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Background

Large-scale semantic processing and strong computer assistance of mathematics and science is our inevitable future. New combinations of AI and reasoning methods and tools deployed over large mathematical and scientific corpora will be instrumental to this task. The AITP conference is the forum for discussing how to get there as soon as possible, and the force driving the progress towards that.

This year AITP will be co-located with a meeting of WG5 of Cost Action European Research Network on Formal Proofs.

Topics

Sessions

There will be several focused sessions on AI for ATP, ITP, mathematics, relations to general AI (AGI), Formal Abstracts, linguistic processing of mathematics/science, modern AI and big-data methods, and several sessions with contributed talks. The focused sessions will be based on invited talks and discussion oriented. Most of the sessions will be scheduled in the afternoons to allow US participants.

Confirmed (Virtual) Participants/Speakers (TBC)

João AraújoUniversidade Nova de Lisboa
Johannes BrandstetterMicrosoft Research
Kevin BuzzardImperial College London
Walter DeanUniversity of Warwick
Michael R. DouglasStony Brook University
Thibault GauthierCzech Technical University in Prague
Ben GoertzelSingularityNET
Thomas C. HalesUniversity of Pittsburgh
Mikoláš JanotaUniversity of Lisbon
Cezary KaliszykUniversity of Innsbruck
Peter KoepkeUniversity of Bonn
Michael KinyonUniversity of Denver
Tomáš MikolovCzech Technical University in Prague
Alberto NaiboUniversity Paris 1
Miroslav OlsakIHES
Adam PeaseArticulate Software
Michael RawsonTU Wien, Austria
Talia RingerUniversity of Illinois at Urbana-Champaign
Stephan SchulzDHBW Stuttgart
Martin SudaCzech Technical University in Prague
Josef UrbanCzech Technical University in Prague
Robert VeroffUniversity of New Mexico
Petr VojtěchovskýUniversity of Denver
Freek WiedijkRadboud University Nijmegen
Stephen WolframWolfram Research

Invited talks

João AraújoForbidden Substructure Theorems
Johannes BrandstetterHow GNNs and Symmetries can help to solve PDEs
Kevin BuzzardFormalizing Fermat
Walter Dean and Alberto NaiboMathematical difficulty, SAT solvers, and bounded arithmetic
Ben GoertzelThe Role of Automated Theorem-Proving in Neural-Symbolic Approaches to Artificial General Intelligence
Michael Rawson ML4ATP: What I Wish I Had Known 5 Years Ago
Talia RingerConcrete Problems in Proof Automation
Stephen WolframTheorem Proving in Metamathematics, the Universe and More

Dates

AITP solicits contributed talks. Selection of those will be based on extended abstracts/short papers of 2 pages (excluding references) formatted with easychair.cls. Submission is via EasyChair. Accepted contributions will be published in an informal book of abstracts available from this website. The extended abstracts are considered non-archival.

