And starting the sharing.

And I'm lucky I have slides.

Yes, it looks like I have slides.

Deeper.

Segment two.

Right, so.

Okay, so.

What we did last week was.

We talked about fragment two, which is essentially the same as fragment one, but with pronouns, pronouns like he, she, it, and we want to chase down the phenomenon of anaphora.

It's kind of a three-tick to develop an honest to goodness, semantic, pragmatic analysis module, which we didn't have in fragment one because it was very, very easy.

And so what we did was we introduced the pronouns, the pronoun. We have the idea to.

Translate into variables and PLNQ, so we extended PLNQ with variables and then.

We started looking into inference.

For this fragments and the central part here is there's two central parts.

One of the central parts is.

We're looking at model generation tableaus.

And I'll come to that in a minute that will have consequences.

We're going to look at if we want to do model generation tableaus, we have to introduce new variables that can actually do something with.

With these variables.

And we're using variables for two things. We're using it.

We're using variables for world knowledge.

If we have in our examples, humans don't bite dogs, then we have something of the form.

It is not the case that dog that bite X, Y.

If X is a dog and Y the other way around.

If X is a human and dog is a dog.

Yeah, and Y is a dog. There we go.

And we somehow have to from this general form of world knowledge that applies to everything, we have to kind of instantiate that to particular dogs like Fido.

Right, and John.

But we want to derive from this X doesn't bite Y.

We want to derive that Peter doesn't bite Fido.

And we do this with this rule here.

Oh yeah, there we go. If we have some kind of information.

Like the one that X doesn't bite Y, then we can instantiate all the variables by any individual we happen to know.

And in this case, X goes to Peter and John and Y goes Fido or the other way around.

Okay, so that's the mechanism. We have a new mechanism which is instantiating with variable the variables as we see fit.

And the other one is that if we have a if we have an input sentence, we're going to mark those by putting them into a box.

We could have done anything else, but this is the only thing I came up with.

Which is basically if we know if we have an input sentence, a, then we're going to have to deal with the input sentence having barriers.

Right, variables standing for pronouns, if they come from the translation.

So we have to do something with pronouns. So we have to instantiate the variables as well.

But instead of being free to instantiate them, we're going to have to instantiate them in all possible combinations.

Because that's what at least in the beginning these anafra do.

They couldn't be resolved to anything we know about.

Okay, so we give ourselves the thing we have to keep in mind here is on the one hand, this that H here, which is the.

The set H here, which is the.

Of our universe, which is the individuals we know.

I'm not I'm using here PLNQ with variables, but no functions, no function symbols.

So we don't have the father of Peter lying around. We only have Peter around and maybe John who happens to be the father.

So whenever we want to do something, we're going to do these relations instead of functions.

The reason being that I would like to keep this avant universe finite.