Conjunctive categorial grammars and Lambek grammars with additives

• Main Authors: Kuznetsov, Stepan L, Okhotin, Alexander
• Format: Journal Article
• Language: English
• Published: 26-05-2024
• Subjects: Computer Science - Computation and Language; Computer Science - Logic in Computer Science; Mathematics - Logic
• DOI: 10.48550/arxiv.2405.16662

A new family of categorial grammars is proposed, defined by enriching basic
categorial grammars with a conjunction operation. It is proved that the
formalism obtained in this way has the same expressive power as conjunctive
grammars, that is, context-free grammars enhanced with conjunction. It is also
shown that categorial grammars with conjunction can be naturally embedded into
the Lambek calculus with conjunction and disjunction operations. This further
implies that a certain NP-complete set can be defined in the Lambek calculus
with conjunction. We also show how to handle some subtle issues connected with
the empty string. Finally, we prove that a language generated by a conjunctive
grammar can be described by a Lambek grammar with disjunction (but without
conjunction).