Description Logics with Concrete Domains and Functional Dependencies

Description Logics (DLs) with concrete domains are a useful tool in many applications. To further enhance the expressive power of such DLs, it has been proposed to add database-style key constraints. Up to now, however, only uniqueness constraints have been considered in this context, thus neglecting the second fundamental family of key constraints: functional dependencies. In this paper, we consider the basic DL with concrete domains ALC(D), extend it with functional dependencies, and analyze the impact of this extension on the decidability and complexity of reasoning. Though intuitively the expressivity of functional dependencies seems weaker than that of uniqueness constraints, we are able to show that the former have a similarly severe impact on the computational properties: reasoning is undecidable in the general case, and NExpTime-complete in some slightly restricted variants of our logic

Functional Dependencies in OWL ABox

Functional Dependency (FD) has been extensively studied in database theory. Most recently there have been some works investigating the implications of extending Description Logics with functional dependencies. In particular the OWL ontology language offers the functional property property allowing simple functional dependency to be specified. As it turns out, more complex FD specified as concept constructors has been proved to lead to undecidability in the general case, which restricts its usage as part of TBOX. This paper departs from previous ones by restricting FDs applicability to instances in the ABOX. We specify FD as a new constructor, an OWL concept. FD instances are mapped to Horn clauses and evaluated against the ABOX according to user’s desired behavior. The latter allows users to determine whether FDs should be interpreted as constraints, assertions or views. Our approach gives ontology users data guarantees usually found in databases, integrated with the ontology conceptual model

Decidable Reasoning in Terminological Knowledge Representation Systems

Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose capabilities go beyond the ones of presently available TKRSs. The new features studied, often required in practical applications, can be summarized in three main points. First, we consider a highly expressive terminological language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, we allow to express inclusion statements between general concepts, and terminological cycles as a particular case. Third, we prove the decidability of a number of desirable TKRS-deduction services (like satisfiability, subsumption and instance checking) through a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases. Our calculus extends the general technique of constraint systems. As a byproduct of the proof, we get also the result that inclusion statements in ALCNR can be simulated by terminological cycles, if descriptive semantics is adopted.Comment: See http://www.jair.org/ for any accompanying file

Introduction to the TPLP special issue, logic programming in databases: From Datalog to semantic-web rules

Much has happened in data and knowledge base research since the introduction of the relational model in Codd (1970) and its strong logical foundations influence its advances ever since. Logic has been a common ground where Database and Artificial Intelligence research competed and collaborated with each other for a long time (Abiteboul et al. 1995). The product of this joint effort has been a set of logic-based formalisms, such as the Relational Calculus (Codd 1970), Datalog (Ceri et al. 1990), Description Logics (Baader et al. 2007), etc., capturing not only the structure but also the semantics of data in an explicit way, thus enabling complex inference procedures.This special issue contains three rigorously reviewed articles addressing problems that span from Query Answering to Data Mining. All these contributions have their roots in the foundational formalisms of Data and Knowledge Bases such as Logic Programming, Description Logic and Hybrid Logics, representing a clear example of the effort that the Database and the Semantic-Web communities are producing to bridge the various schools of thinking in modern Data and Knowledge Management