A constraint on variables in phonology

A CONSTRAINT ON VARIABLES IN PHONOLOGY John T. Jensen University of Colorado Two kinds of variables have been used in generative phonology: abbreviatory variables, which have only one expansion in the application of a given rule to a string; and essential variables, which have many values simultaneously, e.g. the 'star notation' of SPE. Essential variables can be dispensed with entirely if rules are allowed to apply iteratively rather than simultaneously. Abbreviatory variables can be severely constrained by the relevancy condition proposed here, which allows only irrelevant material to intervene between the focus and determinant of a rule. The result is a more highly constrained and more explanatory theory of phonology. The majority of familiar phonological rules act in an entirely local way, in that some segment has an effect on an immediately adjacent segment. A rule of this type that is frequently encountered is one to palatalize a consonant if a high front vowel follows : (1)C -> Cy / ____ i In many equally common rules, some intervening material is permitted or required between the determinant (segment causing the change) and the focus (segment undergoing the change).1 At some stage the West and North Germanic languages had an umlaut rule of approximately this form: (2)V^ [-back]/ ____ C0/ In this rule, a vowel affects another vowel across any number of consonants. We express the fact that the intervening material can contain only consonants by means ofthe notation C0. However, it is not an accident that only consonants can intervene in this rule. It is a general property of umlaut rules (and vowel harmony rules, to be discussed later) that only consonants can intervene between the relevant vowels. Adopting this idea as a general convention, we can rewrite rule 2 as follows : (3)V -» [-back]/ ____ Xi where the content of X is determined by the general convention. Variables like X in 3 have been used in both syntax and phonology since the advent of generative grammar, with a variety of interpretations. Let us first try to clarify some of the confusion found in variable notation. The notation C0 used in rule 2 exemplifies what may be called an abbreviatory variable, to distinguish it from a second type, the essential variable (to be discussed shortly). Abbreviatory variables are interpreted uniquely, with at most one value, which is the maximal possible value. Since X in 3 replaces C0 in 2, it too is an abbreviatory variable. 1 The terms determinant and focus, which I take from Howard 1972, are not yet standard in phonological discussions. The terms used here are defined by the following schematized rule: []— []/ [1X --------inputstructural deter- inter- = focus = focuschangeminant vening material 675 676LANGUAGE, VOLUME 50, NUMBER 4 (1974) Without a general convention to determine the contents of X, it can represent anything at all. For instance, rule 1 might be rewritten with an X variable : (4)C->Cy/ ____ Xi Rule 4 is a perfectly legitimate rule in the conventions of current phonological theory, although I am not aware that anyone has ever proposed such a rule. The reason is obvious. With the convention of maximal expansion, rule 4 will derive 5b, given 5a as input: (5)a. katalani b. kyatalani since the maximal possible value ofX is atalan. It is clear that we do not want to be able to have rules like 4, since such processes are never found in natural languages. One thing wrong with 4 is that it allows the intervening material X to contain possible inputs to the rule. In 5a, the segments t, I, and ? are all possible inputs, but they do not undergo the rule, since by the principle of maximal expansion they must be included in X. A weak form of a constraint that would eliminate rules like 4 has been proposed by Howard 1972, and called the Crossover Constraint; it is paraphrasable as follows : (6)Intervening material must not contain any possible focus. I shall argue that a much stronger constraint is possible, which will both prevent rules like 4 and determine the correct application ofthe majority of segmental rules in phonology. In rule 2, a vowel affects another vowel across only intervening consonants. Vowel harmony rules are...