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Classical automated theorem proving of today is based on ingenious search techniques to find a proof for a given theorem in very large search spaces-often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited.The shift from search based methods to more abstract planning techniques however opened up a paradigm for mathematical reasoning on a computer and several systems of that kind now employ a mix of interactive, search based as well as proof planning techniques.The MEGA system is at the core of several related and well-integrated research projects of the MEGA research group, whose aim is to develop system support for a working mathematician as well as a software engineer when employing formal methods for quality assurance. In particular, MEGA supports proof development at a human-oriented abstract level of proof granularity. It is a modular system with a central proof data structure and several supplementary subsystems including automated deduction and computer algebra systems. MEGA has many characteristics in common with systems like NUPRL, COQ, HOL, PVS, and ISABELLE. However, it differs from these systems with respect to its focus on proof planning and in that respect it is more similar to the proof planning systems CLAM and λCLAM at Edinburgh.

Development graphs are a tool for dealing with structured specifications in a formal program development in order to ease the management of change and reusing proofs. In this work, we extend development graphs with hiding (e.g. hidden operations). Hiding is a particularly difficult to realize operation, since it does not admit such a good decomposition of the involved specifications as other structuring operations do. We develop both a semantics and proof rules for development graphs with hiding. The rules are proven to be sound, and also complete relative to an oracle for conservative extensions. We also show that an absolute complete set of rules cannot exist. The whole framework is developed in a way independent of the underlying logical system (and thus also does not prescribe the nature of the parts of a specification that may be hidden).

We propose a proof representation format for human-oriented proofs at the assertion level with underspecification. This work aims at providing a possible solution to challenging phenomena worked out in empirical studies in the DIALOG project at Saarland University. A particular challenge in this project is to bridge the gap between the human-oriented proof representation format with under-specification used in the proof manager of the tutorial dialogue system and the calculus-and machine-oriented representation format of the domain reasoner.