Okay, so let's restart.

We talked about planning all in all yesterday.

No, Tuesday.

The idea in planning is that now that we have structured world representations,

we have to do something about time and change.

Because it didn't matter when we had atomic states, because we just had so many states

all in all.

We could just basically put them all into the states, make more states for every time

point.

Not a problem, at least conceptually.

Here we have a representation language for the world, a structured one.

Then we have to take care about time.

Actually, we would have had to take care about time in, say, CSP as well.

But we didn't really, because we were mostly talking about configuration problems.

Nothing changes there.

We're just configuring things.

Time doesn't play a role.

But if we were to do scheduling or configurations that can change over time, we would have had

to have a time treatment.

We just didn't go there.

So I'm planning.

We take time seriously.

And we've basically discovered that doing it just with logic isn't very helpful.

If you just add a time attribute argument to everything, then things blow up and the

frame axioms additionally make life hard.

There are logic-based approaches that deal with fluence in a more principled way.

But we're not going into that.

So we've also talked as one of the algorithms about partial order planning.

The idea in partial order planning is that instead of searching for a linear plan, which

you can think of as being overcommitted because it actually linearizes or schedules actions

that are independent, whether you first go to the supermarket and then to the hardware

store and then home or the other way around, doesn't matter.

Of course, it does matter that you first go to the supermarket and then eventually go

home.

If you go home in between, that's not going to be a good plan.

So the idea is that we build these partial orderings, partial orderings between steps,

we call them, actions actually, particular actions.

And we take care of which of the preconditions of the actions are actually achieved, fulfilled.

And that gives us a backbone of a plan, say, when we're in this kind of a state.

We know these are the things we have to eventually do.

But some of these steps actually threaten, I think one more yes, threaten the precondition

achievement of other steps.

If we only have kind of the things like the causal links that tell us first we have to

do this and then we have to do that.

So we know we have to go to the supermarket at some point.

But if we, and nothing keeps me from doing that, put that after the go to the hardware

store, then we're no longer at the hardware store.

So we have to take care that this never happens, which is why we have these temporal links

that say, well, this has to be before that.

We have to buy a drill here before we go to the supermarket.