Lean Kernels in Description Logics

  • Rafael PeñalozaEmail author
  • Carlos Mencía
  • Alexey Ignatiev
  • Joao Marques-Silva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10249)


Lean kernels (LKs) are an effective optimization for deriving the causes of unsatisfiability of a propositional formula. Interestingly, no analogous notion exists for explaining consequences of description logic (DL) ontologies. We introduce LKs for DLs using a general notion of consequence-based methods, and provide an algorithm for computing them which incurs in only a linear time overhead. As an example, we instantiate our framework to the DL \({\mathcal {ALC}}\). We prove formally and empirically that LKs provide a tighter approximation of the set of relevant axioms for a consequence than syntactic locality-based modules.



We would like to thank Beatriz Peñaloza for her help on statistical methods. Carlos Mencía is supported by grant TIN2016-79190-R.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Rafael Peñaloza
    • 1
    Email author
  • Carlos Mencía
    • 2
  • Alexey Ignatiev
    • 3
  • Joao Marques-Silva
    • 3
  1. 1.Free University of Bozen-BolzanoBolzanoItaly
  2. 2.University of OviedoGijónSpain
  3. 3.University of LisbonLisbonPortugal

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