The Complexity and Generative Capacity of Lexicalized Abstract Categorial Grammars

Yoshinaka, Ryo; Kanazawa, Manabu

doi:10.1007/11422532_22

Cited by 15 publications

(11 citation statements)

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“…Note that P att(X) is finite (maybe empty). Now, for any π ∈ P att(X) choose an enumeration of edges in π and introduce a k-ary predicate symbol X π , where k is the number of edges in π (obviously, An LLG of a general form can generate an NP-complete language, just as an ACG (see [YK05]). We give the following, last example as another try to convince the reader that the geometric language of cowordisms is indeed intuitive and convenient for analyzing language generation.…”

Section: Llg and Multiple Context-free Grammarsmentioning

confidence: 99%

Cobordisms and commutative categorial grammars

Slavnov

2021

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Section: Llg and Multiple Context-free Grammarsmentioning

confidence: 99%

Cobordisms and commutative categorial grammars

Slavnov

2021

Preprint

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“…It is known that ACG, in general, can generate NP-complete languages [42] (and for unlexicalized ACG, even decidability is an open question).…”

Section: From ⊗-Free Lexicon To Cowordism Cfgmentioning

confidence: 99%

“…ACG are very strong in their expressive power [42] and show remarkable flexibility in many aspects. (Yet, they have their own deficiencies from the point of view of natural language modeling as well, see [30]).…”

Section: Introductionmentioning

confidence: 99%

Classical linear logic, cobordisms and categorial grammars

Slavnov

2019

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We propose a categorial grammar based on classical multiplicative linear logic.This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of linear logic grammars (LLG) are not abstract λ-terms, but simply tuples of words with labeled endpoints and supplied with specific plugging instructions: the sets of endpoints are subdivided into the incoming and the outgoing parts. We call such objects word cobordisms.A key observation is that word cobordisms can be organized in a category, very similar to the familiar category of topological cobordisms. This category is symmetric monoidal closed and compact closed and thus is a model of linear λ-calculus and classical, as well as intuitionistic linear logic. This allows us using linear logic as a typing system for word cobordisms.At least, this gives a concrete and intuitive representation of ACG. We think, however, that the category of word cobordisms, which has a rich structure and is independent of any grammar, might be interesting on its own right.

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“…In the present state of knowledge, semicompleteness is the best we may expect. Indeed, the ACG membership problem is known to be equivalent to provability in multiplicative exponential logic (de Groote et al, 2004;Yoshinaka and Kanazawa, 2005), the decidability of which is still open.…”

Section: Abstract Categorial Grammarmentioning

confidence: 99%