Contributed talks

Boris Shminke. Project proposal: A modular reinforcement learning based automated theorem prover
Chencheng Liang, Philipp Rümmer and Marc Brockschmidt. Exploring Representation of Horn Clauses using GNNs
Joseph Palermo, Johnny Ye and Jesse Michael Han. Synthetic Proof Term Data Augmentation for Theorem Proving with Language Models
Thibault Gauthier. Program Synthesis from Integer Sequences: Initial Self-Learning Run on the OEIS
Anthony Bordg, Yiannos Stathopoulos and Lawrence Paulson. A Parallel Corpus of Natural Language and Isabelle Artefacts
Eser Aygun, Laurent Orseau, Ankit Anand, Xavier Glorot, Stephen Mcaleer, Vlad Firoiu, Lei Zhang, Doina Precup and Shibl Mourad. Proving Theorems using Incremental Learning and Hindsight Experience Replay
Adrian Groza. A Corpus for Precise Natural Language Inference
Martin Suda. Elements of Reinforcement Learning in Saturation-based Theorem Proving
Sean Welleck, Jiacheng Liu, Ximing Lu, Hannaneh Hajishirzi and Yejin Choi. NaturalProver: Grounded Natural Language Proof Generation with Language Models
Sólrún Halla Einarsdóttir, Moa Johansson and Nicholas Smallbone. Towards neuro-symbolic conjecturing
David Cerna, Cezary Kaliszyk and Stanislaw Purgal. Sifting through a large hypothesis space: Revisiting differentiable learning through satisfiability
Pedro Orvalho, Jelle Piepenbrock, Mikoláš Janota and Vasco Manquinho. Project Proposal: Learning Variable Mappings to Repair Programs
Christoph Wernhard. Compressed Combinatory Proof Structures and Blending Goal- with Axiom-Driven Reasoning: Perspectives for First-Order ATP with Condensed Detachment and Clausal Tableaux
Jack McKeown and Geoff Sutcliffe. Reinforcement Learning in E
Chad Brown, Adam Pease and Josef Urban. Embedding SUMO into Set Theory
Albert Jiang, Wenda Li and Mateja Jamnik. Learning plausible and useful conjectures
Chad Brown, Jan Jakubuv and Cezary Kaliszyk. Strategies and Machine Learning for Lash
Filip Bártek and Martin Suda. Project Proposal: Efficient Neural Clause Selection by Weight
Jelle Piepenbrock, Josef Urban, Konstantin Korovin, Miroslav Olšák, Tom Heskes and Mikolas Janota. Learning Instantiation in First-Order Logic
Simon Guilloud, Florian Cassayre and Viktor Kuncak. LISA: Towards a Set-Theoretic Proof Assistant
Peter Koepke and Adrian De Lon. Scaling Naproche
Nikolai Antonov, Jan Hula, Mikolas Janota and Premysl Sucha. Reinforcement Learning for Schedule Optimization
Alexei Lisitsa and Alexei Vernitski. Using machine learning to detect non-triviality of knots via colorability of knot diagrams
Mikolas Janota, Jelle Piepenbrock and Bartosz Piotrowski. Selecting Quantifiers for Instantiation in SMT
Yutaka Nagashima. Evolutionary Computation for Program Synthesis in SuSLik
Bartosz Piotrowski. A small survey of mathematical abilities of modern transformer architectures
Szymon Tworkowski, Maciej Mikuła, Tomasz Odrzygóźdź, Konrad Czechowski, Szymon Antoniak, Albert Jiang, Christian Szegedy, Łukasz Kuciński, Piotr Miłoś and Yuhuai Wu. Formal Premise Selection With Language Models
Yuhuai Wu, Albert Jiang, Wenda Li, Markus Rabe, Charles Staats, Mateja Jamnik and Christian Szegedy. Autoformalization for Neural Theorem Proving
Liao Zhang and Lasse Blaauwbroek. Tactic Characterizations by the Influences on Proof States
Jan Jakubuv, Zarathustra Goertzel, Mikolas Janota and Cezary Kaliszyk. LightGBM Hyperparameter Optimization for Clause Classification in Theorem Proving
Jan Hůla and Mikoláš Janota. Model Discovery for Efficient Search
Zarathustra Goertzel, Adam Pease and Josef Urban. Project Proposal: Formal Ethics Ontology in SUMO
Karel Chvalovský and Josef Urban. Analyzing Proof Components

Post-proceedings

We will consider an open call for post-proceedings in an established series of conference proceedings (LIPIcs, EPiC, JMLR) or a journal (AICom, JAR, JAIR).

Program Committee

Jasmin Christian BlanchetteINRIA Nancy
Michael R. Douglas (co-chair)Stony Brook University
Ulrich FurbachUniversity of Koblenz
Thibault GauthierCzech Technical University in Prague
Thomas C. Hales (co-chair)University of Pittsburgh
Sean HoldenUniversity of Cambridge
Mikoláš JanotaUniversity of Lisbon
Cezary Kaliszyk (co-chair)University of Innsbruck
Michael KinyonUniversity of Denver
Peter KoepkeUniversity of Bonn
Michael KohlhaseFAU Erlangen-Nürnberg
Konstantin KorovinThe University of Manchester
Ramana KumarDeepMind
Adam PeaseArticulate Software
Michael RawsonTU Wien
Stephan Schulz (co-chair)DHBW Stuttgart
Christian SzegedyGoogle Research
Josef Urban (co-chair)Czech Technical University in Prague
Sean WelleckUniversity of Washington
Sarah WinklerUniversity of Innsbruck
Zsolt ZomboriAlfréd Rényi Institute of Mathematics

AITP Program



September 4
19:45 dinner


September 5
14:00-16:30 Chair: Michael Douglas video of the whole day without the first talk

Welcome

Johannes Brandstetter
How GNNs and Symmetries can help to solve PDEs(45m)

J. Piepenbrock, J. Urban, K. Korovin, M. Olšák, T. Heskes and M. Janota
Learning Instantiation in First-Order Logic (25m)

