A Generalization of Equational Proof Theory?

Abstract

Rule based languages focussed in last decade on the use of term rewriting as a modeling tool [5]. To extend modeling capabilities of these languages, we explored recently the possibility of making the rule applications subject to probabilistic choices [2]. Dealing with rewriting with probabilistic firing of rules leads to numerous problems about the understanding of the underlying theoretical notions and results. In [2], we started to discuss what could be the generalizations of the classical notions in rewriting community for abstract reduction systems [1]. The next natural step is to understand if a generalization of equational proof theory for probabilistic systems exists. Our first attempt to do so yielded the theory which is presented in this abstract and which is actually closer to fuzzy logic than probabilities [3].