Planning Diagonalization Proofs

Proof planning is a novel knowledge-based approach for proof construction, which supports the incorporation of mathematical knowledge and the common mathematical proof techniques of a particular mathematical eld. The diagonalization proof technique is a well-known method in theoretical computer science and in mathematics that originated with Can-tor, who used it to show his seminal uncountability results. It is now widely used as a proof technique for unsolvability results and meta-mathematical arguments. In this paper we give an account on how to systematically construct and plan diagonalization proofs: (i) by nding an indexing relation, (ii) by constructing a diagonal element, and (iii) by making the implicit contradiction of the diagonal element explicit. We suggest a declarative representation of the strategy and describe how it is realized in the proof planning environment of the mega-System.