Abstract
The notion of k-valued categorial grammars where a word is associated to at most k types is often used in the field of lexicalized grammars as a fruitful constraint for obtaining several properties like the existence of learning algorithms. This principle is relevant only when the classes of k-valued grammars correspond to a real hierarchy of languages. This paper establishes the relevance of this notion for two related grammatical systems. In the first part, the classes of k-valued non-associative Lambek (NL) grammars without product is proved to define a strict hierarchy of languages. The second part introduces the notion of generalized functor argument for non-associative Lambek (NL ∅ ) calculus without product but allowing empty antecedent and establishes also that the classes of k-valued (NL ∅ ) grammars without product form a strict hierarchy of languages.
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Béchet, D., Foret, A. (2005). k-Valued Non-associative Lambek Grammars (Without Product) Form a Strict Hierarchy of Languages. In: Blache, P., Stabler, E., Busquets, J., Moot, R. (eds) Logical Aspects of Computational Linguistics. LACL 2005. Lecture Notes in Computer Science(), vol 3492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11422532_1
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DOI: https://doi.org/10.1007/11422532_1
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