Many Logics, One Methodology: A Plea for Logical Pluralism in Formalised Reasoning (preprint)

2026-05-26

AI Summary

This work addresses the long-standing limitation of formal reasoning imposed by reliance on a single foundational logic—often termed “logical imperialism”—which has hindered cross-disciplinary theoretical reuse. To overcome this, the paper proposes a logical pluralism methodology grounded in a higher-order logic (HOL) meta-framework. By employing shallow embedding techniques, it unifies multiple non-classical logics within the LogiKEy framework, enabling their flexible coexistence and interoperability at the object-logic level. This approach substantially enhances the expressiveness and reusability of knowledge representations, offering principled support for computational metaphysics and large-scale formalization efforts. Furthermore, it advances modern proof assistants toward a paradigm of multi-logic collaboration, fostering more versatile and integrative formal reasoning systems.

Abstract

This position statement looks back on two decades of work on shallow embeddings of non-classical logics in classical higher-order logic (HOL), a line of research that expanded into a range of logic embeddings in HOL and inspired the LogiKEy logic-pluralistic knowledge representation and reasoning methodology. This paper advances the case for logical pluralism at object-logic level within a unifying meta-logical framework such as LogiKEy, grounding the argument in computational metaphysics. More broadly, it advocates principled support for logical pluralism in modern proof assistants, and cautions against logical imperialism -- the rigid adoption of a single foundational logic for large-scale theory developments -- which impedes the interdisciplinary reuse that LogiKEy is designed to enable.

Problem

• logical pluralism
• logical imperialism
• formalised reasoning
• proof assistants
• computational metaphysics

Innovation

• logical pluralism
• shallow embedding
• higher-order logic
• LogiKEy
• computational metaphysics