Abstract
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 actually – 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.
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Notes
- 1.
We have left out the quantifiers for the variables x, y, and z from the axioms to reduce visual complexity. The always range over the respective base set. Furthermore, all axioms are named; but we only state the names we actually use in the examples.
- 2.
In fact these theory identifiers are not adequate for explanations. We conjecture that verbalization of the primary symbol of the respective theory would be the right choice here – see [Koh14] for these concepts – but leave studying this to future work.
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This work has been supported by the German Research Council (DFG) under grant KO 2428/13-1.
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Iancu, M., Kohlhase, M. (2015). Math Literate Knowledge Management via Induced Material. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds) Intelligent Computer Mathematics. CICM 2015. Lecture Notes in Computer Science(), vol 9150. Springer, Cham. https://doi.org/10.1007/978-3-319-20615-8_12
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DOI: https://doi.org/10.1007/978-3-319-20615-8_12
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