Thanks to @mosabou I got to read about Formal Concept Analysis. What a cool concept! Of the first things that I read was “A First Course in Formal Concept Analysis” (an introduction to the subject without the mathematics). While going through the examples, I kept thinking Where have I seen that before? Relational Databases, that’s where! And it seems that my intuition was correct: see the excellent “Gentle introduction to Relational Lattice” by Vadim Tropashko and the links from there.
[ I vaguely remember Yannis introducing the lattice concept in a database context in a course lecture a few years back, but have to admit of not looking much into it back then. ]
This is mostly a note for people who insist on thinking that theory is disconnected from practice. Especially the ones who write SQL code and insist on not realizing that they deal with sets (and set theory). Stop holding an umbrella and invest some time in your math.