Minimally incomplete sets of Łukasiewiczian truth functions
type: Item
instance of: scholarly article
title: Minimally incomplete sets of Łukasiewiczian truth functions
zbMATH Open document ID: 0544.03003
author: Herbert E. Hendry
published in: Notre Dame Journal of Formal Logic
publication date: 1983-01-01T00:00:00Z
review text: An n-valued truth function is called pure if it is closed on the set \(\{1,n\}\). And, if it can be defined by composition from \(\neg\) and \(\to\), it is said to be Łukasiewiczian or an Ł\(_ n-function\). The author shows the following equivalences for \(n>2:\) a) n-1 is prime; b) the set of Ł\(_ n-functions\) coincides with the set of pure n-valued functions; c) \(\{ \neg,\to,f\}\) is functionally complete if f is non- Łukasiewiczian.
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 3865244
zbMATH Keywords: minimally incomplete sets of Łukasiewiczian truth functions
zbMATH Keywords: functional completeness
zbMATH Keywords: n-valued truth function
reviewed by: Albert Hoogewijs
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093870229
OpenAlex ID: W2023709019
DOI: 10.1305/NDJFL/1093870229
description: scientific article; zbMATH DE number 3865244