consistencies

Consistency is a property of a system, statement, or set of data in which no contradictions can be derived. In logic and philosophy, a collection of propositions is consistent if it is not possible to derive both a statement and its negation from its axioms.

In mathematics and logic, a theory T is consistent if there exists a model in which all the theorems of T are true; equivalently, T does not prove a contradiction. Consistency can be discussed relative to another theory (relative consistency). Gödel’s incompleteness theorems show limits on what sufficiently strong systems can prove about their own consistency.

In computer science and databases, consistency refers to adherence to defined invariants or rules. The ACID paradigm emphasizes consistency as one of the core properties of transactions. In distributed systems, different models describe how data remains consistent across nodes: strong or linearizable consistency aims for a single up-to-date view, while eventual consistency allows temporary divergence with guaranteed convergence over time. Conflict-free replicated data types (CRDTs) provide mechanisms to achieve consistency without centralized coordination.

In statistics and psychometrics, internal consistency measures reliability of a multi-item instrument, indicating whether items consistently reflect the same construct. Cronbach’s alpha and related statistics assess this property, with higher values suggesting more coherent measurement.

In everyday use, consistency also implies reliability, regularity, and predictable behavior. Data processing and quality assurance often require consistency checks to ensure that information adheres to expected formats and invariants.