No abstract

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

We investigate the relationship between set constraints and the monadic class of first-order formulas and show that set constraints are essentially equivalent to the monadic class. From this equivalence we can infer that the satisfiability problem for set constraints is complete for NEXPTIME. More precisely, we prove that this problem has a lower bound of NTIME(c n/ log n). The relationship between set constraints and the monadic class also gives us decidability and complexity results for certain practically useful extensions of set constraints, in particular "negative projections" and subterm equality tests.

We introduce refutationally complete superposition calculi for intentional and extensional clausal λ-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the λ-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higherorder logic.Key words and phrases: superposition calculus, clausal lambda-free higher-order logic, refutational completeness.Extended version of Bentkamp et al., "Superposition for lambda-free higher-order logic" [11].