Extended formula normalization for e-retrieval and sharing of mathematical knowledge

Abstract

Even though only a tiny fraction of mathematical knowledge is available digitally (e.g in theorem prover or computer algebra libraries, in documents with content-markup), our current retrieval methods are already inadequate. With further increase in digitalization of mathematics the situation will get worse without significant advances. When searching a formula, we often want to find not only structurally identical occurrences, but also all (logically) equivalent ones. Furthermore, we want to retrieve whole mathematical theories (i.e. objects with prescribed properties), and we want to find them irrespective of the nomenclature chosen in the respective formalization. In this paper, we propose a normalization-based approach to mathematical formula and theory retrieval modulo an equivalence theory and concept renaming, and apply the proposed algorithm to end-user querying and knowledge sharing. We test the implementation by applying it to a first-order translation of the Mizar library. © Springer-Verlag Berlin Heidelberg 2007.