Varzi, Achille [2000] Supervaluationism and Paraconsistency, in Diderik Batens, Chris Mortensen, Graham Priest, and Jean Paul Van Bendegem (eds.), Frontiers in Paraconsistent Logic, Baldock: Research Studies Press, pp. 279-297.

Supervaluational semantics have been applied rather successfully to a variety of phenomenainvolving truth-value gaps, such as vagueness, lack of reference, sortal incorrectedness. On the other hand, they have not registered a comparable fortune (if any) in connection with truth-value gluts, i.e., more generally, with semantic phenomena involving overdeterminacy or inconsistency as opposed to indeterminacy and incompleteness. In this paper I review some basic routes that are available for this purpose. The outcome is a family of semantic systems in which (i) logical truths and falsehoods retain their classical status even in the presence gaps and gluts, although (ii) the general notions of satifiability and refutability are radically non-classical.