Learnable classes of categorial grammars
Learnable classes of categorial grammars
Handbook of Logic and Language
Handbook of Logic and Language
The Non-Associative Lambek Calculus with Product in Polynomial Time
TABLEAUX '99 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Categorial grammars with iterated types form a strict hierarchy of k-valued languages
CIAA'11 Proceedings of the 16th international conference on Implementation and application of automata
Categorial grammars with iterated types form a strict hierarchy of k-valued languages
Theoretical Computer Science
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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.