Higher-order logic

Higher-order logic (HOL) is a type of formal logic that extends first-order logic by allowing not just objects (like numbers or people) to be quantified, but also properties and functions. This means you can talk about sets of objects, or the relationships between different sets and their members. HOL is powerful for expressing complex ideas and concepts beyond what first-order logic can capture, making it useful in mathematics, computer science, and philosophy. It allows for richer expressions of statements about knowledge, beliefs, and reasoning, enabling more sophisticated analysis of logical relationships.