A Generalization of Equational Proof Theory?

Rapport interne.Recently rule based languages focused on the use of rewriting as a modeling tool which results in making specifications executable. To extend the modeling capabilities of rule based languages, we explored in a previous work the possibility of making the rule applications subject to probabilistic choices, and started to study the generalization of the results in the rewriting community about abstract reduction systems to systems with probabilistic choices. This paper presents a new contribution on this line by presenting a generalization of classical equational proof theory. We obtain a nice proof theory which is sound and complete, and which has initial models