Chencheng Liang, Philipp Rümmer and Marc Brockschmidt
Exploring Representation of Horn Clauses using GNNs(25m)

Alexei Lisitsa and Alexei Vernitski
Using machine learning to detect non-triviality of knots via colorability of knot diagrams(25m)

Sólrún Halla Einarsdóttir, Moa Johansson and Nicholas Smallbone
Towards neuro-symbolic conjecturing (15m)

Albert Jiang, Wenda Li and Mateja Jamnik
Learning plausible and useful conjectures (15m)

16:30-17:00 coffee break
17:00-19:30 Chair: Thomas C. Hales Ben Goertzel
The Role of Automated Theorem-Proving in Neural-Symbolic Approaches to Artificial General Intelligence (45m)

Chad Brown, Adam Pease and Josef Urban
Embedding SUMO into Set Theory (25m)

Simon Guilloud, Florian Cassayre and Viktor Kuncak
LISA: Towards a Set-Theoretic Proof Assistant (15m)

Stephen Wolfram
Theorem Proving in Metamathematics, the Universe and More (60m)

19:30 dinner


September 6
14:00-16:30 Chair: Stephan Schulz video of the whole day

Joao Araujo
Forbidden Substructure Theorems (45m)

Thibault Gauthier
Program Synthesis from Integer Sequences: Initial Self-Learning Run on the OEIS (25m)

E. Aygun, L. Orseau, A. Anand, X. Glorot, S. Mcaleer, V. Firoiu, L. Zhang, D. Precup and S. Mourad
Proving Theorems using Incremental Learning and Hindsight Experience Replay (25m)

Martin Suda
Elements of Reinforcement Learning in Saturation-based Theorem Proving (25m)

Boris Shminke
Project proposal: A modular reinforcement learning based automated theorem prover (15m)

Jack McKeown and Geoff Sutcliffe
Reinforcement Learning in E (15m)

16:30-17:00 coffee break
17:00-19:15 Chair: Cezary Kaliszyk Talia Ringer
Concrete Problems in Proof Automation (45m)

Michael Rawson
ML4ATP: What I Wish I Had Known 5 Years Ago (45m)

Mikolas Janota, Jelle Piepenbrock and Bartosz Piotrowski
Selecting Quantifiers for Instantiation in SMT (15m)

Jan Hůla and Mikoláš Janota
Model Discovery for Efficient Search (15m)

Nikolai Antonov, Jan Hula, Mikolas Janota and Premysl Sucha
Reinforcement Learning for Schedule Optimization (15m)

19:30 dinner


September 7
14:00-16:25 Chair: Peter Koepke video of the whole day

Walter Dean and Alberto Naibo
Mathematical difficulty, SAT solvers, and bounded arithmetic (45m)

Sean Welleck, Jiacheng Liu, Ximing Lu, Hannaneh Hajishirzi and Yejin Choi
NaturalProver: Grounded Natural Language Proof Generation with Language Models (25m)

Anthony Bordg, Yiannos Stathopoulos and Lawrence Paulson
A Parallel Corpus of Natural Language and Isabelle Artefacts (25m)

Y. Wu, A. Jiang, W. Li, M. Rabe, C. Staats, M. Jamnik and C. Szegedy
Autoformalization for Neural Theorem Proving (25m)

Joseph Palermo, Johnny Ye and Jesse Michael Han
Synthetic Proof Term Data Augmentation for Theorem Proving with Language Models (25m)

16:30-17:00 coffee break
17:00-19:30 Chair: Josef Urban Bartosz Piotrowski
A small survey of mathematical abilities of modern transformer architectures (25m)

Kevin Buzzard
Formalizing Fermat (40m)

Peter Koepke and Adrian De Lon
Scaling Naproche (25m)

Panel Discussion (J. Araujo, K. Buzzard, W. Dean, M. Douglas, P. Koepke, A. Naibo, B. Szegedy, F. Wiedijk)
Fermat formalization and Future of Math (60m)

19:30 dinner


September 8
14:00-16:20 Chair: Zsolt Zombori S. Tworkowski, M. Mikuła, T. Odrzygóźdź, K. Czechowski, S. Antoniak, A. Jiang, C. Szegedy, Ł. Kuciński, P. Miłoś and Y. Wu
Formal Premise Selection With Language Models (25m)

David Cerna, Cezary Kaliszyk and Stanislaw Purgal
Sifting through a large hypothesis space: Revisiting differentiable learning through satisfiability (25m)

