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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2016, Volume 26, Issue 4, Pages 525–534 (Mi vuu558)  

This article is cited in 2 scientific papers (total in 2 papers)


An approach to analysis of the set of truth: unlocking of predicate

D. A. Serkovab

a N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia
b Institute of Radioelectronics and Information Technologies, Ural Federal University, ul. Mira, 32, Yekaterinburg, 620002, Russia

Abstract: The term “predicate unlocking” is understood as the reduction of the problem of finding and studying the set of truth of a predicate to the problem of finding and studying the set of fix points of a map. Predicate unlocking provides opportunities for additional investigation of the truth set and also allows one to build the elements of this set with particular properties. There are examples of nontrivial predicate unlocking such as: the predicate “be a stable (weakly invariant) set”, the predicate “be a nonanticipatory selector”, the predicate “be a saddle point”, and the predicate “be a Nash equilibrium”. In these cases, the question of the a priori evaluation of the possibility of unlocking this or other predicate of interest and the question of constructing a corresponding unlocking map remained beyond consideration: the unlocking mappings were provided as ready-made objects. In this note we try to partly close this gap: we provide a formal definition of the predicate unlocking operation, methods for constructing and calculating of the unlocking mappings and their basic properties. As an illustration, the “routine” construction of unlocking mapping for the predicate “be a Nash equilibrium” is carried out. The described approach is far from universality, but, at least, it can be applied to all aforementioned positive examples.

Keywords: truth set of predicate, fixed points of map, Nash equilibrium.


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Bibliographic databases:

UDC: 510.635, 517.988.52, 519.833
MSC: 06E30, 47H04, 47H10, 91B50
Received: 26.10.2016

Citation: D. A. Serkov, “An approach to analysis of the set of truth: unlocking of predicate”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:4 (2016), 525–534

Citation in format AMSBIB
\by D.~A.~Serkov
\paper An approach to analysis of the set of truth: unlocking of predicate
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2016
\vol 26
\issue 4
\pages 525--534

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    This publication is cited in the following articles:
    1. D. A. Serkov, “Unlocking of predicate: application to constructing a non-anticipating selection”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 283–291  mathnet  crossref  elib
    2. D. A. Serkov, “K postroeniyu mnozhestva istinnosti predikata”, Izv. IMI UdGU, 50 (2017), 45–61  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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