Abstract
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.
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Pizzi, C. Generalization and Composition of Modal Squares of Oppositions. Log. Univers. 10, 313–325 (2016). https://doi.org/10.1007/s11787-016-0142-3
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DOI: https://doi.org/10.1007/s11787-016-0142-3