Hierarchical contextual reasoning

Abstract

Computer supported development of proofs requires user interaction even for theorems that are simple by human standards. In this thesis we define a communication infrastructure as a mediator between the user and the automatic reasoning procedures. It is based on a new uniform meta proof theory for contextual reasoning and encompasses most aspects of communication from the presentation of the proof state, via the supply of relevant contextual information about possible proof continuations, to the support for a hierarchical proof development. The proof theory is uniform for a variety of logics. It exploits proof theoretic annotations in formulas for a contextual reasoning style that is as far as possible intuitive for the user while at the same time still adequate for automatic reasoning procedures. Furthermore, concepts are defined to accomodate both the use and the explicit representation of hierarchies that are inherent in problem solving in general.

Das computergestuetzte Beweisen von Theoremen erfordert den Eingriff des menschlichen Benutzers selbst fuer nach menschlichen Maßstaeben einfache Theoreme. Diese Arbeit definiert eine Kommunikationsplattform, die eine synergetische Kooperationsform des Benutzers mit dem Beweisverfahren ermöglicht.