Description Logic Programs: Combining Logic Programs with Description Logic

Abstract

We show how to interoperate, semantically and inferentially, between the leading Semantic Web approaches to rules (RuleML Logic Programs) and ontologies (OWL/DAML+OIL Description Logic) via analyzing their expressive intersection. To do so, we define a new intermediate knowledge representation (KR) contained within this intersection: Description Logic Programs (DLP), and the closely related Description Horn Logic (DHL) which is an expressive fragment of first-order logic (FOL). DLP provides a significant degree of expressiveness, substantially greater than the RDFSchema fragment of Description Logic.We show how to perform DLP-fusion: the bidirectional translation of premises and inferences (including typical kinds of queries) from the DLP fragment of DL to LP, and vice versa from the DLP fragment of LP to DL. In particular, this translation enables one to "build rules on top of ontologies": it enables the rule KR to have access to DL ontological definitions for vocabulary primitives (e.g., predicates and individual constants) used by the rules. Conversely, the DLP-fusion technique likewise enables one to "build ontologies on top of rules": it enables ontological definitions to be supplemented by rules, or imported into DL from rules. It also enables available efficient LP inferencing algorithms/implementations to be exploited for reasoning over large-scale DL ontologies.

Solving Query-Answering Problems for the Semantic Web Using Equivalent Transformation

“…Alternatively, it can be given by a translation into first-order logic, where classes correspond to unary predicates, properties correspond to binary predicates, and subclass/subproperty axioms correspond to implications [11], [12]. More precisely, individuals are equivalent to constants, class expressions are equivalent to first-order formulas with one free variable, and property expressions are equivalent to first-order formulas with two free variables.…”

A Realistic Architecture for the Semantic Web

“…We start with Description Logic Programs (DLP) [GHVD03] and then clarify their relationship with the RDF layer below and the more expressive layers above.…”

“…The rule-set part of the DLP layer is a set of all statements in Description Logic that are translatable into Horn rules [GHVD03]. A Horn rule is a rule of the form (1) where the head and the body consist of only atomic formulas (no negation of any kind).…”

“…However, Datalog certainly resides on top of the image of DLP under the translation described in [GHVD03]. Therefore, modulo such a translation, Datalog can be said to extend DLP.…”

“…With these definitions, we can now formally state (relying on the standard facts about Datalog and default negation) that Datalog extends DLP with respect to the DLP-to-Datalog embedding described in [GHVD03]. The default negation layer similarly extends Datalog with respect to the identity embedding.…”