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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 Sciencesa, Ural Federal Universityb
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
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. 525-534.
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