Quantification and Quantificational Structures 7/21/17 Overview - PowerPoint PPT Presentation

Quantification and Quantificational Structures 7/21/17

Overview • Interpreting DPs (entity denoting, first order quantification, generalized quantification) • Potential for scope interactions • Expressivity of natural language quantification • Linguistically significant typology of quantifiers • Diversity at the interface: nominal and adverbial quantification

First Order Quantification Two Inter-definable Binding Operators

Practice Sentences Single quantifier sentences

Logical translations Unrestricted variables

Alternative (First Order) Representation Restricted variable binding operators

Translation Procedure Determiners provide templates 
 for logical representations

“Quantifier Raising” • Remove quantificational DPs, replacing the by associated (novel) variables. • Translate the DPs using determiner templates, using the NP content as the restriction. • Reassemble the templates into a single formula, using available formulas to replace the scopes of the quantifiers.

Every dog chased some cat.

Generalized Quantifiers Determiners as (second order) relations between sets

Linguistically Significant Classes of Quantifiers • Intersective (symmetric) • Proportional (asymmetric) • Strong vs. Weak DPs • Milsark’s generalization: properties may only be predicated of strong DPs; pivots of existential must be given weak interpretations. • Monotonicity (increasing v. decreasing)

Monotonicity • Increasing: For B ≤ C, then D(A,B) entails D(A,C) • Decreasing: For B ≤ C, then D(A,C) entails D(A,B) • Every man walks slowly. Every man walks. • No man walks. No man walks slowly.

Diversity at the Interface • Determiner (Nominal) quantification vs. • Adverbial Quantification • Fido usually chases a cat. • Pu ff sometimes eats sardines. • Cats rarely chase dogs.

Questions and Discussion