Carpenter, Bob (1999) "The Turing Completeness of Multimodal Categorial Grammars ". European Summer School in Logic, Language and Information. Utrecht.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....from [12,3] for example) one might conjecture that a subclass of the (properly) mildly context sensitive languages is covered. It is clear, however, that the recursively enumerable languages outside the context sensitive class are not covered in general, notwithstanding Carpenter s result [2] that the whole class of general multimodal type logical grammars generate the entire Chomsky Type 0 language class. The reason for this is that Carpenter s result depends crucially on allowing the underlying type logics to be undecidable in general, with the ability to add or delete arbitrary ....

Carpenter, B., The Turing-completeness of multimodal categorial grammars, in: J. Gerbrandy, M. Marx, M. de Rijke and Y. Venema, editors, JFAK: Essays dedicated to Johan van Benthem on the occasion of his 50th birthday, Institute for Logic, Language, and Computation, University of Amsterdam, 1999 Available on CD-ROM at http://turing.wins.uva.nl.

.... Hepple s compilation method for L that was discussed earlier on can be parsed in polynomial time, but the compilation itself has exponential complexity [15] In the multimodal case, it is straightforward to show that CTL with an unrestricted set of structural rules (Moot s NL#R ) are undecidable [5]. If the structural rules are restricted to linear rules, that is, rules that do not introduce new structure into the proof, then the resulting CTL are still PSPACE complete, and their parsing problem is equivalent to that of general context sensitive languages [ 27] The complexity problem can ....

Bob Carpenter. The Turing completeness of multimodal categorial grammars. In Jelle Gerbrandy, Maarten Marx, Maarten de Rijke, and Yde Venema, editors, JFAK. Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday. Amsterdam University Press, 1999.

....of adequacy without using fully context sensitive, or even Turing complete, generative power. CTL permits a range of generative power since it starts from a context free base and allows an individual grammar to contain packages of structural rules which can increase power up to Turing complete [5]. CTL thus cannot be accused of expressive inadequacy; however, this expressive power puts it at odds with CCG s conservatism (also shared by TAG) as is evident in Steedman s comment in [37] p. 44: Although the (weakly context free) Lambek calculus provides an interesting start point. the ....

.... Logics and CCG through simulation 8 contrast Ho man s complexity proofs in [14] with Moortgat s discussion of the collapse of L into the Lambek Van Benthem calculus LP when commutativity is added [23] Perhaps the most important of all complexity results for CTL came from Carpenter who proved in [5] that CTL is Turing complete if there are no constraints on the form of structural postulates. From the above, it should be clear that nding the proper restrictions might be taken to be the key to restraining the generative power of CTL to an acceptable level. Other discussions have pointed in ....

Bob Carpenter. The Turing-completeness of multimodal categorial grammar. Unpublished manuscript. Carnegie Mellon University, 1995.

.... l ; n l ; l and r ; n r ; r where the subscript l or r indicates where the head lies. The other consists in enriching the logic by modalities, or unary connectives, used by pairs one forms a compound which can only be open by the other this causes the calculus to become indecidable [12] but, as in unification grammars, only a small part of the full calculus is used in linguistic applications, in particular because of the particular shape of the actual types of the words in the lexicon. An important ingredient of multimodal categorial grammars is the use of postulates which rule ....

....classic results of Gold [36] guarantee learnability in the limit from 5 The claim that human languages are definable by these grammars is challenged by Michaelis and Kracht 1996, on the basis of an argument that Old Georgian is not semilinear. 6 See the review of expressiveness results in [43] [12] claims that MMCGs can define any recursively enumerable set. 12 examples ( positive texts ) in this idealized situation, but getting to a more realistic learner is surprisingly interesting even here. The finiteness assumption is difficult to defend empirically given our current state of ....

Bob Carpenter. The Turing-completeness of multimodal categorial grammars. Carnegie-Mellon University, 1996.

No context found.

Carpenter, Bob (1999) "The Turing Completeness of Multimodal Categorial Grammars ". European Summer School in Logic, Language and Information. Utrecht.

No context found.

Carpenter, B., The Turing-completeness of multimodal categorial grammars, in: J. Gerbrandy, M. Marx, M. de Rijke and Y. Venema, editors, JFAK: Essays dedicated to Johan van Benthem on the occasion of his 50th birthday, Institute for Logic, Language, and Computation, University of Amsterdam, 1999 Available on CD-ROM at http://turing.wins.uva.nl.

No context found.

Bob Carpenter. The Turing-completeness of multimodal categorial grammar. Unpublished manuscript. Carnegie Mellon University, 1995.

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