OMDoc/knowledge representation

How can mathematical concepts be modeled directly in OMDoc, i.e. without modeling statements or theories about them?

Generalization
Is there "generalization" in OMDoc? -- Michael Kohlhase: Yes, for theories (via theory inclusions). But: Is an example a theory?

In OMDoc, we can express statements about mathematics, but not mathematical objects in itself. So how can we express "all diffable functions are cont." in OMDoc?
 * Yes, one way (easy to understand the mathematics, hard to read off $$\mathcal{C}^1\subset\mathcal{C}^0$$ from it):
 * symbol $$\mathcal{C}^1$$ (for interpretation: identify this with "the set of diffable functions")
 * its definition
 * symbol $$\mathcal{C}^0$$ (for interpretation: identify this with "the set of continuous functions")
 * its definition (e.g. $$\epsilon/\delta$$)
 * theorem: $$\mathcal{C}^1\subset\mathcal{C}^0$$
 * its proof
 * Another way (harder to understand/write, easier to read off $$\mathcal{C}^1\subset\mathcal{C}^0$$ from it):
 * theory "continuous functions" (for interpretation: identify this with "the set of continuous functions")
 * ... including a symbol and a definition
 * theory "diffable functions" (for interpretation: identify this with "the set of diffable functions")
 * ... including a symbol and a definition, and the proof for the theory inclusion from diff to cont

In any case, we can't write $$\mathcal{C}^1\subset\mathcal{C}^0$$ directly! It must be extracted from OMDoc! --Christoph 21:33, 16 January 2007 (CET)