Aside from their canonical interrogative use, wh-words are used in many languages to build a range of quantificational expressions. What syntactic and semantic strategies are employed to quantify over the alternatives introduced by wh-words? To answer this question, I have investigated a number of non-interrogative wh-constructions — often with Hadas Kotek — in Toba Batak (Austronesian), Chuj (Mayan), Tibetan, Burmese, and English.

In many languages, quantificational meanings are formed by combining a wh-word with an additional morpheme, which is often a scalar focus particle or disjunctor (see e.g. Haspelmath 1997: 157). I am currently developing a framework for the compositional semantics of wh-quantification in the two-dimensional Alternative Semantics framework of Rooth (1985, 1992) which models various attested forms of wh-quantification, and helps us explain the prevalent use of disjunctors and focus particles in wh-quantification.

A cross-linguistically common pattern of wh-quantification is wh-even NPIs in Tibetan. Hadas Kotek and I present a new compositional syntax/semantics for wh-even NPIs, improving upon previous analyses such as Ramchand (1996), with implications for the analysis of ‘even.’ Our analysis uses both the scalar and additive meanings introduced by ‘even,’ and crucially computes these two meanings with different scopes. I am exploring an extention of this account to the behavior of wh-even NPIs in Japanese and other languages.

In recent work in progress, I have investigated the Tibetan particle yin.n’ang which has three uses: (a) as a counterexpectational discourse particle (like English ‘but’ or ‘however’), (b) as a scalar concessive particle, and (c) to form wh-free choice items. Morphologically, yin.n’ang is transparently the combination of a copular verb, conditional ending, and scalar particle (e.g. ‘even’). I develop a compositional semantics for three functions from these ingredients, and also advocate for the extension of this approach to Japanese demo and similar particles in Dravidian languages, which have similar distributions and morphological makeup.

An example of a more complex particle involved with wh-quantification is manang in Toba Batak, which is a disjunctor but also forms wh-NPIs and wh-free choice items. I propose that manang is the spellout of maximally two logical operators: J, which collects the ordinary semantic values of disjuncts into a set of alternatives, and ∃, which creates an existential quantifier from a set of alternatives. In the Alternative Semantics framework, I derive the different disjunctive and wh-quantifying uses of manang and various constraints on their interpretation. I additionally report on the use of manang in embedded questions.

Hadas Kotek and I have investigated bare wh-indefinites and free relatives in Chuj, an understudied Mayan language of Guatemala. We show that indefinite free relatives in Chuj are equivalent in size to definite free relatives, as proposed by Caponigro (2003), contrary to a conjecture by Šimík (2011) that indefinite free relatives are always reduced clauses. We have also contributed a survey of non-interrogative uses of wh-words in the language.

In other work, Hadas and I have investigated the syntax and semantics of wh-words used as relative pronouns. Using the intervention effect diagnostics which we pioneered, we show that relative pronouns in English non-restrictive relatives are interpreted in-situ within their pied-piping constituents via focus alternative computation. We show that this supports the view that non-restrictive relatives are proposition-denoting, rather than property-denoting.

Return to all projects