Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Contrary description logic: Gentzen deduction system

  • 43 Accesses


Traditional description logics are based on complementary rather than contrary concepts. This work proposes a contrary description logic based on the contrary concept constructors ~,◃ (instead of ¬). A Gentzen-type deduction system is applied to make the system sound and complete with the three-valued semantics of contrary description logic.

This is a preview of subscription content, log in to check access.


  1. 1

    Parsons T. The traditional square of opposition. Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/ entries/square

  2. 2

    Artale A, Franconi E. Temporal description logics. In: Handbook of Temporal Reasoning in Artificial Intelligence. Oxford: Elsevier, 2005, 1: 375–388

  3. 3

    Baader F, Calvanese D, Mc Guinness D L, et al. The Description Logic Handbook: Theory, Implementation, Applications. Cambridge: Cambridge University Press, 2003

  4. 4

    Baader F, Horrocks I, Sattler U. Chapter 3 description logics. In: Handbook of Knowledge Representation. Oxford: Elsevier, 2007

  5. 5

    Fensel D, van Harmelen F, Horrocks I, et al. OIL: an ontology infrastructure for the semantic web. IEEE Intell Syst, 2001, 16: 38–45

  6. 6

    Zhu W, Li W, Sui Y, et al. Sound and complete Gentzen deduction system for propositional intermediate logic (in Chinese). J Softw, 2016, 27: 209–218

  7. 7

    Avron A. Classical Gentzen-type methods in propositional many-valued logics. In: Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic (ISMVL’01). Washington: IEEE Computer Society, 2001. 287

  8. 8

    Avron A. On the expressive power of three-valued and four-valued languages. J Logic Comput 1999, 9: 977–994

  9. 9

    Rademaker A. A Proof Theory for Description Logics. Berlin: Springer, 2012

  10. 10

    Takeuti G. Proof Theory. 2nd ed. Amsterdam: North-Holland Publishing Company, 1987

  11. 11

    Li W. Mathematical Logic, Foundations for Information Science. Basel: Birkhäuser, 2010

Download references

Author information

Correspondence to Yuefei Sui.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, W., Sui, Y., Luo, J. et al. Contrary description logic: Gentzen deduction system. Sci. China Inf. Sci. 60, 112103 (2017). https://doi.org/10.1007/s11432-015-9050-6

Download citation


  • description logics
  • contradictory
  • contrary
  • soundness
  • completeness