Smartphone connected.

So this is the real question.

Oh wait, I have to share my screen.

Otherwise, zoomies don't see anything.

Okay, that's better.

So zoomies, you may have noticed that the quiz was somewhat easy in question five.

This is what it should have been.

And we'll repair that and have the quizzes out there for you.

Just a general thing about the quizzes.

I think they're probably one thing you want to really look at and try and redo when you are studying for the exam.

Which is why we'll also have a quiz kind of on the stuff we're doing today,

even though I'm not sure how much use it has.

But I want to have a quiz covering the whole content so that you have things to learn.

Because it's also kind of a...

They're also trying to test your understanding.

If any of you can think of good quiz questions, I would be very interested in developing them further and spreading them over.

Developing quiz questions is extremely good for learning.

Right, good.

So, but that's not what we are here for today.

Let's kind of go back to this idea.

To the ideas we've been thinking about last week.

The first idea is extremely simple.

If you have multiple modalities, you just give yourself multiple accessibility relations and multiple boxes.

As a very nice little coincidence of the alphabet,

is that the box opens very nice into opening and closing square brackets.

And the diamond opens very nicely into angle brackets.

Okay, so there's almost nothing to multimodal logic,

except that you would probably want to have multicolored chalk if you want to draw the cryptic models.

Because you have multiple accessibility relations.

And then you can have a red one and a green one.

And I only have white.

Oh, interesting, grey and blue.

Right.

One of the nice applications of this is kind of epistemic logic,

where we have people know and believe in all of those kind of things.

Where you have people kind of for every person, you have a accessibility relation.

You played with that in the quiz.

And another idea here that we've been starting to look at is program logic.

Logic for imperative programs, where you basically for every possible program have a modality.

So lots and lots and lots, countably infinitely many modalities.

Okay.

And you have kind of whereas the epistemic, not the ontage.

Whereas belief, belief logic is mostly about kind of individuals that are given by name.

Here we have kind of modality constructors, program constructors.

And the idea here is the idea of the semantics is going to be that the semantics is that states.

The states really corresponding to the values of variables at a given time.

Okay.

That's what we know in imperative programming.

You have to kind of keep track of which variable has what content.

Sometimes with pen and paper, sometimes with the help of a debugger.