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

A academic position paper advocates for logical pluralism in formal reasoning systems, arguing that multiple non-classical logics should coexist within unified meta-logical frameworks like LogiKEy rather than relying on single foundational logics. The research draws from two decades of work embedding diverse logics in classical higher-order logic, positioning logical pluralism as essential for interdisciplinary knowledge representation and reasoning in computational systems.

This preprint represents a significant philosophical and computational position within formal reasoning research. The authors argue against logical imperialism—the restrictive practice of adopting a single foundational logic for large-scale theory development—in favor of a pluralistic approach that accommodates multiple non-classical logics simultaneously. This matters because real-world reasoning problems often require different logical frameworks optimized for specific domains and applications.

The LogiKEy methodology emerged from two decades of research on shallow embeddings, demonstrating that classical higher-order logic can serve as a meta-logical framework hosting various non-classical logics. This approach enables researchers to leverage the strength of each logic without forcing artificial constraints. The computational metaphysics grounding provides theoretical justification for why multiple logics better represent complex reasoning scenarios than monolithic systems.

For the broader AI and formal systems community, this position challenges prevalent architectural assumptions in proof assistants and automated reasoning tools. Organizations developing knowledge representation systems face pressure to standardize on single logical foundations for simplicity, but this preprint argues such decisions sacrifice expressiveness and domain-specific optimization. The interdisciplinary reuse potential unlocked by logical pluralism could accelerate development across fields relying on automated reasoning—from mathematics to cybersecurity verification.

Looking forward, adoption of pluralistic frameworks in mainstream proof assistants like Coq and Isabelle would signal meaningful shifts in formal methods infrastructure. The critical question becomes whether the computational overhead of supporting multiple logics justifies the flexibility gains, and whether sufficient tool maturity exists for widespread adoption beyond research environments.

• →Logical pluralism enables multiple non-classical logics to coexist within unified meta-logical frameworks rather than enforcing single foundational logics.
• →LogiKEy methodology demonstrates that classical higher-order logic can effectively host and coordinate diverse logical systems for specific reasoning domains.
• →Logical imperialism in formal systems restricts interdisciplinary reuse and prevents optimization for specialized application requirements.
• →Computational metaphysics provides theoretical grounding for why problem-specific logics outperform monolithic logical architectures.
• →Mainstream adoption in proof assistants requires addressing computational efficiency concerns while maintaining expressiveness benefits.