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Russia Yekaterinburg
Section  Mathematics 
Title  An approach to analysis of the set of truth: unlocking of predicate 
Author(s)  Serkov D.A.^{ab} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a}, Ural Federal University^{b} 
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 readymade 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 
UDC  510.635, 517.988.52, 519.833 
MSC  06E30, 47H04, 47H10, 91B50 
DOI  10.20537/vm160407 
Received  26 October 2016 
Language  Russian 
Citation  Serkov D.A. An approach to analysis of the set of truth: unlocking of predicate, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 4, pp. 525534. 
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