And now for my favorite favorite topic, formal logic. Have you seen this wumpus world before?

I'm not sure usually that comes up all the time. This whole idea of a wumpus world, there

is even a Wikipedia article on it. It's basically, it's a non-existent quote unquote video game

which is just the standard situation that's used in almost all of the textbook that have

anything to do with artificial intelligence. So, and of course correspondingly there is

like hundreds of variants of this problem depending on the specific situation. In this

case it looks the following way. We have our agent here in our starting situation and I

hope all of you remember the P's model that we talked about like weeks ago. P's in the

sense of performance measure, environment, actuators, sensors. So we have our agent.

So let's consider what P, E, A, and S in this instance are. This is our environment. We

have a four times four grid of discrete cells. In some cells there is this monster like thingy

called a wumpus and that wumpus apparently doesn't have a shower so it stinks and it's

noticeable that if a wumpus is nearby because the fields surrounding the wumpus have a stench

which we can perceive or which our agent can perceive. There is random pits all over the

board and we can notice that we are close to a pit because in the cells adjacent to

a pit we can perceive a breeze and the goal is to get at a pile of gold which is somewhere

which glitters but the percept that it glitters we can only perceive if we are standing in

the actual cell where the gold lies. So this is our environment here. Our percepts or our

sensors allow us to sense a stench if we are next to a wumpus, a breeze if we are next

to a pit or a glitter if we are standing on the pile of gold. Our actuators is we have

three different actions. We can either turn right by 90 degrees, we can turn left by 90

degrees, we can go forward one step and exactly once we are allowed to shoot an arrow in the

direction we are facing. So these are the actions and our performance measure ultimately

is our goal, namely getting to the gold and getting outside of the cave without being

eaten by the wumpus which happens if we enter a field where the wumpus is and it is not

dead in case we shot it with an arrow. So getting to the gold and leaving and not dying

which is either by being eaten by the wumpus or falling into a pit that also kills us.

Oh right I forgot one percept, if we bump into a wall we will notice that we bumped

into a wall which is nice. So at least we are not completely stupid. Okay so let's

play a small game in the setting. We are starting in the lower left corner and we perceive nothing.

Okay let's maybe decide to step one step to the right so we are in the fields 2, 1 and

we perceive apparently a breeze. From perceiving a breeze we can infer that in one of the adjacent

cells there has to be a pit. It can't be the field that we started on because we started

there. So either in 2, 2 or in 3, 1 there will have to be a pit. So what do we do? We

can't exactly go to the right, we also can't exactly go up so all we are left to do is

basically go left and up and that happens here. And now we perceive a stench. So the

claim is that by perceiving the stench here we know that the wumpus has to be in field

1, 3 and not for example in field 2, 2. How would we know that? Anyone want to argue?

Yeah. Sorry. In the field 2, 1 there is no stench so we know there is no wumpus in 2,

2 then? Or there can't be one? Right, exactly. Which means the wumpus has to be in either

1, 1 where we already know it isn't. We know it's not in 2, 2 exactly as you just said

because we didn't notice a stench in 2, 1 so it has to be in 1, 3. Which is exactly

what it says here. The claim is also, I mentioned that earlier, that now, no I didn't, we now

know by not perceiving a breeze here that there also has to be a pit in 3, 1 and not

as we in the previous step possibly might have thought it might be in 2, 2 as well.

I've already given away the solution well because we don't notice a breeze here. So

it's easy for us to do this kind of inference, this kind of logical arguing so the wumpus

has to be here because we didn't blah, blah, blah, blah, blah. So the basic idea is how

can we build an agent that is able to exploit the same kind of reasoning that we just did.

So the idea is we use a stateful reflex agent that can actually reason about the world we're