https://en.wikipedia.org/wiki/Deductive_database
Deductive databases derive logical consequences based on facts and rules.
Datalog and its superset Prolog are notable instances of this idea, and they make the connection between the relational model and predicate logic particularly evident.
Codd's 1979 paper Extending the Database Relational Model to Capture More Meaning contains additional information about this connection. For example, quoting from Section 3 Relationship to Predicate Logic:
"We now describe two distinct ways in which the relational model can be related to predicate logic. Suppose we think of a database initially as a set of formulas in first-order predicate logic. ..."