Two Many Values: An Algorithmic Outlook on Suszko's Thesis

In spite of the multiplication of truth-values, a noticeable shade of bivalence lurks behind the canonical notion of entailment that many-valued logics inherit from the 2-valued case. Can this bivalence be somehow used to our advantage? The present note briefly surveys the progress made in the last three decades toward making that theme precise from an abstract point of view and extracting some useful procedures from it, harvesting some of its most favorable crops on the domains of semantics and proof-theory.