The Square of Opposition and Generalized Quantifiers

In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. pp. 219--227 (2012)
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Abstract
In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. I will conclude with some consideration on scope interactions between quantifiers.
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Quantifiers in Language and Logic.Peters, Stanley & Westerståhl, Dag

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