Higher-order Logic as Lingua Franca -- Integrating Argumentative Discourse and Deep Logical Analysis

TL;DR

This paper introduces a unified approach using higher-order logic as a common language to analyze argumentative discourse deeply, integrating formal logical structures with dialectical interactions, and provides new foundations for embedding non-classical logics.

Contribution

It presents a novel framework that employs higher-order logic as a lingua franca for encoding arguments and dialectics, along with foundational work on semantical embeddings of non-classical logics.

Findings

Successful analysis of a climate engineering debate excerpt.

More concise characterizations of semantical embeddings achieved.

New foundational approach for embedding non-classical logics in higher-order logic.

Abstract

We present an approach towards the deep, pluralistic logical analysis of argumentative discourse that benefits from the application of state-of-the-art automated reasoning technology for classical higher-order logic. Thanks to its expressivity this logic can adopt the status of a uniform \textit{lingua franca} allowing the encoding of both formalized arguments (their deep logical structure) and dialectical interactions (their attack and support relations). We illustrate this by analyzing an excerpt from an argumentative debate on climate engineering. Another, novel contribution concerns the definition of abstract, language-theoretical foundations for the characterization and assessment of shallow semantical embeddings (SSEs) of non-classical logics in classical higher-order logic, which constitute a pillar stone of our approach. The novel perspective we draw enables more concise and more elegant characterizations of semantical embeddings of logics and logic combinations, which is demonstrated with several examples.