A real semantic web for mathematics deserves a real semantics

Mathematical documents, and their instrumentation by computers, have rich structure at the layers of presentation, metadata and semantics, as objects in a system for formal mathematical logic. Semantic Web tools [2] support the first two of these, with little, if any, contribution to the third, while Proof Assistants [17] instrument the third layer, typically with bespoke approaches to the first two. Our position is that a web of mathematical documents, definitions and proofs should be given a fully-edged semantics in terms of the third layer. We propose a "Math- Wiki" to harness Web 2.0 tools and techniques to the rich semantics furnished by contemporary Proof Assistants