On the Verification of Logically Decorated Graph Transformations

Abstract

We address the problem of reasoning on graph transformations featuring actions such as addition and deletion of nodes and edges, node merging and cloning, node or edge labelling and edge redirection. First, we introduce the considered graph rewrite systems which are parameterized by a given logic L. Formulas of L are used to label graph nodes and edges. In a second step, we tackle the problem of formal verification of the considered rewrite systems by using a Hoare-like weakest precondition calculus. It acts on triples of the form {Pre}(R, strategy){Post} where Pre and Post are conditions specified in the given logic L, R is a graph rewrite system and strategy is an expression stating how rules in R are to be performed. We prove that the calculus we introduce is sound. Moreover, we show how the proposed framework can be instantiated successfully with different logics. We investigate first-order logic and several of its decidable fragments with a particular focus on different dialects of description logic (DL). We also show, by using bisimulation relations, that some DL fragments cannot be used due to their lack of expressive power.