|Title:||The logic of Optimality Theory|
|Comment:||17pp, to appear in the proceedings of WECOL|
|Abstract:||The logic of Optimality Theory
University of Arizona
This paper is an attempt to determine the underpinnings of Optimality Theory,
and what logic might have to do with it. This is important because, without
this kind of work, very strange misunderstandings of the theory crop up. The
goals of the paper are as follows. First, I develop a logical statement of
Optimality Theory. Next, I go on to prove some theorems. Third, I go on to show
how the framework allows us to reason about partial derivations, and provides
promise as the basis of a theory of acquisition and a theory of parsing.
There are a number of results of this paper, but an important one is that I
establish that OT allows for multiple winners. That is, a tableau can have
several winning candidates. This may seem obvious to the reader familiar with
OT, but many presentations of OT imply or even state that this isn't so.