Mathematical Proof Assistants for Teaching Logic: The LogiKEy Methodology

2026-10-06

AI Summary

This study addresses the absence of a unified environment and the difficulty of comparing multiple logics in interdisciplinary logic education. Building upon the LogiKEy methodology, this work employs classical higher-order logic (HOL) as a metalogic to construct a single proof assistant environment within Isabelle/HOL via semantic embedding, thereby enabling the coexistence and interaction of diverse object logics. Furthermore, it proposes a logical pluralism pedagogical framework accompanied by a progressive sequence of case studies ranging from foundational puzzles to metaphysics. This approach has been successfully implemented across multiple years of courses and summer schools, demonstrating its effectiveness and portability in interdisciplinary teaching while robustly addressing concerns regarding the singularity of the chosen metalogic.

Abstract

We report on an approach to teaching logic to mixed groups of computer science, mathematics, and philosophy students, based on the logico-pluralistic LogiKEy methodology, used for more than a decade in courses, summer schools, and tutorials. LogiKEy uses classical higher-order logic (HOL) as a universal metalogic in which object logics, classical and non-classical alike, are encoded by defining their semantics; through these semantical embeddings a single proof assistant (e.g. Isabelle/HOL), with its automated theorem provers and (counter-)model finders, becomes one environment in which students learn, experiment with, and compare logics. After making the pedagogical case for proof assistants in the logic classroom, we present a graded sequence of classroom examples, each transition motivated by a limitation of the preceding representation, by a need for more explicit modelling resources, or by a new application. A liars-and-truth-tellers puzzle leads from propositional to modal logic; the Wise Men puzzle leads on to dynamic epistemic logic; Boolos's curious inference illustrates what a higher-order meta-logic buys, even for automated proof search; Chisholm's paradox takes the sequence into deontic logic, and from standard to dyadic deontic logic; and Gödel's ontological argument brings it to a research-level metaphysical argument. We then rebut the objection that embedding everything in classical HOL is monism rather than pluralism, reflect on three years of teaching such a course, and sketch the portability of the approach beyond Isabelle.

Problem

• logic teaching
• proof assistants
• logical pluralism
• higher-order logic
• LogiKEy

Innovation

• Higher-Order Logic
• Proof Assistants
• LogiKEy Methodology
• Semantical Embeddings
• Logical Pluralism