Full Idea
Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises.
Gist of Idea
Relevant consequence says invalidity is the conclusion not being 'in' the premises
Source
JC Beall / G Restall (Logical Pluralism [2006], 5.3.3)
Book Reference
Beall,J/Restall,G: 'Logical Pluralism' [OUP 2006], p.55
A Reaction
I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems.