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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Notes
- 1.
S is the symbol for the syntactic category of ‘sentence’, VP for ‘verb phrase’.
- 2.
The distinction here introduced is slightly different from the original characterization of definite NPs as filters due to Barwise and Cooper [2] and revisited by Loebner [4]. For example, the classification here proposed has the concept of filter in common with the characterization of NPs in Loebner [4], but the method of “squaring” logical properties of quantifiers involves some not negligible differences. The effect of the inner negation in determining contradiction or contrariness is here the only parameter used in distinguishing quantifiers. As a consequence, three classes of quantifiers are proposed, while Loebner essentially distinguishes only between filters and ultrafilters, as his main concern, in the cited article, is the semantics of definite NPs, and not NPs overall considered as generalized quantifiers.
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D’Alfonso, D. (2012). The Square of Opposition and Generalized Quantifiers. In: Béziau, JY., Jacquette, D. (eds) Around and Beyond the Square of Opposition. Studies in Universal Logic. Springer, Basel. https://doi.org/10.1007/978-3-0348-0379-3_15
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DOI: https://doi.org/10.1007/978-3-0348-0379-3_15
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