Less than zero: Correspondence and the null output

But what if some input has no output? What candidate is the winner of the competition? In phonology, this problem arises primarily and perhaps exclusively in paradigmatic gaps. In a paradigmatic gap, some combination of morphemes in the input is ruled absolutely ungrammatical for apparently phonological reasons, leaving a hole in the paradigm that is filled by periphrasis, suppletion, or allomorphy. Absolute ungrammaticality requires, or so it seems, that all candidates be ruled out. But this is at odds with the fundamental assumption in OT that all constraints are in principle violable: for any input, one of the candidates supplied by GEN will violate the constraints less seriously than the others, and hence will win. No candidate does so badly that it can’t win except insofar as some other candidate does less badly. Therefore, it is impossible for all candidates to be eliminated from contention, which is what seems to happen when there is a gap.