Applied Proof Theory 2022 (APT22) (original) (raw)

An international conference on applied proof theory will be held from 29th August to 2nd September 2022 in Pescara, Italy. The meeting will take place in person, with some online components via Zoom or equivalent construct if required.

Abstract

Proofs in mathematical practice serve to warrant the truth of mathematical theorems. Proof theory, i.e. the abstract study of proofs in logic, arose from Hilbert’s programme for the foundations of mathematics; the aim of the latter was to put abstract mathematics on a firm formal basis by proving its consistency in the meta-mathematics and by finitary methods only. Gödel's incompleteness theorems allegedly show the impossibility of Hilbert's programme as such but thus have stood and mark the beginning of a seminal paradigm shift in proof theory: to use mathematical proofs as a rich source of computational information such as certfied algorithms and effective bounds. Current research in this fast-growing area is known under terms such as dynamical methods, program extraction, and proof mining in mathematics, computer science, and philosophy. Our aim is to present all aspects of the state-of-the-art and foster interdisciplinary exchange.

Scope

Applied proof theory, including:

• proof mining,
• program extraction from proofs,
• proof theory in computer science logic,
• proof theory of non-classical logics,
• dynamical methods,
• related areas.

Sponsors

Participants

will include:

• Luca Aceto (Reykjavik University & Gran Sasso Science Institute)
• Matthias Baaz (Vienna University of Technology)
• Stefano Berardi (University of Turin)
• Fernando Ferreira (University of Lisbon)
• Anton Freund (Technical University of Darmstadt)
• Emanuele Frittaion (Technical University of Darmstadt)
• Makoto Fujiwara (Tokyo University of Science)
• Hajime Ishihara (Japan Advanced Institute of Science and Technology)
• Ulrich Kohlenbach (Technical University of Darmstadt)
• Laurențiu Leuştean (University of Bucharest)
• Genaro López-Acedo (University of Seville)
• Marco Maggesi (University of Florence)
• Stefan Neuwirth (University of Franche-Comté)
• Adriana Nicolae (Babeş-Bolyai University)
• Paulo Oliva (Queen Mary University of London)
• Eugenio Orlandelli (University of Bologna)
• Iosif Petrakis (Ludwig Maximilian University of Munich)
• Mario Piazza (Scuola Normale Superiore)
• Pedro Pinto (Technical University of Darmstadt)
• Nicholas Pischke (Technical University of Darmstadt)
• Thomas Powell (University of Bath)
• Andrei Sipoș (University of Bucharest)
• Matteo Tesi (Scuola Normale Superiore)
• Henry Towsner (University of Pennsylvania)
• Benno van den Berg (University of Amsterdam)
• Jan von Plato (University of Helsinki)
• Andreas Weiermann (Ghent University)

Talks

• Aceto, The importance of being negative: Non-finite axiomatisability results in process algebra
• Amato, Universal Algebra in UniMath
• Baaz, The proof-theoretic analysis of incorrect proofs
• Berardi, An Arithmetical Hierarchy of the Law of Excluded Middle and Related Principles
• Fellin, Glivenko-style results for nuclei in entailment relations
• Ferreira, The abstract type of the real numbers
• Freund, Proof mining nonexpansive operators in Banach spaces
• Fujiwara, Proof interpretations on finite-type arithmetic and uniform provability in reverse mathematics
• Ishihara, Place holders
• Kohlenbach, Proof Theory of Rectangular Operators and the Brezis-Haraux Theorem
• Leuştean, Proof mining in optimization and nonlinear analysis
• López-Acedo, Ulrich insight into the lion-man game
• Maggesi, Building proof and countermodels in HOL Light of the provability logic GL
• Neuwirth, Kreisel and Lorenzen on proofs of the Cantor-Bendixson theorem
• Nicolae, Instances of proof mining in optimization theory
• Oliva, On the structure of realizability and functional interpretations
• Petrakis, Strong negation: from constructive mathematics to the theory of computable functionals TCF
• Pinto, Proof mining on PDE theory
• Pischke, Proof Mining and Monotone Operator Theory
• Powell, Personal reflections on becoming an applied proof theorist, and thoughts for the future
• Sanders, Informal proof mining
• Sipoș, On extracting variable Herbrand disjunctions
• Tesi, On the embedding of intuitionistic logic in the logic of provability GL
• Towsner, Proof Mining in Differential Algebra
• van den Berg, Applicative lattices for modified realizability
• von Plato, Gödel, Barr's theorem, and the logic of provability: account of an anticipation
• Weiermann, On the monotone Bolzano-Weierstraß principle by Harvey Friedman

Schedule

Download it here.

Registraton is open until August 25th.

Limited support is available for PhD students and early postdocs. Please write no later than 25th August to Peter Schuster. Please include a CV, a brief motivation letter and for PhD students a statement by the supervisor.

Conference location

Aula 9-11
University of Chieti–Pescara
viale Pindaro 42, Pescara

Places to eat

Places to eat in Pescara.

Reaching Pescara

Pescara has a small airport,Abruzzo Airport, very close to downtown. If traveling directly to Abruzzo Airport is not an option (very likely!), consider going throughRome Fiumicino Airport. From there, there are many bus connections (3h10m - 4h00m travel time), with eitherProntobus,Di Carlo Bus or Flixbus.

Another option is landing inRome Ciampino Airport: from there you can find bus connections to Pescara (~ 3h30m travel time) withProntobus, Flixbus or itabus. If you are in Rome but not at the airport, all companies above have buses departing from Rome Tiburtina bus station.

You can also reach Pescara by trains departing from Rome Tiburtina train station. However, trains on the line Rome–Pescara are quite slow. On the bright side, the trip by train is interesting since trains pass trough many small rural villages in the innermost part of Italy. If you have time to spare (and no work to do... probably no Internet connection there) it could be an alternative.

If you are in Italy everywhere else, you can reach Pescara by bus (see bus companies above) ortrain.

Accommodations

This is a list of hotels in downtown Pescara or near the place of the conference.

4-stars hotel
Location: center of Pescara, at the seafront (the conference place can be reached by bus in 15 minutes)

4-stars hotel
Location: center of Pescara (the conference place can be reached by bus in 15 minutes)

3-stars hotel
Location: center of Pescara (the conference place can be reached by bus in 15 minutes)

3-stars hotel
Location: close to the university, at the seafront (the workshop place can be reached on foot in 15 minutes)

Location: close to the university (the conference place can be reached on foot in 5 minutes)

3-stars hotel
Location: at the seafront (the conference place can be reached on foot in 15 minutes)