"Logic programming"[0] is what I've always heard this stuff called. I was introduced to it with Prolog.
"Declarative programming"[1] is kind of a superset of logic programming, which may or may not be the aspect that piques your interest.
"Constraint programming"[2] and "Constraint logic programming"[3] are also a perspective on it.
[0] https://en.wikipedia.org/wiki/Logic_programming
[1] https://en.wikipedia.org/wiki/Declarative_programming
[2] https://en.wikipedia.org/wiki/Constraint_programming
[3] https://en.wikipedia.org/wiki/Constraint_logic_programming
1. Symbolic reasoning
2. SAT/SMT/ASP
3. pre-machine-learning formulations of AI