Welcome back everybody.

First things first, for those of you who actually have an eye on the Stuttgart forum, there

was some contention with one of the questions in the quiz on Tuesday.

The one that asked about the consequences of rationality, where one of the answer options

was exploration and autonomy.

The problem here is what exactly do we mean by consequences?

And the counter argument that I would give why that is not a consequence is that we have

lots of rational agents that do not need to explore in any way and that do not need to

be autonomous in any way.

The example that I gave on Stuttgart is if we just implement an agent that plays tic-tac-toe,

then we can literally hard code everything.

We don't need any kind of exploration and we don't need any kind of autonomy and we

would still consider it to be perfectly rational according to the definition of rationality.

Where the definition is an agent is considered rational if it maximizes the expected performance.

The trouble with that is that what I did not realize is that one of the slides literally

said consequences of rationality, colon, autonomy, comma, exploration.

So that is a problem.

Long story short, we will just remove that question from the quiz entirely.

Everyone who tried to do the quiz will get full points on that particular question just

so that we don't unfairly punish people.

I fixed the slide that said that to make it sure that those are possible consequences

of autonomy.

If the example with the tic-tac-toe agent does not entirely convince you, all of AI1

would be another counter example.

In AI1, we considered things like constraint satisfaction, first order theorem proving,

that do those kinds of things, we would consider to be perfectly rational, but none of them

involve any kind of autonomy or exploration.

On that note, those of you who had trouble with the quiz last time because there were

weird client-side issues, I forwarded that to our front-end engineer.

I would hope that that gets fixed by next week.

One possible cause of that might be, I mentioned I think in the first lecture or something,

that the content on Alea currently is horribly outdated anyway because we have a few bugs

in the back-end.

We have by now managed to not fix, but at least circumvent the bugs sufficiently that

at some point this afternoon, three distinct people will press three distinct buttons and

then all of the content will get updated.

I would hope that if we can't find any other bug in the quiz system, that that would already

solve the problem anyway.

At some point this afternoon, all of the content on Alea will be up to date and ideally then

the next Tuesday quiz will run without a hitch, I would hope as much at least.

We've basically finished with all of the pure math stuff with respect to probabilities,

so let me just give a quick summary of what you should know in the long run.

We have probability spaces as the general setup.

On the basis of probability spaces, we can define random variables.

Random variables model the kinds of probabilities that we are actually interested in, which

we can define as just functions on the probability space.

Given random variables and their domains, we can basically define a language based on

the syntax of propositional logic that allows us to talk about the probabilities of various

compound statements based on the random variables that we have and assignments to those random variables.

Events, everything that we can assign a probability to in the first place.