Non-projective Axioms for Pregroup Grammars as Cut Eliminations
Résumé
Grammars based on free pregroups are context free. Thus, for several complex syntactical constructions that are not projective, some types must include a way to cross part of the environment. To solve this problem, cut annotations on the types assigned to special words like clitics or adverbs can be introduced. These annotations that can be seen as a limited form of semantical interpretation replace two normal axiom links by a long distance axiom link. During this reduction, such new links can cross other axioms: they introduce non-projective axioms that are not possible with pregroup grammars.