33 research outputs found
Isabelle/HOL as a Meta-Language for Teaching Logic
Proof assistants are important tools for teaching logic. We support this
claim by discussing three formalizations in Isabelle/HOL used in a recent
course on automated reasoning. The first is a formalization of System W (a
system of classical propositional logic with only two primitive symbols), the
second is the Natural Deduction Assistant (NaDeA), and the third is a one-sided
sequent calculus that uses our Sequent Calculus Verifier (SeCaV). We describe
each formalization in turn, concentrating on how we used them in our teaching,
and commenting on features that are interesting or useful from a logic
education perspective. In the conclusion, we reflect on the lessons learned and
where they might lead us next.Comment: In Proceedings ThEdu'20, arXiv:2010.1583
Teaching Intuitionistic and Classical Propositional Logic Using Isabelle
We describe a natural deduction formalization of intuitionistic and classical
propositional logic in the Isabelle/Pure framework. In contrast to earlier
work, where we explored the pedagogical benefits of using a deep embedding
approach to logical modelling, here we employ a logical framework modelling.
This gives rise to simple and natural teaching examples and we report on the
role it played in teaching our Automated Reasoning course in 2020 and 2021.Comment: In Proceedings ThEdu'21, arXiv:2202.0214
SeCaV: A Sequent Calculus Verifier in Isabelle/HOL
We describe SeCaV, a sequent calculus verifier for first-order logic in
Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct
derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL
as a proof checker for our SeCaV derivations. The interactive features of
Isabelle/HOL make our system transparent. For instance, the user can simply
click on a side condition to see its exact definition. Our formalized soundness
and completeness proofs pertain exactly to the calculus as exposed to the user
and not just to some model of our tool. Users can also write their derivations
in the SeCaV Unshortener, which provides a lighter syntax, and expand them for
later verification. We have used both tools in our teaching.Comment: In Proceedings LSFA 2021, arXiv:2204.0341