Does homotopy type theory teach us anything about imprecise models of the real world?

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Models of the real world are necessarily imprecise. Let’s say

  • the real world looks like $A$
  • the model’s assumptions are $A'$
  • the model derives that $A' \to B'$

Does adding deformations $A' \overset{\rm{deform}}{\rightsquigarrow} A$ to the usual logic allow us to infer anything about $B$ in $B \overset{?}{\leftarrow} B' \overset{\rm{existing\ model}}{\leftarrow} A' \overset{\rm{deform}}{\leftarrow} A$?