From Abstract Rewriting Systems to Abstract Proof Systems

TL;DR

This paper discusses the development of abstract proof systems as a framework for analyzing rule derivability and admissibility in a syntax-independent manner, inspired by abstract rewriting systems.

Contribution

It introduces the concept of abstract proof systems, extending ideas from abstract rewriting systems to formalize rule derivability and admissibility.

Findings

Framework enables syntax-independent analysis of proof rules

Provides general results applicable across different logical systems

Highlights the analogy between rewriting and proof systems

Abstract

Some personal recollections on the introduction of `abstract proof systems' as a framework for formulating syntax-independent, general results about rule derivability and admissibility. With a particular eye on the inspiration I owe to Roel de Vrijer: the analogy with abstract rewriting systems.