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.
• Puff sometimes eats sardines.
• Cats rarely chase dogs.

Questions and Discussion