[Paper Review] Conversational Negation using Worldly Context in Compositional Distributional Semantics

Benjamin Rodatz, Razin A. Shaikh+1 more|arXiv (Cornell University)|May 12, 2021

Topic Modeling28 references4 citations

TL;DR

This paper proposes a novel framework for conversational negation in compositional distributional semantics by integrating worldly context (prior knowledge) with logical negation operations. It introduces a matrix inverse-based negation and demonstrates that combining subtraction negation ($\neg_{sub}$) with a phaser in the word's basis yields the highest correlation (0.635) with human plausibility ratings, significantly improving over pure logical negation.

ABSTRACT

We propose a framework to model an operational conversational negation by applying worldly context (prior knowledge) to logical negation in compositional distributional semantics. Given a word, our framework can create its negation that is similar to how humans perceive negation. The framework corrects logical negation to weight meanings closer in the entailment hierarchy more than meanings further apart. The proposed framework is flexible to accommodate different choices of logical negations, compositions, and worldly context generation. In particular, we propose and motivate a new logical negation using matrix inverse. We validate the sensibility of our conversational negation framework by performing experiments, leveraging density matrices to encode graded entailment information. We conclude that the combination of subtraction negation and phaser in the basis of the negated word yields the highest Pearson correlation of 0.635 with human ratings.

Motivation & Objective

• To address the limitation of purely logical negation in distributional semantics, which fails to capture human-like intuitions about negation.
• To model conversational negation as an operational process that reflects human plausibility judgments, not just logical denial.
• To integrate worldly context—derived from word relationships and entailment hierarchies—into the negation process to improve semantic plausibility.
• To validate the framework using human-rated plausibility data and density matrix representations of graded entailment.
• To establish a modular, extensible framework compatible with DisCoCirc for future extension to sentences and texts.

Proposed method

• Proposes a new logical negation operation using matrix inversion, motivated by its ability to preserve structural relationships in vector space.
• Introduces a worldly context generation method based on WordNet hypernyms and density matrix entailment, using context functions like $\texttt{poly}_x(i)$, $\texttt{exp}_x(i)$, and $\texttt{hyp}_x(i)$.
• Applies a phaser operation in the basis of the negated word to weight context based on entailment distance, enhancing plausibility modeling.
• Uses trace similarity and entailment-based measures ($k_{\textsf{E}}$, $k_{\textsf{hyp}}$) to evaluate plausibility of negated meanings against human ratings.
• Employs density matrices to encode graded entailment information, enabling nuanced modeling of semantic similarity and hierarchy.
• Validates the framework using a human plausibility rating dataset, comparing combinations of negation types, compositions, bases, and context functions.

Experimental results

Research questions

• RQ1 Can worldly context improve the plausibility of logically negated word meanings in distributional semantics?
• RQ2 Which combination of logical negation, composition method, and context function yields the highest correlation with human plausibility judgments?
• RQ3 Does the matrix inverse-based negation outperform or complement existing logical negation methods like subtraction from identity?
• RQ4 How does the choice of basis (e.g., word basis vs. other) affect the performance of conversational negation?
• RQ5 Can context functions that incorporate hypernym distance and entailment strength better model human-like alternative selection in negation?

Key findings

• The combination of subtraction negation ($\neg_{\text{sub}}$) and phaser in the basis of the negated word achieves the highest Pearson correlation of 0.635 with human plausibility ratings.
• All three context functions—polynomial, exponential, and hypernym-based—achieve the same maximal correlation of 0.635, indicating robustness to functional form.
• The context function $\texttt{hyp}_x(i)$, which incorporates WordNet hypernym distance, performs well even at $x=0$ (correlation 0.581), showing the value of entailment-based context.
• Trace similarity and $k_{\textsf{E2}}$ measure of entailment show the strongest interaction with the conversational negation, achieving 0.635 and 0.602 correlation respectively.
• The direction of entailment from the original word to the negated meaning ($w_N$) performs better than the reverse, suggesting that $w_N$ should be seen as an alternative to $w_A$.
• The framework demonstrates that logical negation alone is insufficient; worldly context is essential to produce human-intuitive negation results.