Description Logics, Rules and Multi-context Systems

Abstract

The combination of rules and ontologies has been a fertile topic of research in the last years, with the proposal of several different systems that achieve this goal. In this paper, we look at two of these formalisms, Mdl-programs and multi-context systems, which address different aspects of this combination, and include different, incomparable programming constructs. Despite this, we show that every Mdl-program can be transformed in a multi-context system, and this transformation relates the different semantics for each paradigm in a natural way. As an application, we show how a set of design patterns for multi-context systems can be obtained from previous work on Mdl-programs. As a consequence, any useful constructions developed within the framework of Mdl-programs may be automatically translated to equivalent constructions in the setting of MCSs. Although the idea behind the syntactic translation is suggested in [3] to justify that MCSs generalize the original dl-programs, even this claim is not substantiated beyond an intuitive perspective. Here, we will not only make this syntactic correspondence precise, but discuss in detail the semantic correspondences it entails, and apply it to obtain a set of design patterns for MCSs based on such a set for Mdl-programs. The structure of the paper is as follows. Section 2 recalls the syntax and semantics of Mdl-programs. Section 3 introduces the syntax of MCSs and the translation of Mdl-programs into these. Section 4 summarizes the different semantics of MCSs and relates the semantics of an Mdl-program and those of the MCS it generates. Section 5 applies this correspondence to design patterns for Mdl-programs. Section 6 concludes the paper. 2 Mdl-programs This section presents multi-description logic programs [7], Mdl-programs for short, which are a straightforward generalization of dl-programs, an already established framework for coupling description logic knowledge bases with rulebased reasoning [9, 10]. The main advantage of Mdl-programs, as we will see, is their simplicity. Although they do not possess the level of generality other systems such as Hex-programs [11] or multi-context systems [2] have, Mdl-programs are quite adequate for reasoning within the semantic web, where a lot of effort is being put into developing ontologies, which for the main part are description logic knowledge bases. 2.1 Syntax The purpose of Mdl-programs is to generalize logic programs with special atoms that communicate with external description logic knowledge bases, which we will refer to henceforth simply as "knowledge bases". The key ingredient of Mdl-programs is the notion of dl-atom. A dl-atom relative to a set of knowledge bases Σ = {Σ 1 ,. .. , Σ n } and a function-free first-order signature Φ is DL i [S 1 op 1 p 1 ,. .. , S m op m p m ; Q] (t), where 1 ≤ i ≤ n, each S k is either a concept or role of Σ i , or a special symbol in {=, =}; op i ∈ { , ∪-}; each p k is a unary or binary predicate symbol of Φ, according to whether the corresponding S k is a concept or a role; and Q(t...

Integrity Constraints for General-Purpose Knowledge Bases

“…Proof. Since P corresponds to a positive program, the only equilibrium of M is MM(P) (see [14]). Furthermore, for any I, MM(P I ) includes the facts in all extensional databases and satisfies all rules in R i and all integrity constraints.…”

Information Flow within Relational Multi-context Systems

“…Thus, effort has also been made in adapting some of these best practices to other paradigms and in finding new paradigm-specific patterns [2,20,33]. In this line, we contributed to the study of best practices in the field of systems that can access several knowledge bases by identifying several patterns for Mdl-programs [10] -a powerful and expressive formalism to join description logics with rules, connecting a logic program with description logic knowledge bases by means of special dl-atoms that allow information flow [9], generalizing the original dl-programs [13].…”

“…In turn, MCSs and Hex-programs are essentially incomparable [14]. Mdl-programs are trivially embedded in Hex-programs [14], and they can be faithfully translated in a not-so-trivial fashion into MCSs [4,9].…”

“…The study of these design patterns not only facilitates the development of future MCSs, but also suggests new ways in which their language can be extended. Our departure point was the study of design patterns for multi dl-programs [10] -a generalization of dl-programs [13] with multiple description logic knowledge bases -, which can be seen as a subclass of MCSs by means of a systematic translation [9]. The present study is however much more general than the combination of the work in those two publications.…”