I'm happy that my proposal for an introductory course on Homotopy Type Theory / Univalent Foundations at the European Summer School in Logic, Language and Information 2026 in Prague was accepted!

A great opportunity to make use of @egbertrijke's recently published book, @MartinEscardo's lecture notes (in Agda!) and @danielgratzer and @carloangiuli's book draft!

Links for the curious:
- Egbert's book: doi.org/10.1017/9781108933568 & arxiv.org/abs/2212.11082
- Martín's notes: cs.bham.ac.uk/~mhe/HoTT-UF-in-…
- Daniel and Carlo's book draft: danielgratzer.com/papers/type-…

#logic #typetheory

Introduction to Homotopy Type Theory

This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions.

^arXiv.org

I think my paper on Dummett, proof assistants and pluralism has shaped up rather nicely, and it will be good to see it out in the Proceedings of the Aristotelian Society in a few months’ time. You can read the preprint now.

Thanks to everyone who gave me feedback on earlier drafts, and discussed these issues along the way.

There's more to be done, but I hope to have clarified some issues around how we can think about the relationship between constructive and classical reasoning, and how philosophers might engage with what is going on in the application of dependent type theory in proof assistants, programming language design, and the formalisation and mechanisation of reasoning.

consequently.org/writing/what-…

#logic #prooftheory #typetheory #philosophy

I'm a little puzzled at the salience that is being given to the Apple conclusions on #LLM #reasoning when we have lots of prior art. For example: LLMs cannot correctly infer a is b, if their corpora only contain b is a. #Paper: arxiv.org/abs/2309.12288

#AI #MachineLearning #logic

The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"

We expose a surprising failure of generalization in auto-regressive large language models (LLMs). If a model is trained on a sentence of the form "A is B", it will not automatically generalize to the reverse direction "B is A".

^arXiv.org

Coming up in the new academic year, I get to spend the semester with a fresh bunch of second-year students who are going on to learn some more logic than the first-year basics.

Like last year, in Intermediate Logic we’ll be exploring natural deduction proof theory and different kinds of models for propositional, modal and first-order predicate logic.

New this year, my Doktorvater, Prof. Graham Priest, will be joining us in the last week of classes, so we’ll have a fun back-and-forth about truth-value gaps, gluts and paradoxes to end things with a bit of a bang.

consequently.org/class/2024/py…

#logic #philosophy

#AudioMo: Welcome to the Shift R trick.
I play stuff, I shift R it, I hope it’s OK.

This is a track-stack with two Keyscape sounds, the Double Felt Grand, and the Dulcitone.
Shift R in #Logic is basically like the capture option in #Ableton, IE: even when the transport is stopped, it will capture what you recorded and add it to the focused MIDI track. Doesn't work with audio.