Hierarchical Reasoning in Local Theory Extensions and Applications

We give an overview of results on hierarchical and modular reasoning in complex theories we established in previous work. We present a special type of extensions of a base theory, namely local theory extensions, for which hierarchic reasoning is possible (i.e. Proof tasks in the extension can be hierarchically reduced to proof tasks w.r.t. The base theory). We show how such local theory extensions can be identified and under which conditions locality is preserved when combining theories. We briefly discuss the way we used the possibility of hierarchical reasoning in local theory extensions in various application areas such as automated reasoning in mathematics, verification of reactive, real time and hybrid systems, and description logics.