Natural deduction for Fitting's four-valued generalizations of Kleene's logics
type: Item
instance of: scholarly article
title: Natural deduction for Fitting's four-valued generalizations of Kleene's logics
zbMATH Open document ID: 1385.03032
author: Yaroslav I. Petrukhin
published in: Logica Universalis
publication date: 2018-01-12T00:00:00Z
review text: In [Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 20, No. 1--3, 113--131 (1994; Zbl 0804.03016)] \textit{M. Fitting} studied some four-valued generalizations of the three-valued logics introduced by \textit{S. C. Kleene} [Introduction to metamathematics. Amsterdam: North-Holland Publishing Co.; Groningen: P. Noordhoff N. V., (1952; Zbl 0047.00703)]. The aim of the article under review is to present natural deduction systems, as well as completeness theorems, for some of these four-valued logics. In particular \(\mathbf{FDE}^\rightarrow\), \(\mathbf{FDE}^\leftrightarrow\), plus a new logic introduced in the present paper, called \(\mathbf{FDE}^\leftarrow\).
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03B22
Mathematics Subject Classification ID: 03F03
zbMATH DE Number: 6825511
zbMATH Keywords: Kleene's logics
zbMATH Keywords: four-valued logics
zbMATH Keywords: natural deduction system
zbMATH Keywords: three-valued logics
MaRDI profile type: Publication
full work available at URL: s11787-017-0169-0
OpenAlex ID: W2612676125
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DOI: 10.1007/S11787-017-0169-0
description: scientific article; zbMATH DE number 6825511