that we remind of the additive constant and zero and one are

multiplicative constants.

The top and bottom are the greatest elements.

The top is the greatest element, the bottom is the smallest

element.

And zero and one are neutral elements, respectively,

on the right and on the left.

Is this clear or not quite?

And the other question was whether you

are allowed to use the structural alums absorbing

the classical logic part we were using in calculus,

which absorbs structural alums.

I don't remember myself having to use structural alums

actually, but if you do need, yes, then we

proved for that particular version of calculus

that it is structural alums absorbing.

So yes, in case you need it, which I can do anything you

would, just quote a corresponding theorem

from the lecture.

So I hope this answers the question.

Are there any other questions?

How important were the additive ones?

Yes, so top was like a neutral element.

Actually, you see those guys again in action today

apart from zero, but in a very different system,

playing the same role still.

So top was neutral element for, or like unique element

for lattice mean for this additive conjunction.

Bottom was neutral element for lattice

joins for additive disjunction.

And one was adder.

So I noticed something.

I thought that this was done already.

So I thought that was a little bit more interesting.

OK.

So the third part, let's assume.

Black mine national.

No, no, no.

It's a little look.

No, no, no.

Question.

Yes.

Are you going to put this online or you will put this later?

I will put this online, but every now and then you may be tempted to actually make some notes.

So I will, if I go too quickly, just warn me.

I will try to be reasonable speed.

But this will be just introductory part.

I realized during the linear logic introduction, then doing this kind of things on blackboard,

it really leads to me having to talk a lot and write a lot and you have to write longish quotes or bits of history, which is a song.

So the way I'm going to play today, I'm going to give just the introduction on the slides.