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.
This week we are glad to welcome two visitors here at Swansea, namely Hideki Tsuiki from Kyoto University and Kristijonas Čyra from the Imperial College of London.
Hideki will give a talk on “Infinite Adequacy Theorem through Coinductive Definitions” today at 14:00 as a part of our Theory seminar series and Kristijonas will speak on “Argumentation-enabled Explainable AI Applications” this Thursday at 15:00 at the CoFo.
Professor (Course of Mathematical Science, Graduate School of Human and Environmental Studies, Kyoto University). Ressearch Interests: Computation over Real numbers and Topological spaces, Domains and their topologies, Fractals and their models, Semantics of Programming Languages, Object Oriented Programming, Mathematical Logic, Lambda Calculus.
Postdoctoral Researcher in AI at the Department of Computing, Imperial College London. I manage researchers, enthusiastically supervise and teach students, present my work at top tier international conferences, review and assess the works of others and give highest quality feedback, organise research events, represent and speak on behalf of my colleagues and fellow AI researchers during institutional and public engagement opportunities.
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Ulrich Berger is currently attending the 3rd Workshop on Mathematical Logic and its Applications, Nancy, France, where he will present a talk on Extracting the Fan Functional.
Dongseong Seon (선동성) from KAIST, Korea is visiting Swansea. This Thursday he will give a talk on computing Haar averages as a part of our Theory seminar series. For more infromation on this topic, please click here.
As a part of our Theory Seminars, today we welcomed Ryota Akiyoshi from Waseda University, who gave a talk on Takeuti’s finitism.
Abstract: In this talk, we address several mathematical and philosophical issues of Gaisi Takeuti’s proof theory, who is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He furthered the realization of Hilbert’s program by formulating Gentzen’s sequent calculus for higher-oder logics, conjecturing that the cut-elimination holds for it (Takeuti’s conjecture), and obtaining several stunning results in the 1950-60’s towards the solution of his conjecture.
This talk consists of two parts. (1) To summarize Takeuti’s background and the argument of the well-ordering proof of ordinals up to ε0 , (2) To evaluate it on philosophical grounds. Also, we will explain several mathematical and philosophical issues to be solved. This is joint work with Andrew Arana.
My research fields are philosophy of mathematics and logic, mathematical logic (proof theory), and theoretical computer science (type theory). The main philosophical question in my research is "what is a proof ?".
Ulrich, Monika and Olga attended Hausdorff Trimester Program Types, Sets and Constructions in Bonn, Germany. During this research trip they have participated in the Constructive Mathematics workshop and had a chance to collaborate with partners from the past and existing projects, including COMPUTAL, CONRCON and CID.
Stephane Le Roux is visiting us from Darmstadt. Today he will give a talk on “Concurrent games and semi-random determinacy.”
Abstract: Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite- memory) strategies is equivalent to the existence of winning (finite-memory) strategies in finitely many derived one-player games. Several classical winning conditions satisfy this simple requirement.Under an additional requirement on the winning condition, the non-existence of Player 1 winning strategies from all vertices is equivalent to the existence of Player 2 stochastic strategies almost-sure winning from all vertices. Only few classical winning conditions satisfy this additional requirement, but a fairness variant of omega-regular languages does.
Magne Haveraaen from the University of Bergen is visiting our Department in May-July 2018.
Ulrich and Olga visited Japan as part of the CID project in April 2018.
Work in progress: Hideki Tsuiki and Ulrich Berger working on Gray code.
Amir Tabatabai and Rahele Jalali, both PhD students at the Institute of Mathematics of the Czech Academy of Sciences under the supervision of Pavel Pudlak, are visiting Swansea University 13 Nov – 6 Dec 2017.
Amir will give a talk on Computational Flows in Arithmetic on 16 November.
More information: A computational flow is a pair consisting of a sequence of computational problems of a certain sort and a sequence of computational reductions among
them. In this talk we will explain the basics of the theory of computational
flows and how they make a sound and complete interpretation for bounded
theories of arithmetic. This property helps us to decompose a first order
arithmetical proof to a sequence of computational reductions by which we can
extract the computational content of the low complexity statements in some
bounded theories of arithmetic such as .