A Proof Theory for Description Logics


Description Logics (DLs) is a family of formalisms used to represent knowledge of a domain. They are equipped with a formal logic-based semantics. Knowledge representation systems based on description logics provide various inference capabilities that deduce implicit knowledge from the explicitly represented knowledge. In this thesis we investigate the Proof Theory for DLs. We introduce Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi. It is argued that those systems can improve the extraction of computational content from DLs proofs for explanations purpose.


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  author = {Rademaker, Alexandre},
  title = {A Proof Theory for Description Logics},
  publisher = {Springer},
  year = {2012},
  series = {SpringerBriefs in Computer Science},
  url = {http://dx.doi.org/10.1007/978-1-4471-4002-3}