Okay, sorry about all the technical challenges. So just to recap today, the plan is to do

three things. We'll extend the grammar for prep in four a little bit, just to remind

ourselves of what we did before Christmas. And in particular, I want you to add the the

determiner so that we can use this description operator. Then we finish the tableau machine.

That's really little. We almost were done a few weeks ago, just the witnesses were not

introduced. And number three, we'll start a new fragment. We won't do any AP there,

I think just the grammar and the semantics construction for event semantics.

Good. And as just a very easy warm up,

my proposal is that we do things like if John runs, then every dog runs. I think we don't have

more verbs than that right now, but that we support this kind of sentence in the

sentence. In the grammar and in the semantics instruction, just to as a warm up.

Okay, so this was our grammar. It's very short, though we have lots of categories.

And yeah, I think this will hand over to you.

Yes, so this is the condition, right? John runs, yes. We already have something that's

corresponding to the sentence category, so we can just reuse that.

Do we have to do some kind of check if the statement John runs is true or false?

Not in the grammar at this point. Here we just want to be able to pass it.

The checking will happen later in the tableau machine. It will be implication, yes.

And we're not even there yet. At this point, we don't even think about the meaning.

At this point, it's mostly about the grammars that we can understand the structure of the sentence.

Yes.

We could just do the pen and the complete grammar.

Maybe we'll do it pretty much like a normal sentence, but with a conjunction.

We have conjunction? No, we don't even have that.

The sentence and the sentence.

So you want to do if then, sentence, sentence, to sentence. Yeah, so in this case, John runs

is the sentence. Every dog runs is a sentence. And if we combine it, we get a new sentence.

Does the sentence have a missing thing?

Oh, yes, it has missing things.

Yeah. Okay. And then we need to have it in the concrete syntax to say what

completely is in English. So if then, yeah. And over someone else or?

Okay. Yeah.

Yes.

Good.

And then you get sentences.

That we can even use this rule recursively, which I didn't think about beforehand.

So we say if some dog runs, then John runs, except that some dog runs as a sentence.

So we could also have a if sentence as a condition, which is probably not what we want.

I mean, in a way, this is going to over-generate, but we'll be able to pass on that point.

So maybe it was a good idea actually to have a separate category for conditions.

And so on. But let's just leave it like this for now. It's just to get started with the whole thing.

Okay. So you said already that should correspond to implication somehow.

So if you remember, we write on our logic always here, and then we need to

do the semantics construction where we say for every rule, this is going to make sense.

And so we need a new one. Right. So we had this if then, if then

something where we somehow say it should correspond to implication.

We can, maybe this is a nice example. We can, I think just write here implication.

No, it's not called implication. It's called impel.

And now if some doc runs, then John runs.

So this is exactly what we wanted. Right.