Concrete example first
If (p) and (q) are recognition variables, RTL can build terms like (p\wedge q), (p\vee q), and (p\Rightarrow q). In GFRTU, these are not just symbols: each term gets interpreted as an internal arrow in the sheaf topos.
Formal definition
The Recognition Term Language (RTL) is a typed formal language for recognition expressions whose semantics is interpreted in (R=\mathbf{Sh}(T,J)).
Its interpretation maps well-formed terms and judgments to internal objects and morphisms, with naturality and sheaf-compatibility constraints inherited from the topos semantics.
Why it matters in GFRTU
- It provides a precise syntax for stating recognition claims.
- It links symbolic expressions to sheaf-theoretic semantics.
- It determines part of what generative closure must include.