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Full Idea
The 'modal' account of logical consequence is that it is not possible for the premises to be true and the consequent false (under some suitable notion of possibility).
Gist of Idea
Maybe logical consequence is impossibility of the premises being true and the consequent false
Source
Theodore Sider (Logic for Philosophy [2010], 1.5)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.9
A Reaction
Sider gives a nice summary of five views of logical consequence, to which Shapiro adds substitutional semantics.