Formal Reasoning About Influence in Natural Sciences Experiments

We present a simple calculus for deriving statements about the local behaviour of partial, continuous functions over the reals, within a collection of such functions associated with the elements of a finite partial order. We show that the calculus is sound in general and complete for particular partial orders and statements. The motivation for this work is drawn from an attempt to foster digitalisation in secondary-eduction classrooms, in particular in experimental lessons in natural science classes. This provides a way to formally model experiments and to automatically derive the truth of hypotheses made about certain phenomena in such experiments.