---
tags: logic, ai, category theory
---
# 1st GALAI Workshop, Fri, Jan 26

[GALAI homepage](https://sites.google.com/chapman.edu/galai/home)

---

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.




## **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](https://colab.research.google.com/drive/1aqn0UIhQhwii52ZU3neajVAh35qiAZMH#scrollTo=NX1LJ_DARbwM)



## 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](https://hackmd.io/@alexhkurz/SJ50WIb9T)

## Caleb Schultz Kisby

**Logical Dynamics of Neural Network Learning**

[Slides](https://alexhkurz.github.io/1st-GALAI-workshop/Schultz-Kisby/slides.pdf) ... [Article](https://alexhkurz.github.io/1st-GALAI-workshop/Schultz-Kisby/IteratedHebbian.pdf)

## Alexandru Baltag

**The Topology of Surprise**

[Slides](https://alexhkurz.github.io/1st-GALAI-workshop/Schultz-Kisby/Baltag-Surprise.pdf)

Articles by Alexandru Baltag, Nick Bezhanishvili, David Fernández-Duque:
- [The Topological Mu-Calculus: completeness and decidability](https://arxiv.org/abs/2105.08231), 2021.
- [The Topology of Surprise](https://proceedings.kr.org/2022/4/kr2022-0004-baltag-et-al.pdf), 2022.

## Sonja Smets

**Logic and Computation of Social Behaviour**

- A. Baltag, Z. Christoff, J.U. Hansen and S. Smets. [Logical Models of Informational Cascades](https://www.researchgate.net/publication/257143800_Logical_Models_of_Informational_Cascades). 2013.
- Baltag, A., Christoff, Z., Rendsvig, R.K., Smets, S.: [Dynamic epistemic logics of diffusion and prediction in social networks](https://eprints.illc.uva.nl/id/document/1294) (2016)