Thank you.

So Zoomies, can you see the slides and can you see part of the blackboard?

Hello?

Yes.

Thank you.

Okay, so let's start with, are there any questions so far?

We're still kind of in the phase of setting up the whole thing and we've briefly looked at the general idea, namely

we have natural language here and think English, think Chinese, whatever.

The idea of this method of fragments is that we make language at least partially into formal languages,

which means we know exactly what's in the, what we call a fragment.

We can describe it by using a grammar, standard formal languages technology, and we take the fragment only.

We're not worried about what happens as well in language.

We're worried what happens in our fragments and that we want to translate into logic.

Now, logic is something that has a syntax and semantics, but very importantly, it has the entailment relations.

It basically says all models or all situations that make A true also make B true, which means we can use it,

module a little bit of bridging and so on, to make predictions about truth conditions.

Remember in the truth conditions, that was our methodology, truth conditions, we kind of dream up little situations in which a sentence becomes true or false.

In the gangster example, we dreamt up a case where there's a huge sports car or a sports car where John is driving or those kinds of things.

And in those situations which we write down in logic, we can test for entailment.

And that's really the analog on to differential equations, which make predictions and physics.

The entailment that logic gives up.

I don't know why only logic gives us, allows us modeling here.

The only logic gives us is only partially true. We could add to our thinking.

Is it true that whenever there's been that, and it would say yes or no?

But to me, it feels unsatisfactory. I'd take logic any day, even if it's tedious to write down the whole thing.

The coverage isn't great and all of those kind of things.

But still, this is one way of doing it. There may be others.

By the way, linguistics does the entailment by asking native speakers.

They have armies of students who get asked questions like, if Peter loves Mary, in this and that situation, is Mary happy?

And that gives them the data. We make predictions and of course we test it against our intuitions of language.

So that's really what we're doing.

And the fond hope is that we can kind of parcel out language with different things.

And for each of them have a translation. We might end up in a different logic though.

There's no guarantee that the logic we picked first will actually be strong enough to do everything we need.

And so it's still an experimental modeling science, what we're doing here.

But physics also doesn't know whether ordinary differential equations are enough to do all of physics or whether you have to invent the string theory or something like that, which mathematicians don't even know this path.

So that's kind of the same thing.

Physicists invent math all the time.

Semanticists invent logic all the time.

And we're going to do exactly the same. So the first part of the course will be this.

We start with fragment one, which is embarrassingly simple, which is just basically to show you how it's done.

Then I'll come into class and say, look, I found new data.

How about this?

And then we'll talk about what's going on and so on.

And then we'll think about how do I do it in a grammar and then we'll think about how to translate it into logic and what is the logic in the first place.

And then I get to teach you a new logic, which is nice.

So on and in the end, we probably won't have a situation that's as nice as this, but some of the more pertinent examples I gave you in the example, in the beginning, we will be able to cover.

In particular, this will give you a guide to lots of the semantics literature, which really does that.

But first thing they say is, look, there's this interesting phenomenon.

We'll take this fragment, I'll take that compositional translation and look how nice.