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Abstract

The subject of this work is the development and investigation of a \emph{framework} for the modular and uniform representation and implementation of \emph{non-classical logics}, in particular modal and relevance logics. Logics are presented as labelled natural deduction (or sequent) systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit to establish not only general advantages and limitations of our approach with respect to related ones, but also, by means of a substructural analysis, decidability and complexity results for (some of) the logics we consider. All of our proof systems have been implemented in the generic theorem prover Isabelle, thus providing a simple and natural environment for interactive proof development.