Supervaluationism

In logic, supervaluationism is a semantics for dealing with irreferential singular terms and vagueness. Consider the sentence 'Pegasus likes licorice'. The name 'Pegasus' fails to refer, and there is nothing in the myth that would justify any assignment of values to it, suggesting such a sentence is vacuously true. Yet according to supervaluationism, such borderline statements lack a truth value. Alternatively, consider the statement 'Pegasus likes licorice or Pegasus doesn't like licorice' which is an instance of the valid schema: 'p ∨ ~p' (i.e. 'p or not p'). According to supervaluationism, it should be true regardless of whether or not its disjuncts have a truth value; that is, true in all interpretations. In general, anything true in all precisifications is supertrue; anything false is superfalse.