Reconstructing proofs at the assertion level [chapter]

Xiaorong Huang
1994 Lecture Notes in Computer Science  
Most automated theorem provers su er from the problem that they can produce proofs only in formalisms di cult to understand even for experienced mathematicians. E ort has been made to reconstruct natural deduction (ND) proofs from such machine generated proofs. Although the single steps in ND proofs are easy to understand, the entire proof is usually at a low level of abstraction, containing too many tedious steps. To obtain proofs similar to those found in mathematical textbooks, we propose a
more » ... ew formalism, called ND style proofs at the assertion level, where derivations are mostly justi ed by the application of a de nition or a theorem. After characterizing the structure of compound ND proof segments allowing assertion level justi cation, we show that the same derivations can be achieved by domain-speci c inference rules as well. Furthermore, these rules can be represented compactly in a tree structure. Finally, we describe a system called PROVERB, which substantially shortens ND proofs by abstracting them to the assertion level and then transforms them into natural language.
doi:10.1007/3-540-58156-1_53 fatcat:b3guvz7gy5agth2pbtnvrmow6q