So I want to make a Wompous example.

Okay, remember Wompous?

There were different properties and so on and you looked at how you would express

the knowledge about the Wompous world in propositional logic and it had a lot to

do with propositional variables W2, 3 and so on.

And so if we are, say we have an agent, the agent is in this situation, it has explored three cells here and the agent is here,

it stinks, we know it's okay because we're still alive, these two also are here,

there's a breeze here and what was the V again?

I don't know, doesn't matter, it's just a reminder.

Okay, so you've seen this before right?

Has Dennis done this?

Good, so I'll remind you because it was before Christmas but I'll assume you've seen it before.

So we will give ourselves propositional variables of the form Sij which are true if it stinks in cell ij.

Okay, so in this cell 1,1 we have the knowledge that not S1,1 it is because we don't, we haven't, it's not stinking here.

Here we have S1,2 not S2,1 and so on.

This is kind of the way we express things and Wij is that we use that for the wampus is in ij

and we know that for these three cells we've visited that the wampus isn't here because we haven't been eaten yet.

Assuming, we're assuming that our perception system can actually find out.

Okay, so we also have some kind of knowledge about cells.

For instance, we know that if it doesn't stink in 1,1 we know the wampus isn't in 1,1, it's also not in 1,2 and it's not in 2,1.

You think about it, that's exactly what the wampus knowledge is about here, right?

If it stinks, then it's here or there.

If it doesn't stink, it isn't here or there.

And we have knowledge like that for R2 and R3 as well and then for S2,1 and S1,1,1,2 as well.

And we have knowledge about if it stinks in 1,2, then so on.

We actually have much, much more rule knowledge, right?

We have for every, we have two rules, four, we have stink positive, stink negative, wampus positive, a breeze and so on.

But for the example I want to make, and we have all that knowledge about all 16 cells here, so there's a lot of formula.

I'm going to restrict myself to those knowledge parts that we actually need.

So that's taking an unfair advantage, but it's good because we actually can fit everything on the slide.

So what the agent is interested in, it plans to go to the cell 1,3 and it's interested to know whether the wampus is there.

Okay, so it might be interested saying given this knowledge, in reality we don't know what we need yet, so it would really not be from R1 to R4, but what is it 16 times.

So we would have something like R66 or something like this.

And then we have to, we are interested to show either the wampus is in the cell I want to go or isn't in the cell I want to go.

And you might want to also look for gold and so on, but this should be enough now, right?

So that is something that is quite easy, right?

We can transform this, our knowledge about the world into Claus normal form, which is really, really, really, really simple.

Here they are, they're all literals, so I can just stick the true and false up depending on whether we have a knot in front of it.

That gives me these here, and then I transform all, I transform our rules into clauses.

There are a bunch of those, right?

And then I negate the formula I'm really interested.

If you think in prolog terms, this means is there a wampus in 1, 3?

And we're assuming there is so that we know where to stay away from.

So we can do a proof.

I can resolve, I can get the new clause s12 false, w true 2 2, w12 true by taking the parents, this one and that one,

and we can see that there is a complementary literal here, which gives me that.

And in red, I've tried to verbalize the reasoning so that you understand what's really going on.

So it's basically, if we're assuming the wampus is not in 1, 3, then either there's no stench in 1, 2,

or the wampus is in some other neighbor cell of 1, 2, and so on.

So what we can do once, we can do twice, so we take the s12 true with that complementary literal.