1st GALAI Workshop, Fri, Jan 26

GALAI homepage


Invited Speakers:

  • Alexandru Baltag (University of Amsterdam)
  • Caleb Schultz Kisby (Indiana University Bloomington)
  • Sonja Smets (University of Amsterdam)

Speakers from Chapman Univeristy:

  • Drew Moshier
  • Peter Jipsen
  • Jose Gil-Ferez
  • Alexander Kurz

Local Organizer: Alexander Kurz


Drew Moshier

Relations in Point-Free Topology

We report on progress on a program of investigating relations on point-free topological spaces (locales). As the category of locales is order-enriched, a natural notion of a relation from X to Y is a jointly epi cospan X->C<-Y. Dualizing, these manifest as special spans on the category of frames. Namely, we see that they correspond to the familiar notion of weakening relations between frames that are compatible with the frame structure in an obvious way. Thus, the study of point-free relations is the study of these so-called frame relations.

In the talk today, we build some of the needed techniques to deal with frame relations systematically. As one application, we show that on any frame L, the preorder frame relations on L constitute another frame, dually isomorphic to the coframe of point-free subspaces of L. We then prove directly a known result of Plewe that this frame is ultraparacompact, and also that is satisfies a certain density result. Together, these two properties are strong, and appear to be very nearly characterizing frames that occur as frames of nuclei.

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Peter Jipsen

Using Prover9/Mace4 to Investigate Kripke Frames of Distributive Quasi Relation Algebras

Joint work with Andrew Craig and Claudette Robinson (University of Johannesburg)

Python Notebook on Colab

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Jose Gil-Ferez

A Formal Deductive System for Euclid's Elements (Book I)

Alexander Kurz

The 'Blacktriangle' Calculus

Part of a project with Giuseppe Greco, Apostolos Tzimoulis, Brandon Laing

Slides

Caleb Schultz Kisby

Logical Dynamics of Neural Network Learning

Slides Article

Alexandru Baltag

The Topology of Surprise

Slides

Articles by Alexandru Baltag, Nick Bezhanishvili, David Fernández-Duque:

Sonja Smets

Logic and Computation of Social Behaviour