Consistent

Consistent is a term used in various fields such as mathematics, logic, and computer science to describe a system, model, or statement that does not contain any contradictions. In a broader sense, it can also refer to something that is regularly occurring or has a pattern.

Mathematics

In mathematics, a set of axioms is said to be consistent if there is no theorem that can be derived from these axioms that contradicts another derived theorem. In other words, a consistent set of axioms will never allow for a situation where both a statement and its negation are provable.

Logic

In logic, a consistent theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true. This is the sense used in Gödel's incompleteness theorems.

Computer Science

In computer science, consistency refers to the ability of a system to continue to function in the face of failure. This can refer to the database consistency in the ACID model, or to the consistency in distributed systems, such as the CAP theorem.

See Also

• Consistency (statistics)
• Consistency (knowledge bases)

References

Consistent Resources
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