Logica Universalis

, Volume 10, Issue 2–3, pp 313–325 | Cite as

Generalization and Composition of Modal Squares of Oppositions

  • Claudio PizziEmail author


The first part of the paper aims at showing that the notion of an Aristotelian square may be seen as a special case of a variety of different more general notions: (1) the one of a subAristotelian square, (2) the one of a semiAristotelian square, (3) the one of an Aristotelian cube, which is a construction made up of six semiAristotelian squares, two of which are Aristotelian. Furthermore, if the standard Aristotelian square is seen as a special ordered 4-tuple of formulas, there are 4-tuples describing rotations of the original square which are non-standard Aristotelian squares. The second part of the paper focuses on the notion of a composition of squares. After a discussion of possible alternative definitions, a privileged notion of composition of squares is identified, thus opening the road to introducing and discussing the wider notion of composition of cubes.


Square of oppositions modal logic bimodality cube of oppositions composition of squares 

Mathematics Subject Classification



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© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Emeritus University of SienaMilanoItaly

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