Augmenting Subsumption Propagation in Distributed Description Logics

Abstract

Distributed description logics (DDL) enable reasoning with multiple ontologies interconnected by directional semantic mapping, called bridge rules. Bridge rules map concepts of a source ontology into concepts of a target ontology. Concept subsumptions of the source ontology can be propagated according to a propagation pattern expressed by means of bridge rules into concept subsumptions of the target ontology. In the basic formulation of DDL, such a propagation is mostly limited to cases when pairs of ontologies are directly linked by means of bridge rules. However, when more than two ontologies are involved, one would expect that subsumption propagates along chains of ontologies linked by bridge rules, but the semantics of DDL is too weak to support this behavior. In a recent study, an adjusted semantics for DDL that supports subsumption propagation through chains of bridge rules has been introduced. This study makes use of a so-called compositional consistency requirement that has been employed before in package-based description logics. While the results concerning subsumption propagation under the adjusted semantics are encouraging, there are important drawbacks. In this article we take a wider perspective, and propose a study of several different alternative extensions of the DDL semantics. For each of them we study the formal properties, and we select the one that, according to our analysis, constitutes a good compromise, and for this case we provide a sound and complete tableaux decision procedure.

Distributed First Order Logic

“…We prove the main theorem by induction on φ. Step The DFOL encoding of QML shown above decouples the semantics of the modal operator , captured by bridge rules (38) and (39), and the assumptions on the possible worlds domains, captured by the bridge rule (40). Different assumptions on the possible worlds domains can be encoded by means of different bridge rules on the equality predicate, thus retaining the bridge rules for unchanged.…”

“…In [40] additional constraints on the domain relation are added in order to augment the information flow between different ontologies induced by DDL ontology mappings. Of particular interest are the bridge rules that support the transitive propagation of mappings:…”

Resolving conflicts in knowledge for ambient intelligence

“…Due to their capacity to combine logical reasoning over multiple knowledge sources, MCS have been used to formalize distributed FOL (Ghidini & Serafini, 1998), and later Distributed Description Logic (DDL) (Borgida & Serafini, 2003). The latter approach, in particular, proved to be influential and sparked considerable interest in distributed ontologies, where the power of MCS is used either to make alignments between heterogeneous and possibly ambiguous ontologies that are to be combined in reasoning (Ghidini & Serafini, 2008; Ghidini et al ., 2008), or to facilitate truly distributed inference (Serafini & Tamilin, 2004; Serafini et al ., 2005; Homola & Serafini, 2010). Both directions may be useful in AmI systems, in cases when more than one ontology is employed within a system, possibly governed by independent agents.…”

Decentralized case-based reasoning and Semantic Web technologies applied to decision support in oncology

“…Luciano Serafini, one of the initiators of the DDL formalism, has proposed a formalism and a tableau algorithm for dealing with mappings and axioms involving nominals in DDLs (Serafini, 2007;Homola & Serafini, 2010;Serafini & Homola, 2012). Luciano Serafini, one of the initiators of the DDL formalism, has proposed a formalism and a tableau algorithm for dealing with mappings and axioms involving nominals in DDLs (Serafini, 2007;Homola & Serafini, 2010;Serafini & Homola, 2012).…”

“…In particular, the DDL formalism did not allow the use of nominals in bridge rules and this is still the case in the current version of the D rago system. Luciano Serafini, one of the initiators of the DDL formalism, has proposed a formalism and a tableau algorithm for dealing with mappings and axioms involving nominals in DDLs (Serafini, 2007; Homola & Serafini, 2010; Serafini & Homola, 2012). Thus, the use of nominals in axioms hereafter is justified.…”