Karel Chvalovský and Josef Urban
Analyzing Proof Components (25m)

Jan Jakubuv, Zarathustra Goertzel, Mikolas Janota and Cezary Kaliszyk
LightGBM Hyperparameter Optimization for Clause Classification in Theorem Proving (25m)

Chad Brown, Jan Jakubuv and Cezary Kaliszyk
Strategies and Machine Learning for Lash (25m)

Liao Zhang and Lasse Blaauwbroek
Tactic Characterizations by the Influences on Proof States (15m)

16:30-17:00 coffee break
17:00-18:50 Chair: Konstantin Korovin Christoph Wernhard
Compressed Combinatory Proof Structures and Blending Goal- with Axiom-Driven Reasoning: Perspectives for First-Order ATP with Condensed Detachment and Clausal Tableaux (25m)

Filip Bártek and Martin Suda
Efficient Neural Clause Selection by Weight (25m)

Yutaka Nagashima
Evolutionary Computation for Program Synthesis in SuSLik (15m)

Pedro Orvalho, Jelle Piepenbrock, Mikoláš Janota and Vasco Manquinho
Project Proposal: Learning Variable Mappings to Repair Programs (15m)

Adrian Groza
A Corpus for Precise Natural Language Inference (15m)

Zarathustra Goertzel, Adam Pease and Josef Urban
Project Proposal: Formal Ethics Ontology in SUMO (15m)


19:30 dinner


September 9
10:00-12:30 Discussions in groups
12:30-14:00 lunch and departure from the center


September 10 (optional for participants staying in Aussois)
10:00-16:30 Excursion/Discussions in groups


WG5 meeting program (preliminary)



September 5
9:00-11:00 Cezary Kaliszyk
Discussion of Machine-learning-based methods in TP
September 6
9:00-11:00 Peter Koepke
Discussion of Controlled Natural Languages in Reasoning
September 7
9:00-11:00 Discussions in Groups
September 8
9:00-11:00 Discussions in Groups

Picture from the conference

Pictures from the previous conferences

Location, Prices and Further Local Information

The conference will take place from September 4 to September 9 2022 in the CNRS Paul-Langevin Conference Center located in the mountain village of Aussois in Savoy. Dominated by the "Dent Parrachée", one of the highest peaks of La Vanoise, Aussois is located on a sunny plateau at 1500 m altitude, offering a magnificent panorama of the surrounding mountains and a direct access to the downhill ski slopes or cross country slopes in winter. The total price for accommodation and food for the five days will be around 500 EUR (600 EUR was planned, but thanks to the EPN support registration is free). Online participation will be most likely for free but may be limited to relevant participants.

Arrival/Departure:

Aussois is less than 2h from the airports of Lyon, Geneve, Chambery, Annecy, Grenoble and Turin. There are trains and buses to Modane from these airports. Aussois is 8km from the Modane TGV station with direct trains from/to Paris. We will organize a bus for the participants from there to Aussois. Further buses to these airports / station can be found here and it is easy to get a taxi from Modane to Aussois and back.

The first meal is dinner on September 4 and the last meal is lunch on Friday September 9 . The planned departure of our bus from Modane to Aussois is at around 19:15 pm on Sunday, September 4 . The bus will wait for the TGV train from Paris arriving to Modane at 18:46. The train starts at 14:43 in Paris Gare de Lyon, and it also stops in Lyon-St Exupery at 16:39 and in Chambery-Challes-E at 17:44. The distance from Modane to Aussois is 8km and there are taxis and alternative buses.

We have not yet set the time for the departure of the bus after lunch on September 9 . This will be optimized based on your departure flights during the conference (but taking taxi back to Modane is easy). The center will close after our last session on Friday. If you want to stay for the weekend, the center recommends Hotel des Mottets which is 5 minutes from the center and their prices are very reasonable: https://www.hotel-lesmottets.com/ . If you registered, please fill in this Google form to indicate if you plan to take our bus to Modane, your food preferences, whom you want to share a room with, if you plan to stay longer, etc.

Funding

The travel and accommodation of a number of participants (approximately 17) will be supported by the Cost Action CA20111 - European Research Network on Formal Proofs.

If you want to be funded, you need to:

COST (European Cooperation in Science and Technology) is a funding agency for research and innovation networks. Our Actions help connect research initiatives across Europe and enable scientists to grow their ideas by sharing them with their peers. This boosts their research, career and innovation.

The details of the funding allocation are still being clarified.