Herbrand universe

The Herbrand universe is a foundational concept in logic and automated reasoning. It consists of all the possible basic objects or terms that can be constructed using the constants and functions defined in a logical language. Think of it as the complete "universe" of all raw elements that can be created without any assumptions beyond what’s explicitly given. These elements serve as the building blocks for generating logical statements and testing their validity. In essence, the Herbrand universe provides a structured set of objects used to explore whether a logical formula can be true within that framework.