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Contrasting applications of logic in natural language syntactic description
 Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress
, 2005
"... 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 semanti ..."
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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: modeltheoretic syntax (MTS). MTS takes grammars to be sets of statements of which (algebraically idealized) wellformed 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.
Derivational Phonology and Optimality Phonology: Formal Comparison and Synthesis
, 2003
"... This thesis conducts a formal comparison of Optimality Theoretic phonology with its predecessor, Rulebased Derivational phonology. This is done in three studies comparing (i) rule operations and Faithfulness constraint violations, (ii) serial rule interaction and hierarchical constraint interaction ..."
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This thesis conducts a formal comparison of Optimality Theoretic phonology with its predecessor, Rulebased Derivational phonology. This is done in three studies comparing (i) rule operations and Faithfulness constraint violations, (ii) serial rule interaction and hierarchical constraint interaction, and (iii) derivational sequences and harmony scales. In each, the extent of the correlation is demonstrated, and empirical implications of their differences drawn out. Together, the studies demonstrate that there is no case in which the two frameworks mimic each other at all three points at once: the “Duke of York gambit”, where one rule is reversed by another, is the one case where rule ordering and constraint ranking converge, yet the complexity of this composite mapping demonstrably exceeds that of the inputoutput mappings of Optimality Theory. It is also argued that the Duke of York mapping is generally unexplanatory, and that its availability falsely predicts that a vowel inventory may be reduced to one in some contexts by deletion and then insertion. The failure of this prediction is illustrated from Yokuts, Chukchee and Lardil. A synthesis of derivational and optimality phonology is then presented in which
The Evolution of ModelTheoretic Frameworks in Linguistics
"... 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 ..."
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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