Structural Analysis of Precomplete Classes and Closure Diagrams in Multi-Valued Logic

Document Type : Research Paper

Author

1 Incarnet Math Modelling & ComplexNetworks LTD, 32 Komitas Ave, Yerevan, Armenia

2 Institute for Information Transmission Problems of RAS, Bolshoy Karetny per. 19, Moscow, Russia

Abstract

This paper develops a mathematical framework to ensure the functionality and efficiency of digital electronics built on multi-valued logic (MVL). We investigate the properties of precomplete classes and closure for families of MVL functions, focusing on the existence and structure of R-closed sets in \(P_k\) for \(k \geq 4\). Our work provides a systematic analysis of logical bases and their representations through structured diagrams, with a particular focus on Boolean and MVL functions. We rigorously classify \(R_2\)-complete families in \(P_3\)-spaces and propose extensions for the minimal linear superposition operator. Furthermore, we highlight how MVL significantly enhances information density in memory storage systems,
providing pivotal benefits for cutting-edge computational systems. These results bridge theoretical advancements and practical implementations in computer science and logic.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 21, Issue 6
November and December 2024
Pages 127-145

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