Chapter

Around and Beyond the Square of Opposition

Part of the series Studies in Universal Logic pp 219-227

The Square of Opposition and Generalized Quantifiers

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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.

Keywords

Generalized quantifiers Semantics Logical duality

Mathematics Subject Classification

03B65 68Q55