Abstract: 
Natural Deduction for Non-Classical Logics

David Basin and Seán Matthews and Luca Viganò


We present a framework for machine implementation of families of non-classical logics with Kripke-style 
semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of 
labelled formulae, and a theory of labels characterizing the properties of the Kripke models. By appropriate 
combinations we capture both partial and complete fragments of large families of non-classical logics such as 
modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of correctness 
and proof normalization. We have implemented our work in the Isabelle Logical Framework.