Augmenting Mathematical Formulae for More Effective Querying & Presentation

1 Summary Scientists and engineers search regularly for well‐ established mathematical concepts, expressed by mathematical formulae. Conventional search en‐ gines focus on keyword based text search today. An analogue approach does not work for mathe‐ matical formulae. Knowledge about identifiers alone is not sufficient to derive the semantics of the formula they occur in. Currently, for formula related inquiries the solution is to consult domain experts, which is slow, expensive and non‐deter‐ ministic. Consequently, core concepts to enable formula related queries on potentially large datasets are needed. While earlier attempts addressed the problem as a whole, I identify three mutually or‐ thogonal challenges to formula search. The first challenge, content augmentation, is to collect the full semantic information about indi‐ vidual formula from a given input. Most funda‐ mentally, this might start with digitization of ana‐ logue mathematical content, captures the con‐ version from imperative typesetting instructions (i.e. TEX) to declarative layout descriptions (i.e. presentation MathML) but also deals about infer‐ ring the syntactical structure of a formula (i.e. the expression tree often represented in content MathML). In addition, this first challenge involves the association of formula metadata such as con‐ straints, identifier definitions, related keywords or substitutions with individual formulae. The second challenge is content querying. This ranges from query formulation, to query pro‐ cessing, actual search, hit ranking to result presentation. There are different forms of for‐ mula queries. Standard ad‐hoc retrieval queries, where a user defines the information need and the math information retrieval system returns a ranked list given a particular data set. Similar is the interactive formula filter queries, where a user filters a data set interactively until she de‐ rives at the result set, which is relevant to her needs. Different are unattended queries that run in the background to assist authors during editing or readers to identify related work while viewing a certain formula. The third challenge is content indexing for grow‐ ing data sets. This challenge includes the scalable execution of the solutions to the two aforemen‐ tioned challenges. While well‐established from the area of database systems i.e. XML processing and indexing can be applied, math specific com‐ plexity problems require individual solutions. Augmented content (challenge 1) opens up addi‐ tional options for similarity search, and poten‐ tially improves the search results regardless of the applied similarity measure. In order to sepa‐ rate the effect of content augmentation from in‐ trinsic improvements …