Full Idea
Supervaluationist logic (now with a 'definite' operator D) fails to preserve certain classical principles about consequence and rules of inference. For example, reduction ad absurdum, contraposition, the deduction theorem and argument by cases.
Gist of Idea
Some of the principles of classical logic still fail with supervaluationism
Source
R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3)
Book Reference
'Vagueness: a Reader', ed/tr. Keefe,R /Smith,P [MIT 1999], p.30
A Reaction
The aim of supervaluationism was to try to preserve some classical logic, especially the law of excluded middle, in the face of problems of vagueness. More drastic views, like treating vagueness as irrelevant to logic, or the epistemic view, do better.