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

TL;DR

This paper extends Minimalist Categorial Grammars with Chomsky's phases using a logical framework based on Par- tially Commutative Logic, enabling a formal account of linguistic phenomena like the PIC.

Contribution

It introduces a novel logical encoding of Chomsky's phases within Minimalist Categorial Grammars using PCL, combining commutative and non-commutative properties.

Findings

Successfully encodes Chomsky's phases in the logical framework.

Provides a logical account of the PIC.

Extends the expressiveness of MCG with phase encoding.

Abstract

This article presents an extension of Minimalist Categorial Gram- mars (MCG) to encode Chomsky's phases. These grammars are based on Par- tially 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 pro- pose to adding Chomsky's phases with the non-commutative tensor product of the logic. Then we could give account of the PIC just by using logical prop- erties of the framework.