from Geometry and Meaning, Dominic Widdows (cont'd):

“There are many important and interesting examples. In logic, the meet of A and B is the conjunction A AND B, because it is the most general concept that is implied by both of A and B. The join of A and B is the disjunction A OR B, because it is the most specific concept that implies both A and B...

Set theory and vector spaces are also examples of lattices, and we will see that they are the underlying lattices of different brands of logic. In set theory, the join of two sets is their set union, and the meet of two sets is their set intersection. In a vector space, the join of two subspaces is the smallest subspace that contains both of them, and the meet is the largest subspace contained in both of them. The meet is the same as with set theory - it is just their intersection. The join is however more general than in set theory, because the join of two lines is not a cross-shape (the union of two lines) but the plane containing them both (the cross-shape plus all the lines joining any two points on the cross-shape)...