Manfred Kerber Proof Planning: a Practical Approach to Mechanized Reasoning in Mathematics

The attempt to mechanize mathematical reasoning belongs to the first experiments in artificial intelligence in the 1950 (Newell et al., 1957). However, the idea to automate or to support deduction turned out to be harder than originally expected. This can not at least be seen in the multitude of approaches that were pursued to model different aspects of mathematical reasoning. There are different dimension according to which these systems can be classified: input language (e.g., order-sorted first-order logic), calculus (e.g., resolution), interaction level (e.g., batch mode), proof output (e.g., refutation graph), and the purpose (e.g., automated theorem proving) as well as many more subtle points concerning the fine tuning of the proof search. In this contribution the proof planning approach will be presented. Since it is not the mainstream approach to mechanized reasoning, it seems to be worth to look at it in a more principled way and to contrast it to other approaches. In order to do so I categorize the systems according to their purpose. The different attempts can be roughly categorized into three classes: machineoriented automated theorem provers, interactive proof checkers, and humanoriented theorem provers. In the rest of the introduction we shall take a closer look at these different categories.