On implicatively implicit extensions in three-valued logic

Recieved: 09/01/2023

Accepted: 11/07/2023

Published: 01/27/2024

Keywords: implicatively implicit extension, three-valued logic

To cite this article

Marchenkov S.S. On implicatively implicit extensions in three-valued logic. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2024. N 1, p.9-17 https://doi.org/10.55959/MSU/0137-0782-15-2024-47-1-9-17.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Marchenkov S.S. (Lomonosov Moscow State University (MSU))

Abstract

The implicatively implicit extensions of all 27 single functions of three-valued logic are characterized. It is established that among them there are both extensions that coincide with the known implicatively closed classes, and extensions that are not closed with respect to the superposition operation. In addition, it is shown that for any k > 3, any implicatively implicit extension in Pk contains the class Hk of all homogeneous functions from Pk.