Glushkov’s evidence algorithm

Letichevsky, Alexander A.; Lyaletski, Alexander V.; Morokhovets, M. K.

doi:10.1007/s10559-013-9534-z

Cited by 3 publications

(2 citation statements)

References 23 publications

(22 reference statements)

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“…Around 1970s, the advances in computer technology and its popularization together with the proliferation of more user-friendly programming languages allowed the mathematical community to initiate several seminal projects like de Bruijn’s Automath [ 20 ], Milner’s LCF [ 58 ] or Glushkov’s Evidence Algorithm [ 54 ]. The Mizar project [ 9 ] started in 1973 under the leadership of Andrzej Trybulec, first at the Płock Scientific Society and since 1976 at the University of Białystok (formerly the University of Warsaw, Białystok Branch), Poland.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

Bancerek¹,

et al. 2017

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“…У 70-х роках минулого століття у відділі теорії цифрових автоматів, яким керував засновник Інституту кібернетики академік Віктор Михайлович Глушков, було розроблено одну з перших у світі систем автоматичного доведення теорем [1], що поклало початок розвитку технології алгебраїчного програмування. Систему APS (Algebraic Programming System) [2] було створено як інструментарій для реалізації алгебраїчних алгоритмів з метою автоматичного доведення тверджень, розв'язання рівнянь у різних теоріях, задач доказового програмування, паралельного програмування, перетворень формальних специфікацій та інших проблем.…”

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Algebraic modeling and its application

Letychevskyi¹

2021

Visn. Nac. Akad. Nauk Ukr.

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The article is devoted to the scientific development of the Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine on the application of algebraic and insertional modeling technologies created on the basis of behavioral algebra. Technologies of formalization, algebraic verification, and testing of software and hardware specifications within the model-driven development method are considered. The use of algebraic modeling in biological research, development of systems based on blockchain platforms, analysis of legal and economic models is covered. One of the main areas of application of these technologies is the field of cybersecurity, which uses the method of algebraic matching and formalization of patterns of vulnerabilities and cyberattacks.

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