Relationship between formal language of mathematical theories and axiomatic systems of the theory of sets

Vershinin, K. P.

doi:10.1007/bf01068586

Cited by 2 publications

(2 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(That time the vocabulary as well as the syntax was certainly Russian.) Two kind of semantics were defined for that part: a transformational one (an algorithm to convert a TL statement into its first-order image) and another one -in the traditional set-theoretical style where ε was interpreted as the membership relation [19]. The last semantics permitted to define the "extension" of every notion (e.g.…”

Section: Theoretical Workmentioning

confidence: 99%

Evidence Algorithm and System for Automated Deduction: A Retrospective View

Lyaletski

Verchinine

2010

Lecture Notes in Computer Science

View full text Add to dashboard Cite

A research project aimed at the development of an automated theorem proving system was started in Kiev (Ukraine) in early 1960s. The mastermind of the project, Academician V.Glushkov, baptized it "Evidence Algorithm", EA 3 . The work on the project lasted, off and on, more than 40 years. In the framework of the project, the Russian and English versions of the System for Automated Deduction, SAD, were constructed. They may be already seen as powerful theoremproving assistants. The paper 4 gives a retrospective view to the whole history of the development of the EA and SAD. Theoretical and practical results obtained on the long way are systematized. No comparison with similar projects is made.

show abstract

Section: Theoretical Workmentioning

confidence: 99%

Evidence Algorithm and System for Automated Deduction: A Retrospective View

Lyaletski

Verchinine

2010

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Further investigations within the framework of the system of automation of deduction SAD were devoted to the study of the relation between a formal language for writing mathematical theories and axiomatic systems of set theory [11], a combination of rules of resolution and paramodulation with a number of heuristics that reflect the specificity of the theory of linear spaces [12], consideration of an environment and deductive transformations in it that are destined for the solution of problems from various domains in which the apparatus of logical deduction is used [13], and description of a system of processing of mathematical texts, which is realized on ES computers [14].…”

Section: Algebra Of Algorithms and Systems Of Algorithmic Algebrasmentioning

confidence: 99%

Formation and Development of Ideas of Artificial Intelligence in V. M. Glushkov’s Works

Kapitonova

2005

Cybern Syst Anal

View full text Add to dashboard Cite

51Ideas and means of artificial intelligence are considered that are developed in works of V. M. Glushkov and are used in brain modeling, computer-aided training, automata theory, and systems of algorithmic algebras.Keywords: model of the brain, algorithms and coding, experiments in training of machines, automata theory, discrete transformers, algebra of algorithms, system of algorithmic algebras.

show abstract

Relationship between formal language of mathematical theories and axiomatic systems of the theory of sets

Cited by 2 publications

References 1 publication

Evidence Algorithm and System for Automated Deduction: A Retrospective View

Evidence Algorithm and System for Automated Deduction: A Retrospective View

Formation and Development of Ideas of Artificial Intelligence in V. M. Glushkov’s Works

Contact Info

Product

Resources

About