29th European Summer School in Logic, Language, and Information
University of Toulouse (France), 17-28 July, 2017

Quantifiers & Determiners

Christian Retoré, Mark Steedman

Workshop First week, from 17:00 to 18:30


The compositional interpretation of determiners relies on quantifiers — in a general acceptation of this later term which includes generalised quantifiers, generics, definite descriptions i.e. any operation that applies to one or several formulas with a free variable, bounds it and yields a formula or possibly a generic term (the operator is then called a subnector, following Curry). There is a long history of quantification in the Ancient and Medieval times at the border between logic and philosophy of language, before the proper formalisation of quantification by Frege.

A common solution for natural language semantics is the so-called theory of generalised quantifiers. Quantifiers like "some, exactly two, at most three, the majority of, most of, few, many, …" are all described in terms of functions of two predicates viewed as subsets.

Nevertheless, many mathematical and linguistic questions remain open.

On the mathematical side, little is known about generalised and vague quantifiers, in particular on their proof theory. On the other hand, even for standard quantifiers, indefinites and definite descriptions, there exist alternative formulations with choice functions and generics or subnectors (Russell’s iota, Hilbert-Bernays, eta, epsilon, tau). The computational aspects of these logical frameworks are also worth studying, both for computational linguistic software and for the modelling of the cognitive processes involved in understanding or producing sentences involving quantifiers.

On the linguistic side, the relation between the syntactic structure and its semantic interpretation, quantifier raising, underspecification, scope issues,... are not fully satisfactory. Furthermore extension of linguistic studies to various languages have shown how complex quantification is in natural language and its relation to related phenomena like generics, plural and mass nouns.

Finally, and this can be seen as a link between formal models of quantification there by now exist psycholinguistic experiments that connect formal models and their computational properties to the actual way human do proceed sentences with quantifiers, and handle their inherent ambiguity, difficulty in understanding and complexity.

This workshop aims at gathering logicians and linguists to present their latest advances in the study of quantification.