In Jean-Yves Beziau & Dale Jacquette (eds.), Around and beyond the Square of Opposition. Birkhäuser-Springer. pp. 229--239 (2012)

Stamatios Gerogiorgakis
Universität Erfurt
I try to explain the difference between three kinds of negation: external negation, negation of the predicate and privation. Further I use polygons of opposition as heuristic devices to show that a logic which contains all three mentioned kinds of negation must be a fragment of a Łukasiewicz-four-valued predicate logic. I show, further, that, this analysis can be elaborated so as to comprise additional kinds of privation. This would increase the truth-values in question and bring fragments of (more generally speaking) Łukasiewicz-n-valued predicate logics into the scene.
Keywords Privation  Negation  Łukasiewicz-n-valued predicate logic
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