# Week 4_McCarthy Ch 2.12 4-4.5.2.pptx - How to Construct an...

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How to Construct an Analysis 1
2.11 Constraint Ranking by Algorithm and Computer: 2 Constraint Demotion (Tesar and Smolensky 1998, 2000) The main idea in constraint demotion is that a loser-favoring constraint moves down in the hierarchy from some initial ranking until all of its Ls are dominated by Ws, but no further. Recursive Constraint Demotion algorithm (RCD) Begin by assembling all of the information that can contribute to ranking into a single table called the support, since it supports the inferences about ranking.
3 The first step in RCD is to identify all of the constraints that favor no losers. These are the constraints that have no Ls in their columns. Constraints that favor no losers are undominated. They belong at the top of the constraint hierarchy.
4 The next step is to hide the *Complex-Syllable, *C unsyll , and Max-C columns in the support, since there is nothing more to learn from them. We also must hide any losers that are disfavored by any of these three constraints. Those losers have been fully accounted for, so their performance on lower-ranking constraints is irrelevant to the ranking. For example, *Complex-Syllable favors the winner over *[la:n.hin], so *[la:n.hin]’s row has to be hidden.
5 The recursive step that gives RCD its name. (A recursive procedure is one that takes its own output as further input. Looking only at the considerably diminished support table (88), search again for any constraints that favor no losers. Here, Dep meets this criterion. Dep is therefore placed in the constraint hierarchy below the top-ranked constraints..]
6 The recursive step that gives RCD its name. (A recursive procedure is one that takes its own output as further input. Looking only at the considerably diminished support table (88), search again for any constraints that favor no losers. Here, Dep meets this criterion. Dep is therefore placed in the constraint hierarchy below the top-ranked constraints..]
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9 RCD can be straightforwardly implemented in a computer program, and the freely downloadable OTSoft package includes RCD among its many features (Hayes et al. 2003).
2.12 The Logic of Constraint Ranking and Its Uses: 10 Elementary Ranking Condition An ERC contains all of the information about constraint ranking that is provided by a single winner~loser comparison. An ERC is therefore the same as a single row of a support table like (85) – it contains W, L, or an empty cell for every constraint Which winner~loser pairs are most informative about ranking?= When does one ERC entail another ERC?
2.12 The Logic of Constraint Ranking and Its Uses: 11 Since every L must be dominated by some W, ERC (a) tells us that Constraint1 dominates both Constraint2 and Constraint3. ERC (b) tells us only that Constraint1 dominates Constraint3, so ERC (a) is more informative.