A Framework for Proof Systems

Meta-logics and type systems based on intuitionistic logic are commonly used for specifying natural deduction proof systems. We shall show here that linear logic can be used as a meta-logic to specify a range of object-level proof systems. In particular, we show that by providing different polarizations within a focused proof system for linear logic, one can account for natural deduction (normal and non-normal), sequent proofs (with and without cut), and tableaux proofs. Armed with just a few, simple variations to the linear logic encodings, more proof systems can be accommodated, including proof system using generalized elimination and generalized introduction rules. In general, most of these proof systems are developed for both classical and intuitionistic logics. By using simple results about linear logic, we can also give simple and modular proofs of the soundness and relative completeness of all the proof systems we consider.

• Type: Journal
• Year: 2010
• Where: JAR
• Authors: Vivek Nigam, Dale Miller
• Keywords: Intuitionistic Logics, JAR 2010, Linear Logic, Proof Systems