A Model-Theoretic Framework for Theories of Syntax

A Model-Theoretic Framework for Theories of Syntax James Rogers Institute for Research in Cognitive Science University of Pennsylvania Suite 400C, 3401 Walnut Street Philadelphia, PA 19104 j rogers©linc, cis. upenn, edu Abstract A natural next step in the evolution of constraint-based grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanism--to express syntactic theories purely in terms of the properties of the class of structures they license. By fo- cusing on the structural properties of lan- guages rather than on mechanisms for gen- erating or checking structures that exhibit those properties, this model-theoretic ap- proach can offer simpler and significantly clearer expression of theories and can po- tentially provide a uniform formalization, allowing disparate theories to be compared on the basis of those properties. We dis- cuss L2,p, a monadic second-order logical framework for such an approach to syn- tax that has the distinctive virtue of be- ing superficially expressive--supporting di- rect statement of most linguistically sig- nificant syntactic properties--but having well-defined strong generative capacity-- languages are definable in L2K,p iff they are strongly context-free. We draw examples from the realms of GPSG and GB. 1 Introduction Generative grammar and formal language theory share a common origin in a procedural notion of grammars: the grammar formalism provides a gen- eral mechanism for recognizing or generating lan- guages while the grammar itself specializes that mechanism for a specific language. At least ini- tially there was hope that this relationship would be informative for linguistics, that by character- izing the natural languages in terms of language- theoretic complexity one would gain insight into the structural regularities of those languages. More- over, the fact that language-theoretic complexity classes have dual automata-theoretic characteriza- tions offered the prospect that such results might provide abstract models of the human language fac- ulty, thereby not just identifying these regularities, but actually accounting for them. Over time, the two disciplines have gradually be- come estranged, principally due to a realization that the structural properties of languages that charac- terize natural languages may well not be those that can be distinguished by existing language-theoretic complexity classes. Thus the insights offered by for- mal language theory might actually be misleading in guiding theories of syntax. As a result, the em- phasis in generative grammar has turned from for- malisms with restricted generative capacity to those that support more natural expression of the observed regularities of languages. While a variety of dis- tinct approaches have developed, most of them can be characterized as constrain~ based--the formalism (or formal framework) provides a class of structures and a means of precisely stating constraints on their form, the linguistic theory is then expressed as a sys- tem of constraints (or principles) that characterize the class of well-formed analyses of the strings in the language. 1 As the study of the formal properties of classes of structures defined in such a way falls within domain of Model Theory, it's not surprising that treatments of the meaning of these …

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