Proof-Nets, Hybrid Logics and Minimalist Representations

Inthis paper, we aim at giving alogical account of the representationalist view on minimalist grammars by refering to the notion of Proof-Net in Linear Logic. We propose at the same time a hybrid logic, which mixes one logic (Lambek calculus) for building up elementary proofs and another one for combining the proofs so obtained. Because the rst logic is non commutative and the second one is commutative, this brings us a way to combine commutativity and non commutativity in the same framework. The dynamic of cut-elimination in proof-nets is used to formalise the move-operation. Otherwise, we advocate a proof-net formalism which allows us to consider formulae as nodes to which it is possible to assign weights which determine the nal phonological interpretation.

• Type: Journal
• Year: 2000
• Where: GRAMMARS
• Authors: Alain Lecomte
• Keywords: GRAMMARS 2000, Hybrid Logic, Linear Logic, Logic