{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

eval - LINGUIST 726 Mathematical Methods in Linguistics...

This preview shows pages 1–4. Sign up to view the full content.

LINGUIST 726: Mathematical Methods in Linguistics September 30, 2004 Formalizing Optimality Theory: Some Preliminaries 1 Rajesh Bhatt 1 The Basics of Optimality Theory 1.1 What an OT Grammar Consists Of A set of inputs A function GEN that given an input generates a set of candidates A set of constraints A constraint hierarchy A function EVAL that given a candidate set and a constraint hierarchy re- turns the set of optimal candidates. 1.2 Strictness of Domination An OT grammar is a special case of the computational problem known as con- straint satisfaction/optimization. Input: a set of constraints ( ) and a set of weights associated with the constraints ( ). a set of candidates ( ) Goal: To determine which candidate satisﬁes the constraints optimally 1 Thanks to Andries Coetzee and Joe Pater for answering my questions. The good ideas within are taken from Chs. 1 and 2 of Coetzee (2004); the inadequacies are mine.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
We can model how well a particular candidate satisﬁes the constraints by the following function : (1) (to be consistent with how things are done in OT, I assume that if , then satisﬁes to a greater extent than does.) The optimization problem now reduced to determining the (or the subset of ) such that . We could think of the ordering of the weights as giving us something like the ranking in OT. Consider the following constraints with the suggested weights: i. *A : must not contain an a , weight 5 ii. *B : must not contain a b , weight 1 Case 1: Let a, b . Then ( a )=5and ( b )=1 Hence b is the optimal candidate. Case 2: Let a, bbbbbb . Then ( a )=5and ( bbbbbb )=6 Hence a is the optimal candidate. What we see here is that a ‘lower ranked’ constraint can overturn the judgement of a ‘higher ranked’ constraint. This is quite different from what happens in OT. In OT, a lower ranked constraint can never overturn the judgement of a higher ranked constraint. This property of an OT grammar is referred to as strictness of domination (cf. McCarthy (2002) and references therein), and restricts unbounded constraint interaction - what we could call ‘bargaining’ between groups of con- straints. In an OT grammar which ranked *A above *B , a would not be optimal in either grammar. 2
We can thus think of OT as a constraint optimization system where if is ranked above , then , the weight associated with is incommensurably larger than , the weight associated with . 1.3 What we want from an OT Grammar Any OT grammar must be able to give us the set of most optimal candidates given a set of candidates and a constraint hierarchy. In addition, there are certain other decisions one can make concerning what we get from an OT grammar. 1.3.1 Bipartition or a Ranking Given a set of candidates , an OT grammar could return us: (i) a bipartition of into a set of winners and a set of losers: Winners Losers The winners are all equally optimal and more optimal than the losers. No infor- mation is represented concerning further ranking among the losers. (ii) a rank-ordering of

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 12

eval - LINGUIST 726 Mathematical Methods in Linguistics...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online