Define Abstract Semantics
- Define what is a semantics for the term language. Do it incrementally: cartesian category + strong monad + partial function type + nat + dyn ...
- Define the semantic interpretation of the term language in any such category
- Define what is a semantics for the precision logic. Do it incrementally and on top of (1): thin double cartesian category + thin double strong monad + ...
- Define the semantic interpretation of the logic in any such heterogeneous model
- Define what is a semantics for the homogeneous fragment of the precision logic: preorder enriched rather than thin double.
- Show how to construct a heterogenous model from a homogeneous model