Frederick Maier

Paraconsistent OWL and related logics

The Web Ontology Language OWL is currently the most prominent formalism for representing ontologies in Semantic Web applications. OWL is based on description logics, and automated reasoners are used to infer knowledge implicitly present in OWL ontologies. However, because typical description logics obey the classical principle of explosion, reasoning over inconsistent ontologies is impossible in OWL. This is so despite the fact that inconsistencies are bound to occur in many realistic cases, e.g., when multiple ontologies are merged or when ontologies are created by machine learning or data mining tools.In this paper, we present four-valued paraconsistent description logics which can reason over inconsistencies. We focus on logics corresponding to OWL DL and its profiles. We present the logic

Recent advances in integrating OWL and rules (technical communication)

\mathcal {SROIQ}4

Interdefinability of defeasible logic and logic programming under the well-founded semantics

, showing that it is both sound relative to classical

Extending Paraconsistent \mathcal{SROIQ}

\mathcal {SROIQ}

A better uncle for OWL: nominal schemas for integrating rules and ontologies

and that its embedding into

A MapReduce Algorithm for EL

\mathcal {SROIQ}

Reconciling OWL and non-monotonic rules for the Semantic Web

is consequence preserving. We also examine paraconsistent varieties of

Reconciling OWL and Rules

\mathcal{EL}^{++}

Extending paraconsistent SROIQ

, DL-Lite, and Horn-DLs. The general framework described here has the distinct advantage of allowing classical reasoners to draw sound but nontrivial conclusions from even inconsistent knowledge bases. Truth-value gaps and gluts can also be selectively eliminated from models by inserting additional axioms into knowledge bases. If gaps but not gluts are eliminated, additional classical conclusions can be drawn without affecting paraconsistency.

Distributed Reasoning with EL++ using MapReduce

As part of the quest for a unifyinglogic for the Semantic Web Technology Stack, a central issue is finding suitable ways of integrating description logics based on theWeb Ontology Language (OWL) with rule-based approaches based on logic programming. Such integration is difficult since naive approaches typically result in the violation of one ormore desirable design principles. For example, while both OWL 2 DL and RIF Core (a dialect of the Rule Interchange Format RIF) are decidable, their naive union is not, unless carefully chosen syntactic restrictions are applied. We report on recent advances and ongoing work by the authors in integrating OWL and rules. We take an OWL-centric perspective, which means that we take OWL 2 DL as a starting point and pursue the question of how features of rule-based formalisms can be added without jeopardizing decidability. We also report on incorporating the closed world assumption and on reasoning algorithms. This paper essentially serves as an entry point to the original papers, to which we will refer throughout, where detailed expositions of the results can be found.