Labelled proof nets for the syntax and semantics of natural languages

We propose to represent the syntax and semantics of natural languages with labelled proof nets in the implicative fragment of intuitionistic linear logic. Resource-sensitivity of linear logic is used to express all dependencies between the syntactic constituents of a sentence in the form of a proof net. Phonological and semantic labelling of the proof net from its inputs to the unique output are used to produce the well-formed phonological form and the semantic representation of a sentence from entries of a lexicon. In this way we obtain a linguistic model of great flexibility because labelling is not completely determined logically: it is used to introduce linguistic constraints which go beyond the underlying logic.