A calculus for the common rules of \(\wedge\) and \(\vee\)
type: Item
instance of: scholarly article
title: A calculus for the common rules of \(\wedge\) and \(\vee\)
zbMATH Open document ID: 0707.03006
DOI: 10.1007/BF00370205
author: Wolfgang Rautenberg
published in: Studia Logica
publication date: 1989-01-01T00:00:00Z
review text: Let \(\vdash^*\) denote the common sequential rules for \(\wedge\) and \(\vee\). Let \(\vdash^{\wedge}\) denote the sequential rules for \(\wedge\), and \(\vdash^{\vee}\) denote those for \(\vee\). The author's main questions are: (a) Is \(\vdash^*\) finitely based?, and: (b) Are \(\vdash^{\wedge}\) and \(\vdash^{\vee}\) the only proper non-trivial strengthenings of \(\vdash^*?\) As his work shows: ``Both questions have a positive answer, but the proofs are not as easy as one might expect.'' But his work has far greater theoretical and technical interest than these two questions about \(\wedge\) and \(\vee\) might indicate. He indicates how such question might be of interest to computer science. His work brings out that there are challenging problems in the area of asking analogous questions for other dual operators.
Mathematics Subject Classification ID: 03B22
zbMATH DE Number: 4160683
zbMATH Keywords: dual connectives
zbMATH Keywords: finite axiomatizability
zbMATH Keywords: common sequential rules for \(\wedge \) and \(\vee \)
reviewed by: Charles F. Kielkopf
MaRDI profile type: Publication
cites work: Joins and Direct Products of Equational Classes
cites work: On a fragment of the implicative propositional calculus
cites work: 2-element matrices
cites work: Q3760525
description: scientific article; zbMATH DE number 4160683