Explanation in variable phonology: An exponential model of morphological constraints

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Abstract
Variationist treatments of phonological processes typically provide precise quantitative accounts of the effects of conditioning environmental factors on the occurrence of the process, and these effects have been shown to be robust for several well-studied processes. But comparable precision in theoretical explanation is usually elusive, at the current state of the discipline. That is, the analyst is usually unable to say why the parameters should have the particular values that they do, although one can often explain relative ordering of environments. This article attempts to give a precise explanation — in the form of a quantitative theoretical prediction — of one robust quantitative observation about English phonology. The reduction of final consonant clusters (often called -t,d deletion) is well-known to be conditioned by the morphological structure of a target word. Deletion applies more in monomorphemic words (e.g., mist) than in inflected words (e.g., missed). In the theory of lexical phonology, these classes of words are differentiated by derivational history, acquiring their final clusters at different levels of the morphology. The theory further postulates that rules may apply at more than one level of the derivation. If -t,d deletion is treated as a variable rule with a fixed rate of application (p0) in a phonology with this architecture, then higher rates of application in underived forms (where the final cluster is present underlyingly and throughout the derivation) are a consequence of multiple exposures to the deletion rule, whereas inflected forms (which only meet the structural description of the rule late in the derivation) have fewer exposures and lower cumulative deletion. This further allows a precise quantitative prediction concerning surface deletion rates in the different morphological categories. They should be related as an exponential function of p0, depending on the number of exposures to the rule. The prediction is empirically verified in a study of -t,d deletion in seven English speakers.