Let me do something else instead.

So we have given ourselves a method and indeed a calculus

for dealing with world models and computing new probabilities

from old probabilities.

Now the question, of course, is does that help any?

And you remember in the beginning,

we had given ourselves this problem of we have the Wumpus

world partially explored where we know we've visited three

cells about which we have full information.

We are assuming reliable sensors at the moment.

And we have two gray cells which we

know partial information about because we have breezes in both

one, two, and two, one.

And we know nothing about the darker gray ones.

Now the question is, where should the agent move next?

Typical agent situation.

You have to decide on an action.

In this case, we know that all the gray ones

are unsafe because there's a breeze in the neighboring one

which says any of those could have a pit.

OK?

And last time we talked about that,

there was a consensus, don't go into the middle.

Essentially, by gut feeling, I have the feeling.

Right?

Gut feeling is great.

But what we really want, once it gets close,

we really want to have the quantitative way of telling.

Even if to your gut it looks quite similar,

you really want to know and have the real margin here.

So let's see whether our machinery works on this.

And as you probably predicted, will,

which is why I have the example here, of course.

But how does it work?

So what are we going to do?

We have a language for talking about probabilities

and its propositional logic.

So we have to kind of instantiate that language.

And then we do that with the usual propositional variables

we did last semester.

So we have a variable Pij, which just basically says,

there's a pit in square i and j.

And Bij, which is there's a breeze at square i and j.

And we're not talking about wumpus and glitter

and stench and all of those kind of things.

We're only concentrating on the pits here to keep things simple.

And of course, we want to see the full joint probability

distribution.

We know that if there is a pit at 1, 2 up to a pit to this,

then by the product rule, which is what we're really interested