Abstract not found

Abstract. Formal syntax has hitherto worked mostly with theoretical frameworks that take grammars to be generative, in Emil Post’s sense: they provide recursive enumerations of sets. This work has its origins in Post’s formalization of proof theory. There is an alternative, with roots in the semantic side of logic: model-theoretic syntax (MTS). MTS takes grammars to be sets of statements of which (algebraically idealized) well-formed expressions are models. We clarify the difference between the two kinds of framework and review their separate histories, and then argue that the generative perspective has misled linguists concerning the properties of natural languages. We select two elementary facts about natural language phenomena for discussion: the gradient character of the property of being ungrammatical and the open nature of natural language lexicons. We claim that the MTS perspective on syntactic structure does much better on representing the facts in these two domains. We also examine the arguments linguists give for the infinitude of the class of all expressions in a natural language. These arguments turn out on examination to be either unsound or lacking in empirical content. We claim that infinitude is an unsupportable claim that is also unimportant. What is actually needed is a way of representing the structure of expressions in a natural language without assigning any importance to the notion of a unique set with definite cardinality that contains all and only the expressions in the language. MTS provides that.

The varieties of mathematical basis for formalizing linguistic theories are more diverse than is commonly realized. For example, the later work of Zellig Harris might well suggest a formalization in terms of CATE-

This chapter provides general arguments for replacing Optimality Theory with a theory that employs ordered rules and derivations. Between 1968 and 1993 the majority of phonologists worked within a theoretical framework of Derivational Phonology (DP), whose central proposition is that the surface

Theory comparisons have always enjoyed a prominent role in modern linguistics. Surprisingly, though, almost all comparative studies base their results exclusively on the meticulous analysis of empirical data, which is a laborious process. So-called model theoretic approaches have recently emerged as an intriguing alternative for specific problems (Rogers 1998, Potts and Pullum 2002,

The amount of material copied varies between a single C (mavit / ma-m-vit ‘lion(s)’) and CV (hodai / ho-ho-dai ‘rock(s)’). The former is preferred unless copying a single C would give rise to an illicit coda or cluster, in which case CV is copied. In contrast to previous analyses of similar patterns in Tohono O’odham and Lushootseed, I analyze the reduplicant as an infix rather than a prefix. The infixation of the reduplicant can be generated via constraints requiring the first vowel of the stem to correspond to the first vowel of the word. Furthermore, the preference for copying the initial consonant of the word can be generated by extending positional faithfulness to the base-reduplicant relationship. I argue that the infixation analysis is superior on two grounds. First, it reduces the C vs. CV variation to an instance of reduplicant size conditioned by phonotactics. Second, unlike the prefixation analyses, which must introduce a new notion of faithfulness to allow syncope in the base just in the context of reduplication (e.g. “existential faithfulness ” (Struijke 2000a)), the infixation analysis uses only independently necessary constraints of Correspondence Theory.