Implicit completeness criterion in three-valued logic in terms of maximal classes

TL;DR

This paper explores implicit expressability in three-valued logic, describing maximal classes and establishing an implicit completeness criterion, thus advancing understanding of functional representations within this logical framework.

Contribution

It introduces a description of all implicitly maximal classes in three-valued logic and formulates an implicit completeness criterion, extending prior work on implicit expressability.

Findings

Describes the system of all implicitly maximal classes in three-valued logic.

States the implicit completeness criterion for these classes.

Abstract

Implicit expressability was introduced by A.V. Kuznetsov in 1979 as generalization of functional expressability. Set of functions is called implicitly complete if any function has an implicit representation over this set. The system of all implicitly maximal classes in three-valued logic is described. The implicit completeness criterion is stated.