Full Idea
The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X.
Gist of Idea
A sentence follows from others if they always model it
Source
JC Beall / G Restall (Logical Pluralism [2006], 3.2)
Book Reference
Beall,J/Restall,G: 'Logical Pluralism' [OUP 2006], p.29
A Reaction
This why the symbol |= is often referred to as 'models'.