DFLOW: Duality For Logic On Words

Short Summary
The mathematical theory of Stone duality underlies a deep connection between syntax and semantics in logic and theoretical computer science, and allows for powerful applications in both of these research fields. The aim of this project is to apply the topological methods provided by Stone duality to the study of the expressive power of logic in describing formal languages of both finite and infinite words.

Coordinates
The project started in January 2016. Sam van Gool is the post-doc research fellow on the project. The outgoing phase (2016-2017) took place at the Department of Mathematics of City College of New York and is supervised by Benjamin Steinberg. The return phase (2018) took place at the Institute for Logic, Language and Computation of the University of Amsterdam and will be supervised by Yde Venema. The project was concluded in December 2018. For more information, feel free to send an e-mail to Sam.

Project Highlights

(also see the full lists of Publications and Talks.)

2018

February 2019: the paper Pro-aperiodic monoids and model theory by Sam van Gool and Benjamin Steinberg was accepted for publication in the Israel Journal of Mathematics.
September-December 2018: the project invited five researchers close to the project to the University of Amsterdam for collaborations, and to give talks at the ILLC's Algebra Coalgebra Seminar.
July 2018: talk at International Conference on Semigroups, Lisbon, Portugal, disseminating the work in the project to the wider research community in semigroup theory.
April 2018: research visits to CUNY and Fordham University, with talks in the local seminars.
March 2018: research visit to Computer Science Department, University of Oxford, with a talk in the verification group seminar.
February 2018: research visit to the Mathematics Department (Laboratoire J.A. Dieudonné), Université de Nice, with two talks in the duality working group.
February 2018: research visit to the Mathematics Department, Università degli Studi di Milano.
January 2018: new preprint by Sam van Gool and Benjamin Steinberg: Pointlike sets for varieties determined by groups.

2017

September 2017: invited tutorial on formal languages, semigroups and duality, for a target audience of logicians and linguists, at TbiLLC 2017, Lagodekhi, Georgia.
September 2017: invited talk at Geometry and non classical logics (SYSMICS), Salerno, Italy.
August 2017: new preprint by Sam van Gool and Benjamin Steinberg: Merge decompositions, two-sided Krohn-Rhodes, and aperiodic pointlikes.
August 2017: the paper Sheaves and duality (preprint) by Sam van Gool and Mai Gehrke was accepted for publication in Journal of Pure and Applied Algebra.
May 2017: presentation at AMS Spring Eastern Sectional Meeting, special session on Model Theory, Hunter College, New York, New York.
May 2017: the paper Uniform interpolation and compact congruences (preprint) by Sam van Gool, George Metcalfe and Constantine Tsinakis was accepted for publication in Annals of Pure and Applied Logic.
April 2017: invited talk at ALCOP 2017, Glasgow, Scotland.
March 2017: presentation at STACS 2017 of the paper Pro-aperiodic monoids via saturated models (extended technical report) by Sam van Gool and Benjamin Steinberg.
January 2017: talk at Mathematics Department Colloquium of New Mexico State University.

2016

November 2016: invited 3-hour tutorial at Berkeley-Stanford Circle in Logic and Philosophy.
November 2016: presentation at {Symmetry, Logic, Computation} workshop, part of the thematic semester on Logical Structures in Computation at Simons Institute, Berkeley.
October 2016: two presentations at AMS Fall Western Sectional Meeting, special sessions on Recent Trends in Semigroup Theory and on Algebraic Logic, Denver, Colorado.
September 2016: new technical report by Sam van Gool and Benjamin Steinberg: Pro-aperiodic monoids via saturated models.
August 2016: new submitted preprint by Sam van Gool and Mai Gehrke: Sheaves and Duality.
July 2016: presentation of the paper Monadic second order logic as the model companion of temporal logic (Ghilardi and van Gool) at LICS 2016.
June 2016: the paper A model-theoretic characterization of monadic second order logic on infinite words (Ghilardi and van Gool) was accepted for publication in Journal of Symbolic Logic.
June 2016: presentation at ToLo V by Sam van Gool on the progress made joint with Benjamin Steinberg in the first part of the project.
May 2016: new submitted preprint by Sam van Gool, George Metcalfe and Constantine Tsinakis: Compact Congruences and Uniform Interpolation.
Apr 2016: talk by van Gool in the CUNY Logic Workshop about the progress made joint with Benjamin Steinberg in the first part of the project.
Apr 2016: the paper Monadic second order logic as the model companion of temporal logic (Ghilardi and van Gool) was accepted for a presentation at LICS 2016.
Mar 2016: talk by van Gool in the A|C seminar at ILLC in Amsterdam about the progress made joint with Benjamin Steinberg in the first part of the project.
Feb 2016: talk at Vanderbilt University in Nashville about ongoing joint work with George Metcalfe, Costas Tsinakis and Silvio Ghilardi on duality, compact congruences, and MSO.
Jan 2016: new preprint by Silvio Ghilardi and Sam van Gool: Monadic second order logic as the model companion of temporal logic.

Project funded by Horizon 2020, The EU Framework Programme for Research and Innovation, under the Global Fellowship scheme of the Marie Skłodowska-Curie Actions, grant 655941.

Last updated: 25 February 2019.