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 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)
In this paper 1 , we continue to develop our approach to theorem proof search in the EA-style, that is theorem proving in the framework of integrated processing mathematical texts written in a 1st-order formal language close to the natural language used in mathematical papers. This framework enables constructing a sound and complete goal-oriented(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)
New sequent forms* of the famous Herbrand theorem are proved for first-order classical logic without equality. These forms use the original notion of an admissible substitution and a certain modification of the Herbrand universe, which is constructed from constants, special variables, and functional symbols occurring only in the signature of an initial(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)