The Square of Opposition and Generalized Quantifiers
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.
KeywordsGeneralized quantifiers Semantics Logical duality
Mathematics Subject Classification03B65 68Q55
- 5.Mostowsky, A.: On a generalization of quantifiers. Fundam. Math. 44, 12–36 (1957) Google Scholar
- 6.Parsons, T.: The traditional square of opposition. In: Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/square (2006)
- 7.Peters, S., Westerståhl, D.: Quantifiers in Language and Logic. Oxford University Press, Oxford (2006) Google Scholar