Okay. Welcome back. The quiz is over. So we note AI2 quizzes are a thing. Did everything

work? Good. You can see the quiz was a bit too long. Response rates started dropping

after 23 and communications started picking up at about the same time, which tells me

it was a bit too long and even the last 20 stragglers actually almost all made it to

the finish line. That's okay. Even the communication is okay because after all what I want with

the quizzes is that you start thinking about things and start learning. That's what they're

for. I've been preaching you to communicate. So that's okay as long as you don't disturb

the others. Okay. So are there any questions about admin and all of those kind of things?

If there are any... Yes? No. Actually, I must confess I don't know. Florian does the homeworks

and stuff. Good. Well done. Homeworks are for you. So by all means, do homeworks. Okay. Any more

questions? If that's not the case, then we start looking at probabilistic reasoning again.

So remember, we're doing the hard stuff this semester. So not like last semester where

fully observable deterministic environments where we could observe in which state the

world is and we could predict with certainty what my actions will do and as a consequence,

our model-based agents were able to keep track of the world with keeping exactly one world

state in mind, we're now graduating to uncertain worlds or uncertain models where we basically

have a set of possible worlds, either because we can't see or observe all the world because

we don't know which state we're actually in or because our actions are uncertain. We don't

know what the outcome of the action is. So we have to do better. Instead of... And the

consequence of this was that instead of the world states being single worlds, we had lots

of possible worlds and since not all worlds are created equal, we basically have graduated

to probability distributions over possible worlds. And that's kind of what we want to

do. And we've been modelling this and the important thing to realise, and I would like to stress

that again, is that it's not the world that's uncertain. We as the agent are uncertain about

the state of the world. Big difference. Okay? So there's nothing undetermined about the world,

it's just our knowledge is partial. Okay? And therefore we have to take into account all the

possibilities and weigh them against each other. So did we do that? Well, the main tool was

probability spaces which gives us a mathematical model. The way we're doing this is what we've

kind of done also in logic-based agents. We have descriptions of the world. The language we're

describing the world in is one that has conjunctions, disjunctions, implications and negations,

which means we have a propositional logic essentially. And the propositional variables

in this world are the outcomes of the... The outcomes of the random variables we have defined.

Just like in propositional logic, we define a couple of Boolean variables. Right? The Boolean

variable, it is sunny outside, which may be true or false. In this setting, we have random

variables. They serve exactly the same purpose. Only that it's not just true or false, it's a

much richer structure, namely a probability distribution. And then we can just like in

propositional logic, we combined propositions into bigger propositions and so on. Here we're

combining events into bigger and bigger propositions. And we can compute with them the rules are not the

logical rules. So you're not finding De Morgan or something like this. The rules for computing

here are the laws of probability. In other words, the Kolmogorov axioms. So that's one of the

things we did. And it turns out that this was not enough. We need some way of taking observations

into account. That's what our agents do. They're continual online procedures that keep on observing

the world. They go outside, they see, aha, it's sunny, or the dentist agent kind of takes out

this iron hook and starts scraping your teeth. All of those kind of things. You get more and more

evidence and as you collect evidence, your model of the world, the probability of certain things,

of certain random variable changes. Right? The dentist is sure that you have a cavity if this

hook actually catches. That's why the dentist has the hook. And that's really what our agents have to do.

They continually have perceptions and collect evidence which actually improves the world models.

So, and the idea is with probabilistic reasoning, we want to not only measure probabilities but also

reason with probabilities. If we have a formula about the state of the world, we want to make new