What do you call the act of making two logical terms identical by making suitable substitutions?

The act of making two logical terms identical by making suitable substitutions is called unification. In logic and computer science, particularly in fields such as automated theorem proving and programming language semantics, unification is an important process. It involves finding a substitution that makes different logical expressions or terms the same. This is crucial in various applications, including type checking, query processing in databases, and implementing logic programming languages like Prolog.

Unification works by taking two terms and trying to identify the most general substitution that will make them equal. For example, if you have two terms P(X) and P(Y), a unifying substitution would be to set X equal to Y. The process can become complex when the terms contain variables and various structures, such as lists or nested functions. Unification is foundational in logic programming, where it enables the implementation of rules and queries that can lead to automated reasoning and inference in systems.