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no code implementations • 13 May 2023 • Chad Brown, Adam Pease, Josef Urban

We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory.

no code implementations • 12 Mar 2023 • Jan Jakubův, Karel Chvalovský, Zarathustra Goertzel, Cezary Kaliszyk, Mirek Olšák, Bartosz Piotrowski, Stephan Schulz, Martin Suda, Josef Urban

As a present to Mizar on its 50th anniversary, we develop an AI/TP system that automatically proves about 60\% of the Mizar theorems in the hammer setting.

no code implementations • 27 Jan 2023 • Thibault Gauthier, Miroslav Olšák, Josef Urban

We introduce a self-learning algorithm for synthesizing programs for OEIS sequences.

1 code implementation • 7 Oct 2022 • Jelle Piepenbrock, Josef Urban, Konstantin Korovin, Miroslav Olšák, Tom Heskes, Mikolaš Janota

In particular, we develop a GNN2RNN architecture based on an invariant graph neural network (GNN) that learns from problems and their solutions independently of symbol names (addressing the abundance of skolems), combined with a recurrent neural network (RNN) that proposes for each clause its instantiations.

1 code implementation • 4 May 2022 • Zarathustra A. Goertzel, Jan Jakubův, Cezary Kaliszyk, Miroslav Olšák, Jelle Piepenbrock, Josef Urban

We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways.

3 code implementations • 24 Feb 2022 • Thibault Gauthier, Josef Urban

We present a self-learning approach for synthesizing programs from integer sequences.

1 code implementation • 21 Jul 2021 • Karel Chvalovský, Jan Jakubův, Miroslav Olšák, Josef Urban

Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic.

1 code implementation • 14 Jul 2021 • Zarathustra Goertzel, Karel Chvalovský, Jan Jakubův, Miroslav Olšák, Josef Urban

The second addition is motivated by fast weight-based rejection filters that are currently used in systems like E and Prover9.

no code implementations • 31 May 2021 • Zsolt Zombori, Josef Urban, Miroslav Olšák

This leads us to explore how the entropy of the inference selection implemented via the neural network influences the proof search.

no code implementations • 12 Apr 2021 • Liao Zhang, Lasse Blaauwbroek, Bartosz Piotrowski, Prokop Černý, Cezary Kaliszyk, Josef Urban

Learning happens in an online manner, meaning that Tactician's machine learning model is updated immediately every time the user performs a step in an interactive proof.

no code implementations • 10 Feb 2021 • Jelle Piepenbrock, Tom Heskes, Mikoláš Janota, Josef Urban

On these tasks, 3SIL is shown to significantly outperform several established RL and imitation learning methods.

no code implementations • 31 Jul 2020 • Lasse Blaauwbroek, Josef Urban, Herman Geuvers

We present Tactician, a tactic learner and prover for the Coq Proof Assistant.

no code implementations • 29 May 2020 • Josef Urban, Jan Jakubův

We describe several datasets and first experiments with creating conjectures by neural methods.

1 code implementation • 15 Apr 2020 • Zsolt Zombori, Josef Urban, Chad E. Brown

We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus.

no code implementations • 20 Mar 2020 • Lasse Blaauwbroek, Josef Urban, Herman Geuvers

Currently, our predictor can identify the correct tactic to be applied to a proof state 23. 4% of the time.

no code implementations • 11 Mar 2020 • Bartosz Piotrowski, Josef Urban

In this work, we develop a new learning-based method for selecting facts (premises) when proving new goals over large formal libraries.

no code implementations • 13 Feb 2020 • Jan Jakubův, Karel Chvalovský, Miroslav Olšák, Bartosz Piotrowski, Martin Suda, Josef Urban

For the neural guidance, we use symbol-independent graph neural networks (GNNs) and their embedding of the terms and clauses.

no code implementations • 5 Dec 2019 • Qingxiang Wang, Chad Brown, Cezary Kaliszyk, Josef Urban

In our context informal mathematics refers to human-written mathematical sentences in the LaTeX format; and formal mathematics refers to statements in the Mizar language.

no code implementations • 27 Nov 2019 • Miroslav Olšák, Cezary Kaliszyk, Josef Urban

This encoding represents symbols only by nodes in the graph, without giving the network any knowledge of the original labels.

no code implementations • 7 Nov 2019 • Bartosz Piotrowski, Josef Urban, Chad E. Brown, Cezary Kaliszyk

This work investigates if the current neural architectures are adequate for learning symbolic rewriting.

1 code implementation • 30 May 2019 • Zsolt Zombori, Adrián Csiszárik, Henryk Michalewski, Cezary Kaliszyk, Josef Urban

We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP).

1 code implementation • 23 May 2019 • Zarathustra Goertzel, Jan Jakubův, Josef Urban

In this work we describe a new learning-based proof guidance -- ENIGMAWatch -- for saturation-style first-order theorem provers.

1 code implementation • 20 May 2019 • Bartosz Piotrowski, Josef Urban

We present a dataset and experiments on applying recurrent neural networks (RNNs) for guiding clause selection in the connection tableau proof calculus.

no code implementations • 2 Apr 2019 • Jan Jakubův, Josef Urban

We describe a very large improvement of existing hammer-style proof automation over large ITP libraries by combining learning and theorem proving.

no code implementations • 7 Mar 2019 • Karel Chvalovský, Jan Jakubův, Martin Suda, Josef Urban

We describe an efficient implementation of clause guidance in saturation-based automated theorem provers extending the ENIGMA approach.

