We are glad to announce that Professor Jan A Bergstra, formerly Director of Informatics, University of Amsterdam, and chair of Informatics Section of Academia Europaea will be visiting Swansea University next week.

# Author Archives: OP

# 2nd World Logic Day

Today as a part of the 2nd World Logic Day our Theory group commemorated the work of Erik Palmgren (1963-2019), who sadly passed away last year.

Anton Setzer presented Erik’s most influential papers, which had a big impact on Anton’s own research.

# Paul Shafer is coming to Swansea

# Meeting to commemorate the logician Erik Palmgren (1963-2019) on the occasion of the World Logic Day

We meet to remember the great logician Erik Palmgren who sadly passed away in November 2019 .

To honor Erik Palmgren’s work, Anton Setzer will give a talk with the title:

*Palmgren’s interpretation of inductive definitions in type theory and development of higher type universes in type theory.*

The meeting also marks the 2nd World Logic Day.

Venue: Theory Lab (CoFo 209)

Time: 14th of January 2020, 2-3 pm

# Hideki Tsuiki is back in Swansea

We are glad to welcome Hideki Tsuiki in Swansea again. This Thursday we really enjoyed his talk on “Imaginary Cubes — Mathematics, Puzzle, Art and Education”.

**Abstract:** Imaginary cubes are three-dimensional objects with square projections in three orthogonal ways just as a cube has. How many different kinds of imaginary cubes can you imagine? In this talk we show that there are 16 kinds of minimal convex imaginary cubes which includes regular tetrahedron, cuboctahedron, and two objects that we call H and T. As we will explain, H and T have a lot of beautiful mathematical properties related to tiling, fractal, and higher-dimensional geometry, and based on these properties, the speaker has designed a puzzle, constructed three-dimensional math-art objects, and used them for educations at various levels from elemental school to graduate schools. In this talk, I will explain mathematics of imaginary cubes and show the activities I have been engaged in. I will carry a couple of copies of the puzzle and some of the math-art objects so that the audience can enjoy them while I am staying in Swansea.

# 2nd Proof Society Workshop on Proof Theory and its Applications

Following the Summer School, we are really proud to host the 2nd Proof Society Workshop. The workshop was an opportunity to listen to a lot of interesting invited and contributed talks on proof theory and various areas of its application:

**Adam Wyner:** Computational Law – The Case of Autonomous Vehicles

**Yong Cheng:** Exploring the incompleteness phenomenon

**Matthias Baaz:** Towards a Proof Theory for Henkin Quantifiers

**Sonia Marin:** On cut-elimination for non-wellfounded proofs: the case of PDL

**Gilles Dowek:** Logical frameworks, reverse mathematics, and formal proofs translation

**Benjamin Ralph:** What is a combinatorial proof system?

**William Stirton:** Ordinal assignments correlated with notions of reduction

**Oliver Kullmann:** Practical proof theory: practical versions of Extended Resolution

**Anton Setzer** and** Ulrich Berger **on behalf of **Ralph Matthes:** Martin Hofmann’s case for non-strictly positive data types – reloaded

**Laura Crosilla:** Philosophy of mathematics and proof theory

**Takako Nemoto:** Recursion Theory in Constructive Mathematics

**Arno Pauly:** Combinatorial principles equivalent to weak induction

**Antonina Kolokolova:** The proof complexity of reasoning over richer domains

**Joost Joosten:** The reduction property revisited

**Helmut Schwichtenberg:** Computational content of proofs

Thanks to all the speaker and participants and we hope to see you all again soon.

# Summer School: Day 4

Congratulations to Iris van der Giessen for winning the best poster competition and special thanks to Andreas Weiermann for the beautiful picture of Wales that serves as our main prize.

Big thanks to all the speakers and the participants for joining our Summer School. We hope to see you again during the future events by the Proof Society.

# Summer School: Day 2 and 3

We were glad to welcome Takako Nemoto, who joined us on the second day of the Summer School and gave her course on Reverse Mathematics.

As a treat, the participants of the Summer School had a trip to Rhossili and enjoyed a walk along the Welsh coastal path with stunning views. Big thanks to Arved Friedemann and Melissa Antonnelli for the beautiful photos.

# Proof Society Summer School

We are very glad to welcome all the participants of the 2nd International Summer School on Proof Theory.

The first day began with a lecture on **Universal Proof Theory** by Rosalie Iemhoff, followed by Wolfram Pohlers‘ talk on **Ordinal Analysis**, **Bounded Arithmetic** lecture from our own Arnold Beckmann, introduction to **Proof Mining** by Paulo Oliva, Paola Bruscoli’s talk on **Structural Proof Theory** and Anton Setzer’s lecture on **MLTT**.

We were lucky with both the lovely weather and the fact that Bay Campus is located right at the seafront, so the evening brought a nice treat for everyone in a form of a BBQ at the beach. Big thanks to Arnold, Faron for their grilling and Ulrich, Rosalie, Monika, Arved, Aled, Anton, Olga and everyone else who helped with the organisation.