In: Aart Middeldorp, Vincent Oostrom, Femke Raamsdonk, Roel Vrijer (Eds.): Lecture Notes in Computer Science, 3838: Processes, Terms and Cycles: Steps on the Road to Infinity: Essays Dedicated to Jan Willem Klop on the Occasion of His 60th Birthday, pages 554-638. Springer-Verlag, December 2005. URL: http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/1160154823,.
Abstract: By extending nondeterministic transition systems with concurrency and copy mechanisms, Axiomatic Rewriting Theory provides a uniform framework for a variety of rewriting systems, ranging from higher-order systems to Petri nets and process calculi. Despite its generality, the theory is surprisingly simple, based on a mild extension of transition systems with independence: an axiomatic rewriting system is defined as a 1-dimensional transition graph G equipped with 2-dimensional transitions describing the redex permutations of the system, and their orientation. In this article, we formulate a series of elementary axioms on axiomatic rewriting systems, and establish a diagrammatic standardization theorem.