On Herbrand-like Theorems for Cut-free Modal Sequent Logics

Lyaletski, Alexander V.

doi:10.1109/synasc.2009.63

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…Роботи [23,24] містять опис точної відмінності між секвенційними теоремами ербранівського типу для класичного і інтуїціоністського випадків. Подальше вивчення запропонованого підходу привело до побудови в [25] ербранівських теорем для класичної і інтуїціоністської модальних логік без рівності і без правила перетину в їх секвенційному трактуванні, де задіяні поняття допустимості та сумісності. Також відзначимо, що в [25] модальні правила сформульовані у дуже загальному випадку.…”

Section: український період (1998теперішній час)unclassified

“…Подальше вивчення запропонованого підходу привело до побудови в [25] ербранівських теорем для класичної і інтуїціоністської модальних логік без рівності і без правила перетину в їх секвенційному трактуванні, де задіяні поняття допустимості та сумісності. Також відзначимо, що в [25] модальні правила сформульовані у дуже загальному випадку. Єдине, що від них вимагається, так це тільки виконання властивості підформульності.…”

Section: український період (1998теперішній час)unclassified

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V.M. Glushkov and automated theorem proving in Ukraine: evidence algorithm evidence algorithm and SAD systems

Lyaletski¹

2020

MMS

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Fifty years ago, in 1970, Academician V.M. Glushkov published a paper, in which he, along with a discussion of some problems of artificial intelligence, formulated a research program called Evidence Algorithm (EA) describing his vision of the problem of a computer support of human activity in looking for a proof of a particular theorem. V.M. Glushkov proposed to focus attention on the construction of an automated theorem-proving system performing simultaneous investigations in: creating formal natural languages for writing mathematical texts in a form accustomed to a human, constructing a procedure for a proof search based on the evolutionary developing of the machine notion of an evidence of a computer-made proof step, using the knowledge gained by the system during its operation and providing a user with the opportunity to assist to the system in its proof search process. Since the inception of EA, two serious attempts have been made to implement this program. The first led to the emergence in 1978 of a Russian-language automated theorem proving and the second led to the appearance in 2002 of its English-language modification named System for Automated Deduction (SAD). And if the development and trial operation of the first system were discontinued in 1992 after the output from service of the ES-line computers, on which it was realized, the SAD system, being placed on the website “nevidal.org”, is now still available in online mode. That is, at the current time, it is possible to carry out different experiments with the SAD system and to solve various problems that require rigorous mathematical reasoning. This work is devoted to a chronological description of studies on the implementation of the EA program for the entire period of its existence and to the highlighting of peculiarities of both the systems, as well as of their common features and distinguishes. Some possible ways of the further development of the SAD system are given.

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Section: український період (1998теперішній час)unclassified

V.M. Glushkov and automated theorem proving in Ukraine: evidence algorithm evidence algorithm and SAD systems

Lyaletski¹

2020

MMS

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“…Now, the native prover of the current (English) SAD possesses the same features. 6 Later, a theoretical answer on this question was obtained in a number of papers of A.Lyaletski (see, for example, [77,86]); from this point of view, some researches on Herbrand theorems ( [78,79,82,90]) also may seem to be interesting.…”

Section: Experimental Workmentioning

confidence: 99%

Evidence Algorithm and System for Automated Deduction: A Retrospective View

Lyaletski

Verchinine

2010

Lecture Notes in Computer Science

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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.

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On Herbrand-like Theorems for Cut-free Modal Sequent Logics

Cited by 2 publications

References 14 publications

V.M. Glushkov and automated theorem proving in Ukraine: evidence algorithm evidence algorithm and SAD systems

V.M. Glushkov and automated theorem proving in Ukraine: evidence algorithm evidence algorithm and SAD systems

Evidence Algorithm and System for Automated Deduction: A Retrospective View

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