An extended framework for specifying and reasoning about proof systems

Abstract

It has been shown that linear logic can be successfully used as a framework for both specifying proof systems for a number of logics, as well as proving fundamental properties about the specified systems. This article shows how to extend the framework with subexponentials in order to declaratively encode a wider range of proof systems, including a number of non-trivial proof systems such as multi-conclusion intuitionistic logic, classical modal logic S4, intuitionistic Lax logic, and Negri's labelled proof systems for different modal logics. Moreover, we propose methods for checking whether an encoded proof system has important properties, such as if it admits cut-elimination, the completeness of atomic identity rules, and the invertibility of its inference rules. Finally, we present a tool implementing some of these specification/verification methods.