Axiom Pinpointing is Hard

Rafael PeñalozaRafael Peñaloza, Barış SertkayaBarış Sertkaya

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Rafael Peñaloza, Barış Sertkaya
Axiom Pinpointing is Hard
In Bernardo Cuenca Grau and Ian Horrocks and Boris Motik and Ulrike Sattler, eds., Proceedings of the 2009 International Workshop on Description Logics (DL2009), volume 477 of CEUR-WS, 2009

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KurzfassungAbstract
We investigate the complexity of several decision, enumeration and counting problems in axiom pinpointing in Description Logics. We prove hardness results that already hold for the propositional Horn fragment. We show that for this fragment, unless P = NP, all minimal subsets of a given TBox that have a given consequence, i.e. MinAs, cannot be enumerated in a specified lexicographic order with polynomial delay. Moreover, we show that recognizing the set of all MinAs is at least as hard as recognizing the set of all minimal transversals of a given hypergraph, however whether this problem is intractable remains open. We also show that checking the existence of a MinA that does not contain any of the given sets of axioms, as well as checking the existence of a MinA that contains a specified axiom are both NP-hard. In addition we show that counting all MinAs and counting the MinAs that contain a certain axiom are both #P-hard.
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

@inproceedings{ PeSe09,
  author = {Rafael {Pe{\~n}aloza} and Bar\i{}\c{s} {Sertkaya}},
  booktitle = {Proceedings of the 2009 International Workshop on Description Logics ({DL2009})},
  editor = {Bernardo Cuenca {Grau} and Ian {Horrocks} and Boris {Motik} and Ulrike {Sattler}},
  series = {CEUR-WS},
  title = {Axiom Pinpointing is Hard},
  volume = {477},
  year = {2009},
}