Well!

Okay.

Well.

Okay.

I'm recording.

I need to share the screen.

Okay.

So, on Tuesday, we looked a little bit more at the

We looked a little bit more at

the K-Roll helps.

We looked a little bit more at model logic and implemented it in MMT.

So that, in a way, we believe it exists.

And also looked at the translations once more.

And the next step was we extended it to what is called multi-modal logic, where essentially

we give ourselves an index set. And per index, we give ourselves a modality.

Nice thing about boxes is you can kind of open them up in the middle and put the index in there.

For this, I've been assuming that we take just natural numbers.

And that takes care of the case where we have countably many of these modalities.

And for every modality, which we can then kind of mix, we give ourselves an accessibility.

What you should notice and realize is that each of these accessibility relations can be different.

We might have a reflexive one for the transitive one that is reflexive for the other and so on.

And we're going to use those for things like epistemic logic, where we believe

For the belief modality, we need an agent, or by the way, a group of agents that believe something.

And then for deontic logic, we kind of have very different predications on deontic logic.

That under this umbrella term of deontic logic, kind of specify what the deontic aspect you could say that is captured is.

And Tuesday I said that I'm, as a logician, slightly frustrated that you cannot find a good reference.

Deontic logic is S4 or something like this.

And if you think about it, given that deontic is ambiguous, just in this one example among these different facets,

We can see that in a way, all of those give rise to different accessibility relations.

So you would have to, for your, to specify what is actually meaning, you could say a deontic logic of desires might be an S4.

Whereas deontic logic of scheduling might be something completely different.

Okay, so probably, given the university rules, if you think about it, the university rules of desire are something that is a complex thing.

We have rules that are informal, formal rules.

We have the Bavarian law that breaks, the university law.

We have the federal law, the German law that breaks.

We have the Bavarian law, we have the EU law that can sometimes break, German law, and we have the universal declaration of human rights.

And then there's all the constitutions involved.

It's a rather complex object that we would have to model if we wanted to do it very, very correctly.

These modalities kind of give ourselves a huge engineering space, a modologic engineering space, where we can do stuff.

And people are doing that. There's a whole area called legal reasoning, where they worry about law and which one breaks which one, what are the exceptions among those guys.

So we're basically going to disregard all of that.

We're going to just say, oh, it's multimodal.

You can do whatever you want.

We're just going to do the bookkeeping and things like that.

And we've written the whole thing down in the NNP.

The context logic, no, epistemic logic, where the index set is really the agents present in the universal discourse is relatively well understood.

There's a lot of interactions with language here.

One of the phenomena one might want to study is that, for instance, you can have an aphora into belief spaces.

Tom believes that the Easter bunny is real.

He thinks that it has long ears.