Logica Universalis

, Volume 10, Issue 2–3, pp 293–312 | Cite as

Logical Squares for Classical Logic Sentences

  • Urszula Wybraniec-SkardowskaEmail author
Open Access


In this paper, with reference to relationships of the traditional square of opposition, we establish all the relations of the square of opposition between complex sentences built from the 16 binary and four unary propositional connectives of the classical propositional calculus (CPC). We illustrate them by means of many squares of opposition and, corresponding to them—octagons, hexagons or other geometrical objects.


Square of opposition classical propositional connectives truth-value table tautology of classical logic octagon of opposition hexagon of opposition octahedron of opposition 

Mathematics Subject Classification

Primary 03B05 03B65 Secondary 03B80 


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Authors and Affiliations

  1. 1.Department of PhilosophyCardinal Stefan Wyszyński University in WarsawWarsawPoland

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