On Łukasiewicz's four-valued modal logic
type: Item
instance of: scholarly article
title: On Łukasiewicz's four-valued modal logic
zbMATH Open document ID: 0998.03022
DOI: 10.1023/A:1015111314455
author: Josep Maria Font
author: Petr Hájek
published in: Studia Logica
publication date: 2002-07-08T00:00:00Z
review text: The aim of this paper is to survey and analyze Łukasiewicz's four-valued modal logic (denoted as Ł). Section 2 presents Łukasiewicz's system Ł, some mathematical results concerning the classification of the system Ł under several standard criteria, and its main semantic and algebraic properties. The authors outline the translation mapping between Ł and the classical propositional calculus (CPC), and prove their basic result (Theorem 1) showing that a formula \(\varphi\in\text{Ł}\) is a tautology if and only if its corresponding formula \(\varphi^*\in\text{CPC}\) does. In Sections 3 and 4, some counter-intuitive aspects of the system Ł are presented and discussed, based on the consequences derived from the obtained results, combined with Łukasiewicz's own texts and the rich related literature.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03G20
zbMATH DE Number: 1764808
zbMATH Keywords: faithful translations
zbMATH Keywords: intensional logic
zbMATH Keywords: discrete epistemic algebras
zbMATH Keywords: Łukasiewicz's four-valued modal logic
MaRDI profile type: Publication
full work available at URL: a:1015111314455
OpenAlex ID: W1542734653
description: scientific article; zbMATH DE number 1764808