The term deep case denotes a semantic role and is used especially in work influenced by Fillmore (1968).
Fillmore (1968) uses the terms deep structure cases (1968:21), case relationships (1968:21), deep cases (1968:32), which became widely known.
- Fillmore, Charles. 1968. The case for case. In Bach, Emmon & Harms, R. (eds.) Universals in linguistic theory New York: Holt, Rinehart and Winston, 1-90.