Finite Closed Sets of Functions in Multi-valued Logic

IF 0.2 Q4 MATHEMATICS
M. Malkov
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引用次数: 1

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.
多值逻辑中函数的有限闭集
研究了k值逻辑中函数闭集的分类问题。我们建立了有限闭集的分类。这些集合只包含常量和一元函数,因为即使包含二元函数的集合也是无限的。对于所有自然k,存在有限集和最小集的数量公式。我们找到了包含恒等函数f (x)=x或所有k的常数的闭集的数量。我们给出了k到10的包含层上的集合的数量。包含图在k ~ 5时存在,在k=6时我们给出只包含函数f (x)=x和常数0的集合的包含图。我们找到同构集合,只用其中一个同构集合来构建图。
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来源期刊
CiteScore
0.60
自引率
0.00%
发文量
2
期刊介绍: The “Italian Journal of Pure and Applied Mathematics” publishes original research works containing significant results in the field of pure and applied mathematics.
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