Cognitive consistency means that people strive to maintain consistency between their cognitions.
If one of a pair of cognitions follows from the other, so the two are consonant.
If one follows from the converse of the other, then they are dissonant.
If neither follows from the other or from its converse, then they are irrelevant to each other (Cognitive consistency theory, Leon Festinger).
The most prominent are Congruity theory, Balance theory, Equity theory, Cognitive dissonance theory (118).