Storage and computation in the mental lexicon

In the seventies of the previous century, the mathematical properties of formal languages have provided a key source of inspiration to morphological theory. Models such as developed by Lieber (1980) and Selkirk (1984) viewed the lexicon as a calculus, a formal system combining a repository of morphemes with rules for combining these morphological atomic units into complex words. This approach to the lexicon was driven by two fundamental assumptions. First, the lexicon was assumed to be a compositional derivational system. Complex words were believed to be generated from simpler forms (Bloch, 1947; Chomsky and Halle, 1968). Second, following Bloomfield (1933), the set of atomic elements was assumed to comprise any word or formative that is not predictable by rule. Rule-governed combinations of these atomic units, the regular complex words, were assumed not to be available as units in the lexicon, as storage would introduce unnecessary redundancy in the model. Instead of being listed (i.e., stored without analysis or substructure), regular complex words were generated (produced or parsed) by rule. Unsurprisingly, the goal of morphological theory was seen as accounting for which words belong to the set of possible words in the languages of the world. The question of whether a regular complex word exists in a language was regarded as a question addressing performance rather than competence, and hence irrelevant for morphological theory. Although many other formalisms have been developed to replace sequences of rules (Halle and Marantz, 1993; McCarthy and Prince, 1993), these formalisms did not challenge these fundamental assumptions of generative morphology. In optimality theory, for instance, forms still enter into derivational relations, even though the algorithm that relates underlying forms to surface forms is not based on a sequence of rules but on constraint satisfaction. This type of theory of the lexicon is to a surprising extent equally adequate as a competence theory for how a pocket calculator works. A pocket calculator has a set of atomic elements, the symbols on its keys. Its chip is endowed with a small set of arithmetic rules that, when supplied with a legal string, compositionally evaluate this string. Whenever a pocket calculator is requested to evaluate a string such as ’2 + 3’, it computes the outcome. It has no memory that holds the output of previous evaluations of the same string. It never learns from past experience. The balance of storage and computation is shifted totally to the maximization of computation and the minimization of storage.