## QUAD: QUantifiers And Determiners

### Toulouse, Monday July 17 — Friday July 21: 17:00-18:30

### ESSLLI 2017 workshop

### Schedule:

deadline for submissions: **17 March 2017**

submission website: https://easychair.org/conferences/?conf=quad2017

notification to authors: 15 April 2017

final version due: 19 May 2017

conference: 17-21 July 2017

### Presentation:

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, binds 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 , generalised and vague quantifiers, in particular about 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 phenomena like generics, plurals, and mass nouns.

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

All those aspects are connected in the didactics of mathematics and computer science: there are specific difficulties to teach (and to learn) how to understand, manipulate, produce and prove quantified statements, and to determine the proper level of formalisation between bare logical formulas and written or spoken natural language.

This workshop aims at gathering mathematicians, logicians, linguists, computer scientists to present their latest advances in the study of quantification.

Among the topics that wil be addressed are the following :

- new ideas in quantification in mathematical logic, both model theory and proof theory:
- choice functions,
- subnectors (Russell’s iota, Hilbert’s epsilon and tau),
- higher order quantification,
- quantification in type theory

- studies of the lexical, syntactic and semantic of quantification in various languages
- semantics of noun phrases
- generic noun phrases
- semantics of plurals and mass nouns
- experimental study of quantification and generics
- computational applications of quantification and polarity especially for question-answering.
- quantification in the didactics of mathematics and computer science.

### Some recent relevant references:

- Anna Szabolcsi Quantification Cambridge University Press 2010
- Stanley Peters and Dag Westerstahl Quantifiers in Language and Logic Oxford Univ. Press 2010
- Mark Steedman Taking Scope – The Natural Semantics of Quantifiers MIT Press 2012
- Jakub Szymanik. Quantifiers and Cognition, Studies in Linguistics and Philosophy, Springer, 2015.
- Vito Michele Abrusci, Fabio Pasquali, and Christian Retoré. Quantification in ordinary language and proof theory. Philosophia Scientae, 20(1):185–205, 2016.

### Submissions:

The program committee is looking for contributions introducing new viewpoints on quantification and determiners, the novelty being either in the mathematical logic framework or in the linguistic description or in the cognitive modelling. Submitting purely original work is not mandatory, but authors should clearly mention that the work is not original, and why they want to present it at this workshop (e.g. new viewpoint on already published results)

Submissions should be

- 12pt font (at least)
- 1inch/2.5cm margins all around (at least)
- less than 2 pages (references excluded)
- with an abstract of less then 100 words
- submitted in PDF by Easychair here: https://easychair.org/conferences/?conf=quad2017

In case the committee thinks it is more appropriate, some papers can be accepted as a poster with a lightning talk.

Final versions of accepted papers may be slightly longer. They will be published on line. We also plan to publish postproceedings

### Programme committee:

- Christian Retoré (Université de Montpellier & LIRMM-CNRS)
- Mark Steedman (University of Edinburgh)
- Vito Michele Abrusci (Università di Roma tre)
- Mathias Baaz (University of Technology, Vienna)
- Daisukke Bekki (Ochanomizu University, Tokyo)
- Oliver Bott (Universität Tübingen)
- Francis Corblin (Université Paris Sorbonne)
- Martin Hakl (Massachusetts Institute of Technology, Cambridge MA)
- Makoto Kanazawa (National Institute of Informatics, Tokyo)
- Dan Lassiter (Stanford University)
- Zhaohui Luo (Royal Holloway College, London)
- Alda Mari (CNRS Institut Jean Nicod, Paris)
- Wilfried Meyer-Viol (King’s college, London)
- Michel Parigot (CNRS IRIF, Paris)
- Anna Szabolcsi (New-York University)
- Jakub Szymanik (Universiteit van Amsterdam)
- Dag Westerstahl (Stockholm University)
- Bruno Woltzenlogel Paleo (University of Technology, Vienna)
- Richard Zach (University of Calgary)
- Roberto Zamparelli (Università di Trento)