[Paper Review] Separating Argument Structure from Logical Structure in AMR

Johan Bos|arXiv (Cornell University)|Aug 4, 2019

Natural Language Processing Techniques21 references4 citations

TL;DR

This paper proposes extending Abstract Meaning Representation (AMR) with a logical layer that separates predicate-argument structure from scope and quantification, using indexed contexts and constraints to resolve the bound variable and scope representation problems. The approach preserves AMR's core structure while enabling correct inference for negation, quantifiers, and presuppositions, with compatibility to existing AMR tools and corpora.

ABSTRACT

The AMR (Abstract Meaning Representation) formalism for representing meaning of natural language sentences was not designed to deal with scope and quantifiers. By extending AMR with indices for contexts and formulating constraints on these contexts, a formalism is derived that makes correct prediction for inferences involving negation and bound variables. The attractive core predicate-argument structure of AMR is preserved. The resulting framework is similar to that of Discourse Representation Theory.

Motivation & Objective

• To address the bound variable problem in AMR, where quantifiers are incorrectly scoped due to graph-based representation.
• To solve the scope representation problem, where AMR fails to support valid inferences involving negation and complex logical operators.
• To extend AMR with a formal logical layer that enables correct interpretation of negation, quantifiers, and presuppositions.
• To maintain compatibility with existing AMR-annotated corpora and parsing tools.
• To enable comparison with formal semantics frameworks like Discourse Representation Theory (DRT) and support shared semantic parsing resources.

Proposed method

• Extend AMR by introducing a two-layer structure: a predicate-argument layer (original AMR minus polarity) and a logical layer with scope constraints.
• Assign unique indices to each sub-AMR (via numbered slashes, e.g., /1/, /2/) to represent contexts.
• Define logical constraints using symbols: = (identity), ¬ (negation), ⇒ (implication), < (presupposition), and use colons for inclusion (e.g., l:C).
• Use a recursive view of AMR, treating each slash as a sub-AMR, to enable systematic indexing and constraint application.
• Introduce a shorthand notation for common cases: {¬j} for {i:¬j}, {j⇒k} for {i:j⇒k}, and {¬j,j:¬k} for {i:¬j,j:¬k} to simplify annotation.
• Convert the extended AMR into a triple format with IN (membership) and structural triples (e.g., NOT, IF, THEN) for compatibility with standard AMR evaluation tools.

Experimental results

Research questions

• RQ1 How can AMR be extended to correctly represent scope in quantified and negated sentences without altering its core predicate-argument structure?
• RQ2 What formal mechanism allows AMR to handle the bound variable problem, where quantifiers incorrectly scope over all instances?
• RQ3 Can logical constraints be added to AMR in a way that preserves compatibility with existing AMR corpora and parsing tools?
• RQ4 How can the resulting logical structure be represented in a triple format suitable for evaluation and integration with standard AMR pipelines?
• RQ5 To what extent can the annotation process be semi-automated, and what role can machine learning play in scaling the extended AMR format?

Key findings

• The proposed extension successfully resolves the bound variable problem by allowing quantifiers to scope correctly, as demonstrated in examples like 'every snake bit itself' and 'all dogs want to swim'.
• The framework correctly models negation by treating it as a logical operator with scope, avoiding incorrect inferences such as deriving 'Mary left' from 'Mary did not leave'.
• The logical constraints are formally defined and can be converted into a triple format, enabling use with standard AMR evaluation tools like those from Cai and Knight (2013).
• The method supports a modular extension of existing AMR parsers by training on paired AMR and AMR+ datasets, preserving the original AMR structure.
• A shorthand notation for constraints (e.g., {¬j}, {j⇒k}) simplifies annotation while maintaining logical equivalence and reducing cognitive load.
• The approach is compatible with Discourse Representation Theory and enables integration with resources like the Parallel Meaning Bank.