A Type-Logical Account of Quantification in Event Semantics

Abstract

It has been argued that Davidson’s event semantics does not combine smoothly with Montague’s compositional semantics. The difficulty, which we call the event quantification problem, comes from a possibly bad interaction between event existential closure, on the one hand, and quantification, negation, or conjunction, on the other hand. The recent literature provides two solutions to this problem. The first one is due to Champollion [2, 3], and the second one to Winter and Zwarts [13]. The present paper elaborates on this second solution. In particular, it provides a treatment of quantified adverbial modifiers, which was absent from [13].

Appendices

A Appendix

Derivation of expression (24):

Surface realization of expression (24):

B Appendix

This appendix presents a toy grammar that covers the several examples that are under discussion in the course of the paper. It mainly consists of three parts:

• a set of abstract syntactic structures, specified by means of a higher-order signature;

• a surface realization of the abstract structures, specified by means of a homomorphic translation of the signature;

• a semantic interpretation of the abstract structures, specified by means of another homomorphic translation;

Table 1. Abstract syntax

Table 2. Surface realization

Table 3. Semantic types

Table 4. Non-logical constants

Table 5. Semantic Interpretation

1.1 B.1 Abstract Syntax

The signature specifying the abstract syntactic structures is given in Table 1. It uses a type system built upon the following set of atomic syntactic categories:

• $N$, the category of nouns;

• $N _u$, the category of nouns that name units of measurement;

• $NP$, the category of noun phrases;

• $NP _\tau$, the category of noun phrases that denote time intervals;

• $S$ and $S _\circ$, the category of sentences (positive and negative);

• $V$ and $V _\circ$, the category of “open” sentences (positive and negative).

The reason for distinguishing between the categories of positive and negative (open) sentences is merely syntactic. Without such a distinction, the surface realization of a negative expression such as:

would be:

Without this distinction, it would also be possible to iterate negation. This would allow the following ungrammatical sentences to be generated:

1.2 B.2 Surface Realization

The surface realization of the abstract syntactic structures is given in Table 2. This realization is such that every abstract term of an atomic type is interpreted as a string. Accordingly, abstract terms of a functional type are interpreted as functions acting on strings.

1.3 B.3 Semantic interpretation

The semantic interpretation of the abstract syntactic categories is given in Table 3. Besides the usual semantic types $\mathsf {e}$ and $\mathsf {t}$, we also use $\mathsf {v}$, $\mathsf {i}$, and $\mathsf {n}$. These stand for the semantic types of events, time intervals, and scalar quantities, respectively.

The semantic interpretation of the abstract constants is then given in Table 5. This interpretation makes use of the non-logical constants given in Table 4.