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Finite Closed Sets of Functions in Multi-valued Logic
Pure and Applied Mathematics Journal
Volume 6, Issue 1, February 2017, Pages: 14-24
Received: Jan. 3, 2017; Accepted: Jan. 14, 2017; Published: Feb. 20, 2017
Author
M. A. Malkov, Russian Research Center for Artificial Intelligence, Moscow, Russia
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Abstract
The article is devoted to classification of close sets of functions in k-valued logic. We build the classification of finite closed sets. The sets contain only constants and unary functions since sets containing even a two-ary function are infinite. Formulas of the number of finite sets and minimal sets exist for all natural k. We find the numbers of closed sets containing the identity function f (x)=x or a constant for all k. We give the number of sets on levels of inclusions at k up to 10. The inclusion diagrams are present at k up to 5, at k=6 we give inclusion diagrams of sets containing only function f (x)=x and constant 0. We find isomorphic sets and use only one of the isomorphic sets to build the diagrams.
Keywords
Discreat Mathematics, Multi-valued Logic, Function Classification
M. A. Malkov, Finite Closed Sets of Functions in Multi-valued Logic, Pure and Applied Mathematics Journal. Vol. 6, No. 1, 2017, pp. 14-24. doi: 10.11648/j.pamj.20170601.13
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