par Libert, Thierry 
Référence Around and Beyond the Square of Opposition, Springer Basel, page (293-301)
Publication Publié, 2012-01
Référence Around and Beyond the Square of Opposition, Springer Basel, page (293-301)
Publication Publié, 2012-01
Partie d'ouvrage collectif
| Résumé : | We define hypercubes of duality-of which the modern square of opposition is an emblematic example-in proper mathematical terms, as orbits under some action of the additive group Zm 2 , with m ε N. We then introduce a notion of dimension for duality in classical logic and show, for example, how propositional expressions in at most three variables can be classified according to that notion. The paper ends with logical formulations of some representation theorem for Galois connections on powersets, where we see an underlying square of duality. |
