1 code implementation • 2 Nov 2024 • Liao Zhang, David M. Cerna, Cezary Kaliszyk

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP).

no code implementations • 11 Oct 2024 • Daniel Ranalter, Chad E. Brown, Cezary Kaliszyk

Recently an extension to higher-order logic -- called DHOL -- was introduced, enriching the language with dependent types, and creating a powerful extensional type theory.

no code implementations • 6 Mar 2024 • Lasse Blaauwbroek, David Cerna, Thibault Gauthier, Jan Jakubův, Cezary Kaliszyk, Martin Suda, Josef Urban

Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning.

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.

1 code implementation • 13 Aug 2022 • Stanisław J. Purgał, David M. Cerna, Cezary Kaliszyk

Synthesizing large logic programs through symbolic Inductive Logic Programming (ILP) typically requires intermediate definitions.

Inductive logic programming Vocal Bursts Intensity Prediction

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.

no code implementations • 6 Apr 2022 • Stanisław J. Purgał, Cezary Kaliszyk

Existing approaches to learning to prove theorems focus on particular logics and datasets.

no code implementations • 29 Dec 2021 • Stanisław J. Purgał, David M. Cerna, Cezary Kaliszyk

Learning complex programs through inductive logic programming (ILP) remains a formidable challenge.

no code implementations • 21 Jul 2021 • Qingxiang Wang, Cezary Kaliszyk

The heterogeneous nature of the logical foundations used in different interactive proof assistant libraries has rendered discovery of similar mathematical concepts among them difficult.

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 • ICLR 2021 • Dennis Müller, Cezary Kaliszyk

We propose the task of disambiguating symbolic expressions in informal STEM documents in the form of LaTeX files - that is, determining their precise semantics and abstract syntax tree - as a neural machine translation task.

no code implementations • 22 Jan 2021 • Stanisław Purgał, Julian Parsert, Cezary Kaliszyk

Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods.

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 • 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 • 1 Mar 2017 • Cezary Kaliszyk, François Chollet, Christian Szegedy

We propose various machine learning tasks that can be performed on this dataset, and discuss their significance for theorem proving.

Ranked #3 on Automated Theorem Proving on HolStep (Unconditional)

no code implementations • 24 Jan 2017 • Sarah Loos, Geoffrey Irving, Christian Szegedy, Cezary Kaliszyk

Here we suggest deep learning based guidance in the proof search of the theorem prover E. We train and compare several deep neural network models on the traces of existing ATP proofs of Mizar statements and use them to select processed clauses during proof search.

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 • 18 Nov 2016 • Michael Färber, Cezary Kaliszyk, Josef Urban

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

no code implementations • 17 Jun 2016 • Jasmin Christian Blanchette, Cezary Kaliszyk

This volume of EPTCS contains the proceedings of the First Workshop on Hammers for Type Theories (HaTT 2016), held on 1 July 2016 as part of the International Joint Conference on Automated Reasoning (IJCAR 2016) in Coimbra, Portugal.

no code implementations • 11 Sep 2015 • Thibault Gauthier, Cezary Kaliszyk

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar.

no code implementations • 11 Sep 2015 • Thibault Gauthier, Cezary Kaliszyk

When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries.

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 • 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 • 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

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).

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.

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 • 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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