Constraints, Exceptions and Representations

This paper shows that default-based phonologies have the potential to capture morphophonological generalisations which cannot be captured by non-default theories. In achieving this result, I offer a characterisation of Underspecification Theory and Optimality Theory in terms of their methods for ordering defaults. The result means that machine learning techniques for bull(ling declm'ative analyses may not provide an adequate b~is for morphol)honological analysis. I n t r o d u c t i o n In other work, I have shown (EUison 1992, forthcoming) that interesting phonological constraints can be learned despite the presence of exceptions. Each of these constraints imposes a limit the set of possible words at a common level of repre~sentation. In this paper, I consider possible limits to the usefulness of these constraints in representing morphemes and finding concise representations of lexical entries. In order to compare a strictly declarative formalism with other constraint formalisms, a common formal environment must be established. Using model theory to establish the relationship between description and object, and then a modal formalism to define the structures to which constraints apply, we can compare the different effects of strict constraints and defaults. In particular, a strict declarative approach can be compared with other constraint frameworks such as Underspecification Theory (UT) (Archangeli, 1984) and ()ptimality Theory (OT) (Prince & Smolensky, 1993). This discussion is followed in tim latter part of the pal)or by consideration of the possibility of using machine learning to constraint systems that use defaults. M o r p h o p h o n o l o g y To structure the disct~ssion, I offer four desiderata for morphophonology. The first is that the morphophonology must allow concise lexical representations. Where information is predictable, it should not have to be specified in the lexicon. This desideratum is not a matter of empirical accuracy, rather one of scientific aesthetics. For example, English contains no front rounded vowels, so a vowel which is marked as front in the lexicon need not be marked as unrounded. The second desideratum is that the morphophonology should allow generalisations to be made over phonologically conditioned aUomorphs. For example, a representation of the Turkish plural affixes -lar, -ler, that uses the feature [:t:front] is superior to a segmental representation because a single representation for the two allomorphs can be achieved by not specifying the value for this feature in the representation of the morph. The third desideratum requires ttlat the specific allomorphs be recoverable from the generalisations. I f l a r and ler are generalised in a single representation, such as -IAr, then the morphophonology should make the recovery of the allomorphs in the correct environments possible. The final desideratum is, like the first, a matter of scientific aesthetics: a priori abstractions should not be used in an analysis any more than is necessary. For example, the feature [:t:front] should not be used in the analysis of a language unless it is motivated by structures in the language itself. This desideratum may conflict with the first: a priori features may result in a more concise representation. These four desiderata provide a framework for evaluating the relative merits of monostratal systems of phonological constraints with other current theories such as Underspecification Theory and Optimality Theory. M o d e l T h e o r y a n d M o d a l L o g i c A fundamental distinction in any formal account is the distinction between description and object. Failure to make the distinction (:an lead, at best, to confusion, and, at worst, to paradoxes, such as Russell's Paradox. Because this theory is talking about theories, it must make the distinction explicitly by formalising the relationship between description and object. This distinction is pursued in below and developed into a formalism for complex structures in the following section. M o d e l t h e o r y In model theory, the meaning of a statement in a formal l~mguage is provided by means of an INTERPRETATION