A Semantic Approach to the Analysis of Rewriting-Based Systems

Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence and the class of systems at stake. In this paper we show that a number of interesting properties of rewriting-based systems can be investigated in this way, including infeasibility and non-joinability of critical pairs in (conditional) rewriting, non-loopingness of conditional rewrite systems, or the secure access to protected pages of a web site modeled as an order-sorted rewrite theory. Interestingly, this uniform, semantic approach succeeds when specific techniques developed to deal with the aforementioned problems fail.