Event Quantification in Infinitival Complements: A Free-Logic Approach

Abstract

In this paper, I argue that some infinitival complements can be analyzed as an argument of verbs, in the same way of perception verb analysis (Higginbotham 1983). Then, I consider an event quantification problem in infinitival complements, showing that quantificational event semantics (Champollion 2015) and free logic are the keys to solving it.

A Appendix: Formal Syntax for the Quantificational Event Semantics

In this appendix, I offer a simple grammar formalism which the quantificational event semantics is based on.

1.1 A.1 Directional Minimalist Grammar without MOVE

I introduce a (tiny) variant of Directional Minimalist Grammars (DMGs, Stabler 2011). Though the original DMGs have a MOVE operation, here I present a grammar formalism without MOVE to avoid unnecessary complexities. Similar approaches are adopted by Hunter (2010) and Tomita (2016).

Notations. Here I lay out formal notations which I use in this appendix.

A finite set of phonological expressions (or strings) V contains items such as Mary, forbade, (to) leave, ..., and the empty string $\varepsilon$. A set of category features B contains items such as c, d, v, .... This set determines a set of (right and left) selector features $B_{\texttt {=}} = \{ \texttt {b=}\mid \texttt {b}\in B\}\cup \{\texttt {=b}\mid \texttt {b}\in B\}$. Both category and selector features are called syntacitic features. A set of sequences of syntacitic features Syn is defined as $B_{\texttt {=}}^{*}\times B$.

Fig. 1.

Operation for DMGs

Grammar. The grammar formalism consists of a set of category features B, a set of phonological expressions V, and a finite set Lex, which consists of tuples of a phonological expression and a sequence of syntactic features, i.e., $\textit{Lex} \subseteq V\times \textit{Syn}$.

The grammar has a structure-building function called MERGE, which takes two expressions and combines them, concatenating two strings and saturating the leftmost selector feature with a corresponding category feature. This function is a union of two sub-operations, MRG$_1$ and MRG$_2$ shown in Fig. 1.

The set of well-formed expressions is a closure of expressions in $\textit{Lex}$ under MERGE. A derivation is completed when the only remaining feature in the well-formed expression is c.

1.2 A.2 Combination of the Grammar Formalism and Quantificational Event Semantics

On the semantic side of things, a minimalist expression is a sequence of pairs of both a syntactic feature and a semantic component. Following Hunter (2010) and Tomita (2016), I assume that the meaning of each verb consists of multiple semantic components.

First, verbal denotations are assigned to each category feature v in verbs.

where $\mathbf V$ is a verbal predicate constant (e.g. $\mathbf{stabbing }$, $\mathbf{finding }$,...) of type vt.

Second, a thematic predicate is assigned to each selector feature, being separated from the verbal denotation.

Table 2. A fragment for the free-logic approach

where r is a thematic role function of type ve such as ag, th,.... The leftmost selector feature in perceptual verbs is anntated with the different thematic predicate which contains the existence predicate.

A fragment of the grammar formalism with semantics is shown in Table 2.

Composition Scheme. The meaning of complex expressions (sentences and phrases) is composed via MERGE in derivations.

A composition scheme for MERGE is as follows. Along the lines of Tomita (2016), MERGE involves the functional application of an argument Q and a semantic component R assigned to the leftmost selector b= or =b. Then, this semantic component is applied to P, being assigned to the remaining category feature b’.

where P, Q, R, $R_i$ are semantic components, s and t range over sequences of strings in $V^{*}$, $\texttt {b}$ and $\texttt {b}'$ range over category features in B, and $\texttt {f}_i$ ranges over selector features in $B_{\texttt {=}}$ for $1\le i\le n$. Example derivations for Mary saw everyone leave and Mary forbade everyone to leave are shown in Figs. 2 and 3, respectively.

Fig. 2.

Example derivation for Mary saw everyone leave

Fig. 3.

Example derivation for Mary forbade everyone to leave