The pre-machine-learning formulations of AI focused on symbolic reasoning through the dual problems of search and logic. Many problems can be reduced to enumerating legal steps, and SAT/SMT/ASP and related systems can churn through those in a highly optimized and genetic manner.
Thanks... noted a few keywords to expand on further:
1. Symbolic reasoning
2. SAT/SMT/ASP
3. pre-machine-learning formulations of AI