The Turing Completeness of Multimodal Categorial Grammars

In 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. We conclude with a discussion of a restriction to the so-caled weak Sahlqvist lexical rules, for which we can ensure decidability.

[1]  李幼升,et al.  Ph , 1989 .

[2]  Stanley Peters,et al.  On some formal properties of metarules , 1986 .

[3]  Glyn Morrill,et al.  Type Logical Grammar: Categorial Logic of Signs , 1994 .

[4]  P. Stanley Peters,et al.  Context-sensitive immediate constituent analysis—context-free languages revisited , 1969, STOC.

[5]  Glyn Morrill,et al.  Discontinuity in categorial grammar , 1995 .

[6]  Glyn Morrill,et al.  Intensionality and boundedness , 1990 .

[7]  Bob Carpenter,et al.  The Generative Power of Categorial Grammars and Head-Driven Phrase Structure Grammars with Lexical Rules , 1991, Comput. Linguistics.

[8]  Mark Hepple,et al.  The grammar and processing of order and dependency : a categorial approach , 1990 .

[9]  J.A.G. Versmissen.  Grammatical composition: modes, models, modalities : logical and linguistic aspects of multimodal categorial grammars , 1996 .

[10]  Joachim Lambek,et al.  On the Calculus of Syntactic Types , 1961 .

[11]  Nuel Belnap,et al.  Display logic , 1982, J. Philos. Log..

[12]  Geoffrey K. Pullum,et al.  Generalized Phrase Structure Grammar , 1985 .

[13]  M. T. S. Arís.  Gramáticas categoriales, coordinación generalizada y elisión , 1993 .

[14]  N. Kurtonina,et al.  Frames and Labels. A modal analysis of categorial inference , 1995 .

[15]  Esther Kraak,et al.  French Object Clitics: A Multimodal Analysis , 1995 .

[16]  Stanley Peters,et al.  On some formal properties of metarules , 1986 .

[17]  J. Lambek.  The Mathematics of Sentence Structure , 1958 .