Re: lattices, powersets, bitstrings, and efficient OLAP

> I said "almost union" and "almost intersection".  The meet and join
> operations are not quite intersection and union, because the
> intersection and union operations may produce a powerset element that
> doesn't correspond to an element of L; in this example, intersecting
> {0, 2} and {0, 3} gives you {0}, not {} as it should.  I assert
> without even the handwaviest sketch of a proof that you can find a
> unique largest subset or smallest superset in any such case, or at
> least that you can choose your representation such that this is  
> true...

Priestley's "Ordered Sets and Complete Lattices" covers this  
particular example*, and in fact makes the grand tour, with many  
cheerful facts about the square of galois connections, closure  
(hint!) operators, closure systems, and binary relation contexts, all  
of which (along with complete lattices themselves) form a strongly  
connected component.

-Dave

* and includes the somewhat ambiguous phrase that "topless models are  
often to be preferred", which probably changes its denotation between  
the banks of la Plata and those of the Thames.
(incidentally, this subset construction is the reason why calculus is  
so unreasonably effective for total orders, and range query hacks  
abound)

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