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A faithful representation of non-associative Lambek grammars in abstract categorial grammars. (English) Zbl 1197.03032
Summary: This paper solves a natural but still open question: can Abstract Categorial Grammars (ACGs) respresent usual categorial grammars? Despite their name and their claim to be a unifying framework, up to now there was no faithful representation of usual categorial grammars in ACGs. This paper shows that Non-Associative Lambek Grammars as well as their derivations can be defined using ACGs of order two. To conclude, the outcome of such a representation is discussed.

03B65 Logic of natural languages
03B40 Combinatory logic and lambda calculus
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
68Q42 Grammars and rewriting systems
Grail; Grail
Full Text: DOI
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