L′ is typically a proper fragment of L, and the goal is to obtain model-theoretic characterizations of the following form: a set Σ of L-formulas is equivalent to a set Σ′ of L′-formulas if and only if the models of Σ satisfy certain structural properties. These results notwithstanding, the study of model-theoretic characterizations of sets of arbitrary tgds in the axiomatizability/finite axiomatizability approach has remained largely unexplored so far
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
