 Supervaluation theory utilizes the concept of admissible sharpening or precisification of vague predication (see  the entry on  vagueness). I may be unable to assert  truthfully of a given color chip in the red-orange range that it is red, while also being unable to assert that it is not red. Once the notion of red is sharpened or precisified to a particular interval of wave-lengths, I am in a position to assert either the positive proposition “a is red” or its negation “a is not red”, but which one depends on the details of the sharpening. A sentence S is supertrue iff it is true on every sharpening and superfalse if it is false on every sharpening; if is true on some sharpenings and false on others, it is neither supertrue nor superfalse, thus corresponding to a truth-value gap. One salutary result of this approach is that LEM can be retained: P or not P is supertrue since it is true on every sharpening. Hyde (1997) draws on the dual status of gaps and gluts to define a paraconsistent “subvaluation” theory: S is subtrue iff is true on at least one sharpening, subfalse iff it is false on at least one sharpening, and neither subtrue nor subfalse if it is true on some sharpenings and false on others. Given the status of supervaluation and subvaluation as duals, each is equally defensible and applicable to the semantics of vagueness.  Crucially, it is the notion of supertruth, or subtruth as the case may be, that tracks our natural language intuitions of truth, and similarly for falsity. In this sense, the logic of supervaluation is paracomplete (allowing for violations of LEM) and the logic of subvaluation paraconsistent (allowing for violations of LNC). In the tradition of paraconsistent logics, Hyde stresses the need for “quarantining the gluts” to avoid the explosive consequences of ex contradictione quodlibet (see §4).