Hilbert’s Epsilon and Tau in Logic, Informatics and Linguistics

University of Montpellier.  June 10, 11, 12.

Organized by Université de Montpellier and LIRMM-CNRS with the support of Kurt Gödel Society, the ANR project Polymnie and the Hilbert-Bernays project.



This workshop aims at promoting work on Hilbert's Epsilon in a number of relevant fields ranging from Philosophy and Mathematics to Linguistics and Informatics. The Epsilon and Tau operators were introduced by David Hilbert, inspired by Russell's Iota operator for definite descriptions, as binding operators that form terms from formulae. One of their main features is that substitution with Epsilon and Tau terms expresses quantification. This leads to a calculus which is a strict and conservative extension of First Order Predicate Logic. The calculus was developed for studying first order logic in view of the program of providing a rigorous foundation of mathematics via syntactic consistency proofs. The first relevant outcomes that certainly deserve a mention are the two "Epsilon Theorems" (similar to quantifiers elimination), the first correct proof of Herbrand's theorem or the use of Epsilon operator in Bourbaki’s Éléments de Mathématique. In nineties, renewing Russell's ideas on definite descriptions, there has been some work on the interpretation of determiners and noun phrases with Hilbert's epsilon. Nowadays the interest in the Epsilon substitution method has spread in a variety of fields : Mathematics, Logic, Philosophy, History of Mathematics, Linguistics, Type Theory, Computer science, Category Theory and others.

Beside the famous Grundlagen der Mathematik of Hilbert and Bernays, a general presentation of the topic can be found in the webpages of the Stanford Encyclopedia of Philosophy and Internet Encyclopedia of Philosophy.


Registration includes coffee breaks, Thursday and Friday lunches, conference dinner.

Registration fee is 120€ (80€ for members of the University of Montpelier).

To register please connect to the following link: register

To inquiry please email to epsilon2015@easychair.org 


Location and dates

Epsilon2015 is hosted by the Univeristy of Montpellier.

Dates:                 - 10th - 12th of June.

Exact location:  - Faculté des Sciences - Place Eugène Bataillon - 34095 Montpellier cedex 5

                            - building: batiment 16

                            - room: "salle de cours 16.01"

How to reach the Faculté des Sciences:

                            - from the city center and from the train station "Saint Roch": 

                              Take the tramway 1, direction Mosson and stop at "Universités Sciences et Lettres". 

                              Walk along "Avenue Augustin Fliche" until you reach the roundabout. 

                              Take the second exit and you are in Place Eugéne Battalion.

                            - from the airport:

                              Take the airport shuttle, line 120, and stop at "Place de l'Europe"

                              Take the tramway 1, direction Mosson and stop at "Universités Sciences et Lettres".

                              Walk along "Avenue Augustin Fliche" until you reach the roundabout.                        

                              Take the second exit and you are in Place Eugéne Battalion.

Some information on public transportation in Montpellier can be found here (French site).

Travel to Montpellier:

Montpellier airport

Marseille airport has many international flights (the site includes the information for shuttles and trains to Montpellier - about 2 hours)

Trains in France (including fast trains connections with Paris, Lyon, Barcellona)

Useful information concerning your stay in Montpellier can be found here.


Wednesday (10th of June):     

13.00 - 13.30     REGISTRATION & WELCOME

13.30 - 14.30     Invited lecture (Hilbert-Bernays project): Claus-Peter Wirth (University of Saarland) 

                            The descriptive operators iota, tau and epsilon - on their origin, partial and complete specification

                            model-theoretic semantics, practical applicability

14.30 - 15.00     Coffee break

15.00 - 15.30     Bhupinder Singh Anand (Independent scholar, Mumbai)

                            Why Hilbert’s and Brouwer’s interpretations of quantification are complementary and not contradictory

15.30 - 16.00     David DeVidi (University of Waterloo) Corey Mulvihill (University of Waterloo)

                            Buying Logic with Ontological Coin

16.00 - 16.30     Hartley Slater (University of Western Australia)

                            Gödel’s Theorems and the Epsilon Calculus

16.30 - 17.00     Norbert Gratzl (LMU/MCMP) and Georg Schiemer (University of Vienna)

