On the Chase for All Provenance Paths with Existential Rules

In this paper we focus on the problem of how lineage for existential rules knowledge bases. Given a knowledge base and an atomic ground query, we want to output all minimal provenance paths of the query (i.e. the sequence of rule applications that generates an atom from a given set of facts). Obtaining all minimal provenance paths of a query using forward chaining can be challenging due to the simplifications done during the rule applications of different chase mechanisms. We build upon the notion of Graph of Atoms Dependency (GAD) and use it to solve the problem of provenance path loss in the context of forward chaining with existential rules. We study the properties of this structure and investigate how different chase mechanisms impact its construction.