End of the square?

South American Journal of Logic 4 (2):485-505 (2018)
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It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and unique pattern of oppositions that proceeds with colored diagrams and an increasing set of bitstrings.

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Fabien Schang
Universidade Federal de Goiás (PhD)


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