 From these completions we now construct a supervaluation. A supervaluation of \(\bM\) is a partial assignment of truth-values to formulas that makes a formula true if all completions of \(\bM\) make it true, false if they all make it false, and truth-valueless if they disagree. A formula is valid on a supervaluational semantics if and only if it is true on all supervaluations. This semantics validates all and only the theorems of PFL (Bencivenga 1981, Morscher &amp; Simons 2001, pp. 14–18).