The Presentation of Proofs at theAssertion Level

Most automated theorem provers suuer from the problem that they can produce proofs only in formalisms diicult to understand even for experienced mathematicians. EEorts have been made to transform such machine generated proofs into natural deduction (ND) proofs. Although the single steps are now easy to understand, the entire proof is usually at a low level of abstraction, containing too many tedious steps. Therefore, it is not adequate as input to natural language generation systems. To overcome these problems, we propose a new intermediate representation , called ND style proofs at the assertion level. After illustrating the notion intuitively, we show that the assertion level steps can be justiied by domain-speciic inference rules, and that these rules can be represented compactly in a tree structure. Finally, we describe a procedure which substantially shortens ND proofs by abstracting them to the assertion level, and report our experience with further transformation into natural language.