ABSTRACT
This chapter considers the hypothesis that the phonological grammar is an algebraic system. It evaluates the algebraic hypothesis against challenges raised by phonetically grounded explanations, and considers the role of exemplar-based knowledge in phonological system. The algebraic hypothesis predicts that phonological knowledge encodes abstract relations by representing the constituent structure of categories using mental variables. Algebraic accounts of phonology include abstract categories such as "syllable", "onset" and "foot". Each such category appeals to a class of exemplars, yet category and its members are distinct: the notion of a "syllable" is represented separately from its instances, and it cannot be subsumed by them. Moreover, categories such as "syllable" form equivalence classes, as their members are all treated alike with respect to relevant generalizations, irrespective of their frequency in language. Maximum Entropy (Maxent) models have been the subject of much recent interest in phonology. Unlike connectionist networks, Maxent models capture generalizations by inducing grammatical constraints that are encoded separately from lexical instances.
