Uninterpreted

Uninterpreted is an adjective describing something that is not interpreted or assigned a fixed meaning within a particular framework. In logic and computer science, uninterpreted symbols are function and predicate symbols whose interpretation is not specified by the theory itself. They serve as placeholders to enable abstract reasoning about structure and properties independent of a particular implementation.

In logic and model theory, uninterpreted symbols allow the examination of logical consequences without fixing a concrete domain or semantics. A model may assign to each uninterpreted function or predicate a mapping that satisfies the given constraints, but there is no predetermined rule for how the symbol behaves beyond those constraints. This abstraction supports general proofs about form and structure rather than about a specific data domain.

In automated reasoning and formal verification, uninterpreted functions facilitate reasoning about programs and data types in a way that separates control flow and logic from concrete data. A common idea is to use uninterpreted functions and predicates with congruence axioms, such as if a = b then f(a) = f(b), to enable reasoning about equality without committing to explicit interpretations. This is particularly useful when combining symbolic reasoning with theories like arithmetic or arrays.

Interpreted versus uninterpreted are central concepts in many formal frameworks. Interpreted symbols have fixed meanings defined by the theory (for example, standard arithmetic operations), while uninterpreted symbols do not. The distinction enables modular specification, abstraction, and scalable reasoning in areas such as model theory, algebraic specification, and software verification.