## Wednesday, March 21, 2012

### Prince and Smolensky: Optimality theory (2004)

This is essentially a book on phonology, but also a showcase of optimality theory. The main focus of the book is phonetic parsing, i.e., the problem of specifying how to split a word (say, giddyup) into syllables (gid.dy.up). It's written by Alan Prince of Rugter's university and Paul Smolensky of John Hopkins.

Prioritized Constraints and Optimal Candidates
The answer given by optimality theory is that the parse is produced by iteratively throwing away possible parses that violate important constraints. More specifically, the idea is to start with the whole set of possible parses and then go through an ordered list of constraints, progressively rejecting more and more candidates.

The list of constraints may for instance be something like the following (cf. p. 20):
1. A syllable must have an onset
2. The sonority of the syllable nucleus must be higher than or equal to the sonority of the nucleus of any competing syllable.
Applying these two constraints then gives the following procedure for identifying syllables:
2. If some candidates have onsets and others don't, throw away those that don't.
3. Among the candidates that remain, throw away any candidate whose nucleus is not of the highest possible sonority.
After having extracted one syllable in this way, one may repeat the procedure to find extract a second syllable from the string phonemes that are not yet parsed.

Optimality As Maximality
The meat of such a theory of course lies in the specific set of constraints that are identified, and the order they are put in. Price and Smolensky seem to believe that both the constraints and the application procedure is universal. All linguistic difference thus stems from different ordering of constraints in their view.

As they note in chapter 5.2.2, the selection procedure they represent indirectly defines a partial order on the candidate parses of a word. One decides whether p is more "harmonious" than q by first comparing their performance on criterion 1, and if that is undecided, their performance on criterion 2, etc. A correct parse is thus one that is maximal with respect to this ordering.

Although it seems somewhat ridiculous that everything in their system is clear-cut and categorical, there is some plausibility to the claim that people actually use algorithms of this sort. The serial procedure employed in optimality theory is very similar to the take-the-best algorithm introduced by Gerd Gigerenzer and Dan Goldstein.

It's interesting that their morphological system has a lot of equivalents to that of Pānini, to whom they explicitly refer.