Logica Universalis

, Volume 10, Issue 2–3, pp 293–312

Logical Squares for Classical Logic Sentences

Open Access

DOI: 10.1007/s11787-016-0148-x

Cite this article as:
Wybraniec-Skardowska, U. Log. Univers. (2016) 10: 293. doi:10.1007/s11787-016-0148-x


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 

Copyright information

© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

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

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