OK, welcome back to AI 2.

Oh, let's see.

That's better, probably.

We were talking about probabilities yesterday,

starting to build up the machinery that

lets us talk about reasoning under uncertainty

and acting under uncertainty, which

is exactly what we want our agents to be

able to do this semester.

And before we go into the maths, which is rather simple,

and you've probably heard it before,

I would like to make sure that we're

on the same page in what we're really doing here.

And the upshot of everything I tried to say yesterday

was that we are using probabilities

to model incomplete knowledge.

So it's not that the world is uncertain or something

like this as an object per se, but it's we who are,

or the agents who are uncertain about the actual state

of the world.

We're actually trying to model our own limited or the agents'

limited knowledge.

The world itself only has one state.

OK, we just have no idea what that is,

or we have a limited idea of what that might be.

And when we're looking at things like likelihoods

or probabilities, we're really interested in,

of all the possible worlds, how many are in that state

that I'm using to model as a possible world?

In all the possible worlds out there, only one of them

is the actual world.

How many are consistent with cavity equals true?

And there's a slight question there,

which I would like you to think about,

is that the actual possibilities in the world

might actually be quite endless.

We're only caring about a couple of parameters there.

We're only distinguishing certain worlds.

When I'm wondering about, and I only

have limited information about, the weather outside,

it's probably sunny because it was five minutes ago,

but who knows?

Then, of course, the world, there

are a lot of possibilities.

And of course, the world, there are lots of possible world

states in ways that are uninteresting to me.

For instance, exactly how many Chinese people there are.

Not interested in that.

In the moment, I have a rough number there,

but exactly how many there are is completely uninteresting