Strong Equivalence of TAG and CCG

TL;DR

This paper proves that TAG and CCG are equally expressive on trees, showing that simplified CCG can match TAG's full expressive power without empty string lexicon entries.

Contribution

It demonstrates the equivalence of TAG and CCG on trees and identifies minimal conditions for CCG to achieve full expressive power.

Findings

CCG without empty string lexicon entries matches TAG on trees

First-order CCG rules of degree at most 2 suffice for full expressiveness

TAG and CCG have essentially the same expressive power on trees

Abstract

Tree-adjoining grammar (TAG) and combinatory categorial grammar (CCG) are two well-established mildly context-sensitive grammar formalisms that are known to have the same expressive power on strings (i.e., generate the same class of string languages). It is demonstrated that their expressive power on trees also essentially coincides. In fact, CCG without lexicon entries for the empty string and only first-order rules of degree at most 2 are sufficient for its full expressive power.