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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Duilio D'Alfonso
University of Palermo

Citations of this work

Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
Duality in Logic and Language.Lorenz Demey, and & Hans Smessaert - 2016 - Internet Encyclopedia of Philosophy.
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Natural Density and the Quantifier “Most”.Selçuk Topal & Ahmet Çevik - 2020 - Journal of Logic, Language and Information 29 (4):511-523.

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References found in this work

Generalized quantifiers and natural language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Generalized Quantifiers and Natural Language.Jon Barwise - 1980 - Linguistics and Philosophy 4:159.
Quantifiers in Language and Logic.Stanley Peters & Dag Westerståhl - 2006 - Oxford, England: Clarendon Press.
Quantifiers in Language and Logic.Stanley Peters & Dag Westerståhl - 2006 - Oxford, England: Oxford University Press UK.
On a generalization of quantifiers.Andrzej Mostowski - 1957 - Fundamenta Mathematicae 44 (2):12--36.

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