aksioom

Aksioom is a term used in logic and philosophy to denote a basic proposition assumed without proof within a formal system. It serves as a starting point for constructing proofs and theories, and it functions similarly to the conventional notion of an axiom. In some circles, aksioom is used to emphasize the procedural role of foundational statements in a particular framework or to distinguish practical assumptions from more philosophical postulates.

Usage and scope: An aksioom may be a single statement or a schema, depending on the system. It is selected to capture essential properties the system aims to model, such as consistency, object existence, or algebraic structure. In constructive or computational logics, the term is sometimes preferred to highlight algorithmic grounding of the acceptance of the principle.

Relation to other notions: Aksiooms are neither derived nor proven within the system; they are accepted as starting points. They differ from theorems, which follow from them, and from postulates in historical usage, though many texts use "axiom" and "aksioom" interchangeably in practice.

Examples: A generic aksioom could assert that every object in the domain has a property P, or that a particular operation is closed under the domain. The exact content and form depend on the logic, ranging from simple universal statements to more complex schemas.

See also: axiom, postulate, theorem, inference rule, formal system.