Hierarchic Superposition with Weak Abstraction

In this paper we study possibilities of using methods for hierarchical reasoning in local theory extensions for the analysis and verification of parametric hybrid systems, where the parameters can be either constants or functions. Our goal is to automatically provide guarantees that such systems satisfy certain safety or invariance conditions. We first analyze the possibility of automatically generating such guarantees in the form of constraints on parameters, then show that we can also synthesise so-called criticality functions, typically used for proving stability and/or safety of hybrid systems. We illustrate our methods on several examples