Non-convergence in the GLA and variation in the CDA

Given a linguistic theory with constraints/parameters/rules of any generality, learners are faced with what Dresher (1999) calls the credit problem. In terms of Optimality Theory (OT: Prince and Smolensky 1993/2004), there is usually more than one constraint that favors an optimal form over any one of its competitors, and that can be ranked by the learner over the constraints preferring the competitor. One of the most attractive properties of the constraint demotion algorithm (CDA: Tesar and Smolensky 1998) is that it finds a ranking that correctly deals with the learning data (if one exists), without directly stipulating a solution to the credit problem (cf. Dresher 1999). In this paper, I show that an alternative algorithm for learnability in OT, the Gradual Learning Algorithm (GLA: Boersma 1997, 1998, Boersma and Hayes 2001), does not share this property: it fails to converge when presented with a set of data that has multiple interacting instantiations of the credit problem. The advantage of the GLA over the CDA is that it handles variation; in the second part of the paper, I sketch an approach to the learning of variation that makes use of the inconsistency detection properties of the CDA (Tesar 1998).