Tautologies and positive solvability of linear homogeneous systems
type: Item
instance of: scholarly article
title: Tautologies and positive solvability of linear homogeneous systems
zbMATH Open document ID: 0764.15001
DOI: 10.1016/0168-0072(92)90060-D
author: Gennady Davydov
author: Inna Davydova
published in: Annals of Pure and Applied Logic
publication date: 1992-09-27T00:00:00Z
review text: Let \(A=[a_{ij}]\) be an \(m\times n\) real matrix, and let \[ L(a_{ij})=\begin{cases} p_ i, & a_{ij}>0,\\ \neg p_ i, & a_{ij}<0,\\ \text{true}, & a_{ij}=0,\end{cases} \] with propositional variables \(p_ 1,\dots,p_ m\). The main result: The system \(Ax=0\), \(x\geq 0\) has a nontrivial solution iff the formula \(L(A)\) is a tautology.
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15A39
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 60736
zbMATH Keywords: linear inequality
zbMATH Keywords: positive solution
zbMATH Keywords: propositional formula
reviewed by: Józef Drewniak
MaRDI profile type: Publication
cites work: Q5679729
cites work: Algebraic theory of linear inequalities
cites work: Q5633672
cites work: Q3710294
description: scientific article; zbMATH DE number 60736