Consistency

In classical deductive 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 and only 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 traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. The syntactic definition states that a theory is consistent if and only if there is no formula P such that both P and its negation are provable from the axioms of the theory under its associated deductive system.

If these semantic and syntactic definitions are equivalent for any theory formulated using a particular deductive logic, the logic is called complete. The completeness of the sentential calculus was proved by Paul Bernays in 1918 and Emil Post in 1921, while the completeness of predicate calculus was proved by Kurt Gödel in 1930, and consistency proofs for arithmetics restricted with respect to the induction axiom schema were proved by Ackermann (1924), von Neumann (1927) and Herbrand (1931). Stronger logics, such as second-order logic, are not complete.

Cognitive dimensions of notations

Cognitive dimensions or cognitive dimensions of notations are design principles for notations, user interfaces and programming languages, described by researchers Thomas R.G. Green and Marian Petre. The dimensions can be used to evaluate the usability of an existing information artifact, or as heuristics to guide the design of a new one.

Cognitive dimensions are designed to provide a lightweight approach to analysis of a design quality, rather than an in-depth, detailed description. They provide a common vocabulary for discussing many factors in notation, UI or programming language design. Also, cognitive dimensions help in exploring the space of possible designs through design maneuvers, changes intended to improve the design along one dimension.

List of the cognitive dimensions

Thomas Green originally defined 14 cognitive dimensions:

Consistency (database systems)

Consistency in database systems refers to the requirement that any given database transaction must change affected data only in allowed ways. Any data written to the database must be valid according to all defined rules, including constraints, cascades, triggers, and any combination thereof. This does not guarantee correctness of the transaction in all ways the application programmer might have wanted (that is the responsibility of application-level code) but merely that any programming errors cannot result in the violation of any defined rules.

As an ACID guarantee

Consistency is one of the four guarantees that define ACID transactions; however, significant ambiguity exists about the nature of this guarantee. It is defined variously as: