Okay.

Okay, so we're back in theory now.

Remember we, in theory, introduced a slightly castrated fragment one.

Fragment one is kind of maximally boring.

It's actually so boring we didn't do anything with it.

The only thing I used it for was to explain to you this kind of a

of a setup

where

we start out from the natural language utterance.

We make out of it with the help of a concrete, no, an abstract, also not true, a concrete grammar that knows about linearizations.

We make an abstract syntax tree, which really is legitimized by an abstract grammar.

So that's kind of our GF side of things.

And that was dead easy.

Especially since we used English and in English only in the past, so nothing happened.

So, we already know more of GF than we needed in the first fragment.

Then

And really what we did was we crossed the border into MMT land.

So this is GF.

We basically

We used the first of isomorphic transform of the concrete grammar.

And then we did a view.

The view really, what that did was translate

abstract syntax trees, which were the

terms that are the abstract syntax trees are really constructors of grammatical categories.

So grammatical structures.

We basically, every one of these constructors was transferred into an MMT logic plus situation

Which gave us

A logical formula.

Okay.

And then we could really do things like prove them or not prove them.

And the thing I want to show you kind of in a backwards manner here.

I'm not actually very far with writing this up.

But if we want to test our language model,

We have to run certain tests that we have in our repertoire.

We have to run certain tests that we have in our repertoire.

And even though this is not a fragment one

sentence, if we basically look at this sentence, John chased the gangster in the red sports car.

We had to claimed that there are three readings.

And we actually use the logic we translated in which I follow PLMQ.

We have things like we started out with propositional logic, and then we, and it depends on how you think about it.

We can either have fancily named propositional variables, variables of the form of John, Mary, which is really, you can think of a propositional variable name.

Or you can think of those as first order terms.

And the language really doesn't allow any quantifiers yet.

So it's isomorphic or the same.

If you are more in the isomorphic camp.

There's a proof here, if you want it.

Now, we had three readings for this sentence.

And we can characterize them in situation theories.

The first theory has basically two axioms.

One is about chasing.