                            Hilbert’s ε-termes, Russell’s Indefinites and Indexed ε-terms

Thursday (11th of June):

09.30 - 10.30     Invited lecture: Vito Michele Abrusci (University of Roma Tre) 

                            Hilbert's tau and epsilon in proof theory

10.30 - 11.00     Coffee break

11.00 - 11.30    Alexander Leitsch (Vienna University of Technology), Giselle Reis (Inria Saclay) 

                            and Bruno Woltzenlogel Paleo (Vienna University of Technology)

                            Epsilon Terms in Intuitionistic Sequent Calculus

11.30 - 12.00     Thomas Powell (University of Innsbruck)

                            Variations on learning: Relating the epsilon calculus to proof interpretations

12.00 - 12.30     Matthias Baaz (Vienna University of Technology) and Daniel Weller (Vienna University of Technology)

                            Cut-free epsilon-calculus allows a non-elementary speed-up

12.30 - 13.00     Fabio Pasquali (University of Aix-Marseille & I2M CNRS)

                            A categorical approach to the typed Epsilon Calculus

13.00 - 14.30     Lunch

14.30 - 15.00     Wilfried Meyer-Viol (King's College London)

                            Non-Monotonic Logic in the Epsilon Calculus

15.00 - 15.30     Federico Aschieri (Vienna University of Technology)

                            Type Theory, Realizability and Epsilon Substitution Method

15.30 - 16.00     Nissim Francez (Technion) and Bartosz Wieckowski (University of Frankfurt)

                            A proof-theory for first-order logic with definiteness

16.00 - 16.30     Coffee break

16.30 - 17.00     Sergei Soloviev (University of Toulose III, IRIT)

                            Studies of Hilbert’s epsilon operator in the USSR

17.00 - 17.30     Hans Leiß (University of Munich)

                            Equality of Contexts in the Indexed Epsilon-Calculus

20.00                  Dinner at Hôtel Oceania le Métropole

                            3, rue du Clos René

Friday (12th of June)

09.30 - 10.30     Invited lecture: Hartley Slater (University of Western Australia) 

                            Linguistic and philosophical ramifications of the epsilon calculus

10.30 - 11.00     Coffee break

11.00 - 11.30     Ruth Kempson (King's College London), Stergios Chatzikyriakidis (University of Montpellier II, LIRMM)

                            and Ronnie Cann (University of Edimburgh)

                            The interactive Building of Names

11.30 - 12.00     Sumiyo Nishiguchi (Tokyo University of Science)

                            Noun Phrases in Japanese and Epsilon-Iota Calculi

12.00 - 12.30     Koji Mineshima (Ochanomizu University)

                            Epsilon Calculus as Presupposition Theory

12.30 - 13.00     Bruno Mery (University of Bordeaux, LaBRI), Richard Moot (University of Bordeaux, LaBRI) 

                            and Christian Retoré (University of Montpellier, LIRMM)

                            Typed Hilbert’s Operators for the Lexical Semantics of Singular and Plural Determiner Phrases

Program committee 


Daisuke Bekki (Ochanomizu University)

Stergios Chatzikyriakidis (University of Montpellier & LIRMM-CNRS)

Francis Corblin  (University of Paris-Sorbonne & Institut Jean Nicod CNRS)

Michael Gabbay (University of Cambridge)

Makoto Kanazawa (National Institue of Informatics of Tokyo)

Ruth Kempson (King's College, London)

Ulrich Kohlenbach (Darmstadt University of Technology)

Alda Mari (Institut Jean Nicod CNRS & ENS & EHESS)

Richard Moot (University of Bordeaux & LaBRI)

Georg Moser (University of Innsbruck)

Michel Parigot (University of Paris Diderot 7 & CNRS-PPS)

Fabio Pasquali (University of Aix-Marseille & I2M CNRS)

Christian Retoré (University of Montpellier LIRMM-CNRS)

Mark Steedman (University of Edimburgh)

Bruno Woltzenlogel Paleo (Vienna University of Technology)

Richard Zach (University of Calgary)