Finding EL+ justifications using the earley parsing algorithm

  • Authors:

  • Riku Nortje;Katarina Britz;Thomas Meyer

  • Affiliations:

  • Knowledge Systems Group, Meraka, Pretoria, South Africa and University of South Africa, UNISA, South Africa;Knowledge Systems Group, Meraka, Pretoria, South Africa and University of South Africa, UNISA, South Africa;Knowledge Systems Group, Meraka, Pretoria, South Africa and University of South Africa, UNISA, South Africa

  • Venue:
  • AOW '09 Proceedings of the Fifth Australasian Ontology Workshop - Volume 112
  • Year:
  • 2009

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Abstract

Module extraction plays an important role in the reuse of ontologies as well as in the simplification and optimization of some reasoning tasks such as finding justifications for entailments. In this paper we focus on the problem of extracting small modules for EL+ entailment based on reachability. We extend the current notion of (forward) reachability to obtain a bidirectional version, and show that the bidirectional reachability algorithm allows us to transform an EL+ ontology into a reachability preserving context free grammar (CFG). The well known Earley algorithm for parsing strings, given some CFG, is then applied to the problem of extracting minimal reachability-based axioms sets for subsumption entailments. We show that each reachability-based axiom set produced by the Earley algorithm corresponds to a possible Minimal Axiom Set (MinA) that preserves the given entailment. This approach has two advantages -- it has the potential to reduce the number of subsumption tests performed during MinA extraction, as well to minimize the number of axioms for each such test.