Sheaf Semantics
Definition
Sheaf semantics is the rule that interpretations of recognitions are global arrows in the sheaf topos , not separate functions at each trace. Fiberwise data must be compatible and glue to a global interpretation.
Plain-language meaning
You do not interpret a recognition separately in each trace. Instead, you interpret it once, globally, and the local pieces must agree where traces overlap.
Minimal structure
- A trace site and its sheaf topos.
- Recognition fibers with reindexing maps.
- A sheaf condition that enforces gluing.
Entry conditions
Use sheaf semantics only when:
- You can define covers and overlaps of traces.
- You require local interpretations to agree on overlaps.
Example
If a recognition term has local meanings on two overlapping traces, sheaf semantics requires those meanings to coincide on the overlap so they define one global meaning.