Logica Universalis

, Volume 10, Issue 2–3, pp 373–376 | Cite as

Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability

  • Frode BjørdalEmail author


We show that we in ways related to the classical Square of Opposition may define a Cube of Opposition for some useful statements, and we as a by-product isolate a distinct directive of being inviolable which deserves attention; a second central purpose is to show that we may extend our construction to isolate hypercubes of opposition of any finite cardinality when given enough independent modalities. The cube of opposition for obligations was first introduced publically in a lecture for the Square of Opposition Conference in the Vatican in May 2014.


Square of opposition cube of opposition deontic logic 

Mathematics Subject Classification

Primary 03B45 Secondary 03B62 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Universidade Federal do Rio Grande do NorteNatalBrazil
  2. 2.The University of OsloOsloNorway

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