Encoding Labelled Non-Classical Logics in Isabelle

We have used the generic theorem prover Isabelle [181] to implement the non-classical logis we presented. The logical basis of Isabelle is a natural deduction presentation of minimal implicational predicate logic with universal quantification over all higher-types [179].1 We call this metalogic Meta, and to prevent object/meta confusion we use Λ to represent Meta’s universal quantifier and ⇒ for implication.