consistencywith

Consistencywith is a term used to describe the relation of compatibility between two sets of information, claims, or systems. In ordinary language it appears as the phrase “consistency with,” but in technical contexts it may be written as consistencywith, especially when used as a predicate, function name, or formal relation in specifications, data schemas, or software models.

In logic and formal theory, an assertion φ is said to be consistent with a theory T if adding φ to T does not produce a contradiction. Equivalently, the union T ∪ {φ} is satisfiable, meaning there exists a model that satisfies both T and φ. More generally, two sets of statements A and B are consistencywith if A ∪ B has at least one model. This notion underpins model theory, satisfiability, and automated theorem proving, where consistencywith is a criterion for safe extension or combination of assumptions.

In data management and modeling, data D is consistent with a schema S if D satisfies all constraints specified by S, such as type requirements, keys, and referential integrity. Consistencywith in this domain implies no constraint violations and compatibility with established rules or standards.

In policy, legal, and requirements engineering domains, a claim, procedure, or design is described as consistencywith existing laws, regulations, or requirements when it aligns with them and does not introduce conflicting obligations.

Overall, consistencywith denotes a non-contradictory alignment between two sources of information or systems, serving as a basic check for coherence across theories, data, and rules. See also consistency, compatibility, coherence, and satisfiability.