Alexander V. Lyaletski

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Formalizing mathematical argument is a fascinating activity in itself and (we hope!) also bears important practical applications. While traditional proof theory investigates deducibility of an individual statement from a collection of premises, a mathematical proof, with its structure and continuity, can hardly be presented as a single sequent or a set of(More)
In this paper a state of the art of a system of automated deduction called SAD is described ?. An architecture of SAD corresponds well to a modern vision of the Evidence Algorithm programme, initiated by Academician V.Glushkov. The system is intended for accumulating mathematical knowledge and using it in a regular and eecient manner for processing a(More)
In this paper we continue to develop the approach to automated search for theorem proofs started in Kyiv in 1960-1970s. This approach presupposes the development of deductive techniques used for the processing of mathematical texts, written in a formal first-order language, close to the natural language used in mathematical papers. We construct two logical(More)
In this paper, a proof assistant, called SAD, is presented. SAD deals with mathematical texts that are formalized in the ForTheL language (brief description of which is also given) and checks their cor-rectness. We give a short description of SAD and a series of examples that show what can be done with it. Note that abstract notion of cor-rectness on which(More)
Among the tasks of the Evidence Algorithm programme, the verification of formalized mathematical texts is of great significance. Our investigations in this domain were brought to practice in the last version of the System for Automated Deduction (SAD). The system exploits a formal language to represent mathematical knowledge in a " natural " form and a(More)
Dealing with a formal mathematical text (which we regard as a structured collection of hypotheses and conclusions), we often want to perform various analysis and transformation tasks on the initial formulas, without preliminary normalization. One particular example is checking for " ontological correctness " , namely, that every occurrence of a non-logical(More)
  • Zainutdin Aselderov, Konstantin Verchinine, Anatoli Degtyarev, Alexander Lyaletski, Andrey Paskevich, Alexandre Pavlov
  • 2007
This paper is devoted to a brief description of some peculiarities and of the rst software implementation of the System for Automated Deduction, SAD. Architecture of SAD corresponds well to a modern vision of the Evidence Algorithm that was conceived by V. Glushkov as a programme for constructing open systems for automated theorem-proving that are intended(More)