Intelligent Computer Mathematics

Carette, Jacques; Kaliszyk, Cezary; Rabe, Florian; Sorge, Volker; Kerber, Manfred

doi:10.1007/978-3-319-20615-8

Cited by 9 publications

(1 citation statement)

References 44 publications

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“…The Mizar Mathematical Library (MML) is a library of formal mathematics developed on top of the Mizar system (Bancerek et al, 2015). The MML is today one of the largest libraries of formalized proofs, covering most basic domains of mathematics and some computer science proofs.…”

Section: Mizar First-order Problemsmentioning

confidence: 99%

Deep Network Guided Proof Search

Loos

Irving

Szegedy

et al.

EPiC Series in Computing

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Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.Automated first-order theorem provers can aid in the formalization and verification of mathematical theorems and play a crucial role in program analysis, theory reasoning, security, interpolation, and system verification.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. We give experimental evidence that with a hybrid, two-phase approach, deep learning based guidance can significantly reduce the average number of proof search steps while increasing the number of theorems proved.Using a few proof guidance strategies that leverage deep neural networks, we have found first-order proofs of 7.36% of the first-order logic translations of the Mizar Mathematical Library theorems that did not previously have ATP generated proofs. This increases the ratio of statements in the corpus with ATP generated proofs from 56% to 59%.

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Section: Mizar First-order Problemsmentioning

confidence: 99%

Deep Network Guided Proof Search

Loos

Irving

Szegedy

et al.

EPiC Series in Computing

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Towards Standardized Mizar Environments

Naumowicz

2017

Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architectu

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The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar

Bancerek¹,

et al. 2017

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The Mizar system is one of the pioneering systems aimed at supporting mathematical proof development on a computer that have laid the groundwork for and eventually have evolved into modern interactive proof assistants. We claim that an important milestone in the development of these systems was the creation of organized libraries accumulating all previously available formalized knowledge in such a way that new works could effectively re-use all previously collected notions. In the case of Mizar, the turning point of its development was the decision to start building the Mizar Mathematical Library as a centrally-managed knowledge base maintained together with the formalization language and the verification system. In this paper we show the process of forming this library, the evolution of its design principles, and also present some data showing its current use with the modern version of the Mizar proof checker, but also as a rich corpus of semantically linked mathematical data in various areas including web-based and natural language proof presentation, maths education, and machine learning based automated theorem proving.

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Intelligent Computer Mathematics

Cited by 9 publications

References 44 publications

Deep Network Guided Proof Search

Deep Network Guided Proof Search

Towards Standardized Mizar Environments

The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar

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