三值逻辑中的隐含式扩展

Moscow University Computational Mathematics and Cybernetics Pub Date : 2024-03-01 DOI:10.3103/s0278641924010035

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引用次数: 0

摘要

摘要描述了三值逻辑中所有 27 个单位函数的蕴涵式隐含扩展。研究发现，它们既包括与已知蕴涵封闭类重合的扩展，也包括在叠加操作方面不封闭的扩展。研究还表明，对于任意\(k\geqslant 3\) ，\(P_{k}\)中的任何蕴涵式扩展都包含来自\(P_{k}\)的所有同调函数的类\(H_{k}\)。

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Implicatively Implicit Extensions in Three-Valued Logic

Abstract

Implicatively implicit extensions of all 27 one-place functions of three-valued logic are characterized. It is found they include both extensions coinciding with known implicatively closed classes and extensions that are not closed with respect to the operation of superposition. It is also shown that any implicatively implicit extension in \(P_{k}\) contains class \(H_{k}\) of all homogeneous functions from \(P_{k}\) for any \(k\geqslant 3\) .

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Moscow University Computational Mathematics and Cybernetics

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