Encoding Phases using Commutativity and Non-commutativity in a Logical Framework

This article presents an extension of Minimalist Categorial Grammars (MCG) to encode Chomsky's phases. These grammars are based on Partially Commutative Logic (PCL) and encode properties of Minimalist Grammars (MG) of Stabler [22]. The first implementation of MCG were using both noncommutative 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 phases with the non-commutative tensor product of the logic. Then we can give account of the PIC [7] just with logical properties of the framework instead of defining a specific rule.