A tree interpretation of arc standard dependency derivation

TL;DR

This paper presents a novel tree-based interpretation of arc-standard dependency derivations, establishing a unique, ordered, and contiguous tree representation for projective dependency trees, with implications for parsing stability and non-projective handling.

Contribution

It introduces a derivational, tree-interpretation approach to arc-standard dependency parsing, linking derivations directly to ordered tree structures and characterizing projectivity.

Findings

Unique ordered tree representation for projective dependencies

Deterministic correspondence between transitions and tree updates

Practical implementation supports dependency recovery

Abstract

We show that arc-standard derivations for projective dependency trees determine a unique ordered tree representation with surface-contiguous yields and stable lexical anchoring. Each \textsc{shift}, \textsc{leftarc}, and \textsc{rightarc} transition corresponds to a deterministic tree update, and the resulting hierarchical object uniquely determines the original dependency arcs. We further show that this representation characterizes projectivity: a single-headed dependency tree admits such a contiguous ordered representation if and only if it is projective. The proposal is derivational rather than convertive. It interprets arc-standard transition sequences directly as ordered tree construction, rather than transforming a completed dependency graph into a phrase-structure output. For non-projective inputs, the same interpretation can be used in practice via pseudo-projective lifting before derivation and inverse decoding after recovery. A proof-of-concept implementation in a standard neural transition-based parser shows that the mapped derivations are executable and support stable dependency recovery.