This article presents an extension of Minimalist Categorial Grammars (MCG) to encode Chomsky’s
. These grammars are based on Partially Commutative Logic (PCL) and encode properties of Minimalist Grammars (MG) of Stabler . The first implementation of MCG were using both non-commutative properties (to respect the linear word order in an utterance) and commutative ones (to model features of different constituents). Here, we propose to augment Chomsky’s
with the non-commutative tensor product of the logic. Then we can give account of the PIC  just with logical properties of the framework instead of defining a specific rule.
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