Mostgeneral

Mostgeneral (often rendered as most-general or abbreviated as MGU in the context of unifiers) is a descriptive term used in logic, computer science and formal methods to denote an element or solution that is as general as possible while still satisfying a given constraint. It expresses a maximal degree of generality under a partial order that compares specificity: a most-general element is one from which other valid elements can be obtained by further specialization.

In automated reasoning and programming languages, the most common usage is the most general unifier: a substitution that makes two terms identical and is more general than any other unifier, meaning any other unifier can be obtained by composing the most general unifier with an additional substitution. Most general unifiers, when they exist for first-order terms, are unique up to renaming of variables. Efficient algorithms (e.g., Martelli–Montanari) compute MGUs, and unification underlies Prolog execution, type inference, and theorem proving.

The dual notion under anti-unification is the most general generalization (MGG), which finds the least specific term that generalizes given terms; this is used in program analysis, machine learning and symbolic computation. Existence and properties of most-general solutions depend on the formal system and constraints (e.g., theories with associativity or commutativity may lack a unique MGU). Applications span logic programming, type systems, symbolic computation and automated deduction.