Math Literate Knowledge Management via Induced Material

Mathematicians integrate acquired knowledge into a mental model. For trained mathematicians, the mental model seems to include not just the bare facts, but various induced forms of knowledge, and the amount of this and the ability to perform all reasoning and knowledge operations taking that into account can be seen as a measure of mathematical training and literacy. Current MKM systems only act on the bare facts given to them; we contend that they --- their users actuallyi¾?--- would profit from a good dose of mathematical literacy so that they can better complement the abilities of human mathematicians and thus enhance their productivity. In this paper we discuss how we can model induced knowledge naturally in highly modular, theory-graph based, mathematical libraries and establish how to access it to make it available for applications, creating a form of mathematical literacy. We show two examples of math-literate MKM systems --- searching for induced statements and accessing a knowledge via induced theories --- to show the utility of the approach.