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Concepts as Modalities in Description Logics

5 pagesPublished: May 25, 2019


Motivated by the colloquial language term of a “glass gummy bear”, an additional type of concept composition for description logics is suggested. This composition type is then axiomatically formalized and called concept generalization. Consistency of the formalization is checked. By proving axiom K and Go ̈del rule, it is shown that this logic is in fact a multi-modal logic. Concepts could be both modal operators and predicate symbols. A Kripke semantics is presented (the adequacy is future work). In this semantics, the TBox axioms hold for any view, assertions in the ABox hold for the natural view (a selected world in the Kripke structure) only. The relationship to other formalisms is outlined. Further examples are discussed at the end.

Keyphrases: concept composition, Description Logics, multi-modal logic

In: Christoph Benzmüller, Xavier Parent and Alexander Steen (editors). Selected Student Contributions and Workshop Papers of LuxLogAI 2018, vol 10, pages 43--47

BibTeX entry
  author    = {Lukas Gr\textbackslash{}"atz},
  title     = {Concepts as Modalities in Description Logics},
  booktitle = {Selected Student Contributions and Workshop Papers of LuxLogAI 2018},
  editor    = {Christoph Benzm\textbackslash{}"uller and Xavier Parent and Alexander Steen},
  series    = {Kalpa Publications in Computing},
  volume    = {10},
  pages     = {43--47},
  year      = {2019},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2515-1762},
  url       = {},
  doi       = {10.29007/9cxg}}
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