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The Turing-Completeness of Multimodal Categorial Grammars (1996)
| Venue: | JFAK: Essays dedicated to Johan van Benthem on the occasion of his 50th birthday. Institute for Logic, Language, and Computation, University of Amsterdam. Available on CD-ROM at http://turing.wins.uva.nl |
| Citations: | 13 - 0 self |
BibTeX
@INPROCEEDINGS{Carpenter96theturing-completeness,
author = {Bob Carpenter},
title = {The Turing-Completeness of Multimodal Categorial Grammars},
booktitle = {JFAK: Essays dedicated to Johan van Benthem on the occasion of his 50th birthday. Institute for Logic, Language, and Computation, University of Amsterdam. Available on CD-ROM at http://turing.wins.uva.nl},
year = {1996}
}
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Abstract
this paper, we demonstrate that the multimodal categorial grammars are in fact Turing-complete in their weak generative capacity. The result follows from a straightforward reduction of generalized rewriting systems to a mixed associative and modal categorial calculus. It turns out that we should not be surprised that seemingly arbitrary kinds of operations can be coded in multimodal categorial grammars. In this paper, we show that any computable grammar can be coded as a multimodal categorial grammar. From the standpoint of formal linguistics, this opening of the computational floodgates might even appear to be inevitable. Simply compare the introduction of general transformations in transformational grammars [Peters and Ritchie 1973], metarules in phrase structure grammars [Uszkoreit and Peters 1986], and lexical rules in categorial and phrase structure systems [Carpenter 1991], all of which have been shown to be Turing-complete. Although steps may be taken to restrict the power of these systems to ensure decidability, such moves appear rather ad hoc because of their lack of linguistic motivation. For instance, consider the restrictions against metarule self application [Gazdar et al. 1985], or the finite bound placed on unary phrase structure rules (and by association, empty categories) by [Kaplan and Bresnan 1982]. Natural language syntax is a difficult matter, and no formalism has even come close to providing a universal system in which all and only natural language grammars can be expressed. Perhaps even more discouraging is the fact that no grammars for particular languages have ever been developed that even come close to covering a naturally occurring range of data in a theoretically clean fashion. On the other hand, the grammar fragments that are typically propo...
Keyphrases
multimodal categorial grammar mixed associative modal categorial calculus computational floodgate weak generative capacity formal linguistics general transformation arbitrary kind natural language grammar natural language syntax clean fashion phrase structure system straightforward reduction phrase structure finite bound fact turing-complete metarule self application gazdar linguistic motivation universal system lexical rule difficult matter transformational grammar peter grammar fragment ad hoc computable grammar unary phrase structure rule empty category particular language
