I have trouble understanding this kind of talk. What's a problem domain, what's its dimension and normalization, and what's the high order logic all about? Can we use plain words people from our grandfather generation can recognize?
Dimension = Customers, Accounts, Users, Widgets, Inventory
Higher-Order Logic = combining basic functional building blocks in order to compose more complex functionality. SQL enables direct, declarative access to the whole space of higher-order functions. E.g. You want the list of widgets made 3 quarters ago but scoped to one factory line, and only when a certain rotation of employees was on the factory floor? You got it. That's like 10-15 lines of SQL.
The term "higher order logic" typically means program logic that uses higher order functions. An object-oriented programming style is inherently higher order because objects typically contain functions and are passed to methods.
The term "higher order logic" can also mean a system of logic that allows statements about logical statements. [2]
[1] https://en.wikipedia.org/wiki/Higher-order_function [2] https://en.wikipedia.org/wiki/Higher-order_logic