In the context of the ACID principles for database transactions "Consistency" denotes the characteristic of a transaction to transform a consistent state of the database into another consistent state. Consistency is the one characteristic of a transaction which can normally not be enforced by a transaction manager. The code of the transaction itself must ensure this consistency, e.g. by testing if enough money is on a checking account before paying out money or by ensuring that if a supplier of goods is removed from the database, also all goods it supplied are removed. Please note that it is not required that the database has a consistent state during the whole execution time of the transaction, only at the end.

From the consistency of one transaction one can deduce that a schedule of several concurrent transactions will preserve the consistency of the whole database, too, as long as the schedule is serializable. The proof is easy, since a serializable schedule means that an equivalent serial schedule exists. In that serial schedule all transactions are executed one after another and therefore transform the database through a series of (consistent) states to the final consistent state.

Ensuring the consistency of the whole database by demanding that each transaction maintains it can be seen as the implicit way to ensure database consistency. The consistency constraints of the database are encoded implicitly within the transactions, e.g. by comparing the account balance vs. the credit line in the first example above. This has the disadvantage that one single transaction which ends in an inconsistent state (e.g. due to a programming error) can invalidate the whole database. In another approach therefore the consistency criteria are stored explicitly within the database as rules and consistency constraints. Using these the DBMS can then check on its own if the final state of a transaction is consistent. If not, the transaction will be aborted. This achieves more protection against inconsistencies but implementation - of the database but also of the error responses of transactions - becomes more difficult.

In the context of mathematical logic and more specifically, Boolean algebra, consistency is an important notion. A collection of statements is said to be consistent if the statements can all be true simultaneously. A simple way of determining if a (hopefully small) collection of statements is consistent or not is to use a truth table.

The concept of consistency is important in refutation strategy, a method of determining the validity of an argument. In this method, the conclusion to the proposed argument is negated, then all the statements are checked for consistency. If the argument and the negated conclusion are mutually inconsistent, then the original conclusion must be valid.

Con*sist"ence (?), Con*sist"en*cy (?), n. [Cf. F. consistance.]

1.

The condition of standing or adhering together, or being fixed in union, as the parts of a body; existence; firmness; coherence; solidity.

Water, being divided, maketh many circles, till it restore itself to the natural consistence. Bacon.

We are as water, weak, and of no consistence. Jer. Taylor.

The same form, substance, and consistency. T. Burned.

2.

A degree of firmness, density, or spissitude.

Let the expressed juices be boiled into the consistence of a sirup. Arbuthnot.

<-- p. 308 proofed -->

3.

That which stands together as a united whole; a combination.

The church of God, as meaning whole consistence of orders and members. Milton.

4.

Firmness of constitution or character; substantiality; durability; persistency.

His friendship is of a noble make and a lasting consistency. South.

5.

Agreement or harmony of all parts of a complex thing among themselves, or of the same thing with itself at different times; the harmony of conduct with profession; congruity; correspondence; as, the consistency of laws, regulations, or judicial decisions; consistency of opinions; consistency of conduct or of character.

That consistency of behavior whereby he inflexibly pursues those measures which appear the most just. Addison.

Consistency, thou art a jewel. Popular Saying.

 

© Webster 1913.

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