An efficient context-free parsing algorithm
Communications of the ACM
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
On categorial grammars as logical information systems
ICFCA'10 Proceedings of the 8th international conference on Formal Concept Analysis
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We study mathematical and algorithmic properties of Lambek's pregroups and illustrate them by the French noun phrase. An algorithm of complexity n3 to solve the reduction problem in an arbitrary free pregroup as well as recognition by a pregroup grammar is presented. This algorithm is then specified to run in linear time. A sufficient condition for a language fragment that makes the linear algorithm complete is given.