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.


Lean Meat Description Logics (DLs) Locality-based Modules (LBMs) Linear Time Overhead Relevant Axioms 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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