LACL '97 Selected papers from the Second International Conference on Logical Aspects of Computational Linguistics
Lambek Grammars Based on Pregroups
LACL '01 Proceedings of the 4th International Conference on Logical Aspects of Computational Linguistics
An Algebraic Approach to French Sentence Structure
LACL '01 Proceedings of the 4th International Conference on Logical Aspects of Computational Linguistics
An Algebraic Analysis of Clitic Pronouns in Italian
LACL '01 Proceedings of the 4th International Conference on Logical Aspects of Computational Linguistics
Pregroup grammars with letter promotions
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Pregroup grammars with letter promotions: Complexity and context-freeness
Journal of Computer and System Sciences
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Pregroup grammars are a context-free grammar formalism introduced as a simplification of Lambek calculus. This formalism is interesting for several reasons: the syntactical properties of words are specified by a set of types like the other type-based grammar formalisms; as a logical model, compositionality is easy ; a polytime parsing algorithm exists. However, this formalism is not completely lexicalized because each pre-group grammar is based on the free pregroup built from a set of primitive types together with a partial order, and this order is not lexical information. In fact, only the pregroup grammars that are based on primitive types with an order that is equality can be seen as fully lexicalized. We show here how we can transform, using a morphism on types, a particular pregroup grammar into another pregroup grammar that uses the equality as the order on primitive types. This transformation is at most quadratic in size (linear for a fixed set of primitive types), it preserves the parse structures of sentences and the number of types assigned to a word.