In formal concept analysis (FCA) implications relate sets of properties (or, synonymously, of attributes).
The knowledge acquisition method called attribute exploration uses implications.
[2] A set C of attributes is a concept intent if and only if C respects all valid implications.
The system of all valid implications of a formal context is closed under the natural inference.
This basis consists of all implications of the form P→P"\P, where P is a pseudo-intent, i.e., a pseudo-closed set in the closure system of intents.