1 code implementation • 6 Mar 2019 • Chad E. Brown, Thibault Gauthier, Cezary Kaliszyk, Geoff Sutcliffe, Josef Urban

This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms.

Logic in Computer Science

no code implementations • NeurIPS 2018 • Cezary Kaliszyk, Josef Urban, Henryk Michalewski, Mirek Olšák

The strongest version of the system is trained on a large corpus of mathematical problems and evaluated on previously unseen problems.

no code implementations • 10 May 2018 • Qingxiang Wang, Cezary Kaliszyk, Josef Urban

Our experiments show that our best performing model configurations are able to generate correct Mizar statements on 65. 73\% of the inference data, with the union of all models covering 79. 17\%.

no code implementations • 2 Apr 2018 • Thibault Gauthier, Cezary Kaliszyk, Josef Urban

Techniques combining machine learning with translation to automated reasoning have recently become an important component of formal proof assistants.

no code implementations • 2 Apr 2018 • Thibault Gauthier, Cezary Kaliszyk, Josef Urban, Ramana Kumar, Michael Norrish

We implement a automated tactical prover TacticToe on top of the HOL4 interactive theorem prover.

1 code implementation • 12 Feb 2018 • Zarathustra Goertzel, Jan Jakubův, Stephan Schulz, Josef Urban

Watchlist (also hint list) is a mechanism that allows related proofs to guide a proof search for a new conjecture.

1 code implementation • 9 Feb 2018 • Bartosz Piotrowski, Josef Urban

ATPboost is a system for solving sets of large-theory problems by interleaving ATP runs with state-of-the-art machine learning of premise selection from the proofs.

no code implementations • 23 Jan 2017 • Jan Jakubův, Josef Urban

ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers.

no code implementations • 29 Nov 2016 • Cezary Kaliszyk, Josef Urban, Jiří Vyskočil

We study methods for automated parsing of informal mathematical expressions into formal ones, a main prerequisite for deep computer understanding of informal mathematical texts.

no code implementations • 26 Nov 2016 • Jan Jakubuv, Josef Urban

Inventing targeted proof search strategies for specific problem sets is a difficult task.

no code implementations • 18 Nov 2016 • Michael Färber, Cezary Kaliszyk, Josef Urban

We study Monte Carlo Tree Search to guide proof search in tableau calculi.

2 code implementations • NeurIPS 2016 • Alex A. Alemi, Francois Chollet, Niklas Een, Geoffrey Irving, Christian Szegedy, Josef Urban

We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics.

no code implementations • 23 May 2016 • Chad Brown, Josef Urban

Certain constructs allowed in Mizar articles cannot be represented in first-order logic but can be represented in higher-order logic.

no code implementations • 20 Oct 2014 • Cezary Kaliszyk, Josef Urban, Jiri Vyskocil

We discuss the differences between our direct implementation using an explicit Prolog stack, to the continuation passing implementation of MESON present in HOLLight and compare their performance on all core HOLLight goals.

no code implementations • 20 Oct 2014 • Cezary Kaliszyk, Lionel Mamane, Josef Urban

We report the results of the first experiments with learning proof dependencies from the formalizations done with the Coq system.

no code implementations • 6 Jun 2014 • Sebastiaan Joosten, Cezary Kaliszyk, Josef Urban

This paper reports our initial experiments with using external ATP on some corpora built with the ACL2 system.

no code implementations • 14 May 2014 • Cezary Kaliszyk, Josef Urban, Jiri Vyskocil, Herman Geuvers

The goal of this project is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semi-automated translation between informal and formal mathematics by statistical machine-translation methods, (ii) to develop such methods oriented at the formalization task, and in particular (iii) to combine such methods with learning-assisted automated reasoning that will serve as a strong semantic component.

no code implementations • 11 Feb 2014 • Cezary Kaliszyk, Josef Urban, Jiří Vyskočil

Machine Learner for Automated Reasoning (MaLARea) is a learning and reasoning system for proving in large formal libraries where thousands of theorems are available when attacking a new conjecture, and a large number of related problems and proofs can be used to learn specific theorem-proving knowledge.

no code implementations • 11 Feb 2014 • Cezary Kaliszyk, Josef Urban

We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs.

no code implementations • 10 Oct 2013 • Cezary Kaliszyk, Josef Urban

Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians.

no code implementations • 10 Oct 2013 • Cezary Kaliszyk, Josef Urban

As a present to Mizar on its 40th anniversary, we develop an AI/ATP system that in 30 seconds of real time on a 14-CPU machine automatically proves 40% of the theorems in the latest official version of the Mizar Mathematical Library (MML).

1 code implementation • 19 Sep 2013 • Cezary Kaliszyk, Josef Urban

HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system.

no code implementations • 9 Aug 2013 • Daniel Kühlwein, Josef Urban

MaLeS is an automatic tuning framework for automated theorem provers.

no code implementations • 12 Jan 2013 • Josef Urban

BliStr is a system that automatically develops strategies for E prover on a large set of problems.

no code implementations • 29 Nov 2012 • Cezary Kaliszyk, Josef Urban

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of answering a wide range of mathematical queries automatically.

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