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Okay, so

So last time we talked about kind of MMT theory, and this idea, two ideas really that I want to come back to

Is that we can use all of these arrows, which are inclusions and more, including a view which will be will become important today.

As a way of modular rising, whatever situation we want to describe. Remember, we want to use this eventually to have elaborate

Ways of describing kind of a standard situations.

The gangster and the red sports car, you need some stuff that is in the same, that's always there. We always need a gangster, we always need a sports car and so on. But we also have different assumptions.

And the

The assumption is that we kind of have stuff that's always there, which can be extended in various ways.

That's one of the things we're going to use this for. And the other one is, which we looked at with this diagram is

We have this way of talking about a situation

And about the base level, domain level, we have the logics like first of all logic or whatever funny logic we're going to dream up one level up.

Whereas these are essentially also exactly the same kind of theories.

And we need all the material we introduce in the logic like and or by all of those kinds of things.

Down here. So we basically include a little bit more the meta relation is a little bit more.

But think of it as an inclusion.

And you can already see what's happening to say here where you have, say, the equals as something that comes from the logic.

And in this situation, I want to start something completely new.

And I want to show you what is called the method of fragments that was introduced

More than 50 years ago by now by a philosopher called Richard Montague.

And he had this idea

That

Given that language, something like English is kind of an amorphous blob that is also kind of

fragmented as a at the edges.

Right. What is English is kind of a fuzzy.

And he wanted to do logic. He wanted to do language scientifically.

And so he had this idea that instead of studying all of English.

He would say, well, let's take out

A

phenomenon.

So here.

Box it in with what we call a fragment.

This is just a sub language of English that is captured by say, a context free grammar.

But

Contains all the data that we're interested in.

Peter love Mary and John chase the gangsta in the red sports car or something like this.

And

Have a fragment given by by a grammar and we try to fully

Look at the phenomena in in the data.

And

Then when you've done that, and it makes the right predictions, you start extending

This fragment one

Fragment two. And the idea is that you kind of

English with lots of little fragments and ideally you can kind of collect them up

A joint story of large parts of things.