Argumentative Topology: Finding Loop(holes) in Logic

TL;DR

This paper introduces a novel topological framework for analyzing word embeddings to detect logical structures, such as circular reasoning, using shape-based analysis techniques from dynamical systems.

Contribution

It presents Topological Word Embeddings, a new method combining topological data analysis with word embeddings to uncover logical shapes in text.

Findings

Successfully captures circular argument structures

Demonstrates shape-based logic detection in embeddings

Provides a new perspective on logical analysis in NLP

Abstract

Advances in natural language processing have resulted in increased capabilities with respect to multiple tasks. One of the possible causes of the observed performance gains is the introduction of increasingly sophisticated text representations. While many of the new word embedding techniques can be shown to capture particular notions of sentiment or associative structures, we explore the ability of two different word embeddings to uncover or capture the notion of logical shape in text. To this end we present a novel framework that we call Topological Word Embeddings which leverages mathematical techniques in dynamical system analysis and data driven shape extraction (i.e. topological data analysis). In this preliminary work we show that using a topological delay embedding we are able to capture and extract a different, shape-based notion of logic aimed at answering the question "Can we find a circle in a circular argument?"