Papers for

logic course instructors

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Logic teaching method unifies multiple logics in one tool

Mathematical Proof Assistants for Teaching Logic: The LogiKEy Methodology

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.

Tue 6 OctArtificial IntelligenceLogic in Computer Science
The gist
Teaching logic can be complicated because there are many different types of logic, like classical, modal, and deontic. The authors present a way to teach these diverse logics using one proof assistant tool by encoding them all in a universal logical framework called higher-order logic. This lets students explore and compare different logics interactively, using puzzles and examples that increase in complexity. Their decade-long experience shows this method supports learning a wide range of logical reasoning styles in one environment.
Open → 2610.08214v1