A Cube of Opposition for Predicate Logic

Jørgen Fischer Nilsson*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


Abstract: The traditional square of opposition is generalized and extended to a cube of opposition covering and conveniently visualizing inter-sentential oppositions in relational syllogistic logic with the usual syllogistic logic sentences obtained as special cases. The cube comes about by considering Frege–Russell’s quantifier predicate logic with one relation comprising categorical syllogistic sentence forms. The relationships to Buridan’s octagon, to Aristotelian modal logic, and to Klein’s 4-group are discussed. Graphic Abstract: The photo shows a prototype sculpture for the cube. [Figure not available: see fulltext.].

Original languageEnglish
JournalLogica Universalis
Issue number1
Pages (from-to)103-114
Publication statusPublished - 1 Mar 2020


  • Aristotelian square of opposition
  • Buridan’s octagon
  • Klein’s 4-group
  • Predicate logic


Dive into the research topics of 'A Cube of Opposition for Predicate Logic'. Together they form a unique fingerprint.

Cite this