## Djalali Today on Ranking

Come to the Greenberg room at 12:15 today for the Phonetics and Phonology workshop. Our very own Alex Djalali will be talking about his work on “A constructive solution to the ranking problem in Partial Order Optimality Theory”.

I give a solution to the ranking problem in Partial Order Optimality Theory (PoOT), which can be stated as follows: Allowing for free variation, given a finite set of input/output pairs, i.e., a dataset, that a speaker knows to be part of some language, how can learn the set of all PoOT grammars under some constraint set compatible with that dataset?

For an arbitrary dataset, we provide set-theoretic means for constructing the set of all PoOT grammars compatible with that dataset. Specifically, we determine the set of all strict orders of constraints that are compatible with dataset. As every strict total order is in fact a strict order, our solution is applicable in both PoOT and classical optimality theory (COT), showing that the ranking problem in COT is a special instance of a more general one in PoOT.