Some Closed Classes of Three-Valued Logic Generated by Symmetric Functions

TL;DR

This paper investigates specific closed classes of three-valued logic generated by symmetric functions that predominantly output 1, providing criteria for when these classes have bases, thus advancing understanding of their structural properties.

Contribution

It introduces criteria for the existence of bases in closed classes of three-valued symmetric logic functions, expanding theoretical knowledge in many-valued logic systems.

Findings

Criteria for bases existence are established.

Characterization of symmetric functions with specific output patterns.

Structural properties of three-valued logic classes are clarified.

Abstract

Closed classes of three-valued logic generated by symmetric funtions that equal $1$ in almost all tuples from $\{1,2\}^n$ and equal $0$ on the rest tuples are considered. Criteria for bases existence for these classes is obtained.