+1: Lattice as abelian group with inner product.
-1: Lattice as poset with meet and join

(of course I'm biased by number theory, though I admit that I have
heard of the second kind of lattice.  ;-)

That being said, I'm glad people are working on the poset kind of
lattice: I'd wanted to do so for a while, but too many other projects
intervened.  I'll try to chip in a bit.

David

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