We've talked about logic yesterday and we've mainly, I tried to convince you of a couple

of things.

One was that logic is easy.

Logics can be very small.

And the other thing I wanted to convince you of is there's more than one logic.

In fact, logics make very good pets.

You might have more than one logic as a pet.

Okay, and you develop logic as descriptions of particular worlds.

Remember in the agent, the logic is actually the language in which to describe the world

model.

The world model is just a set of sentences in that particular logic that's implemented

in the agent.

There are lots of different agents in different environments and so it's not a surprise that

they need different tools to survive.

I.e. they need different logics.

Logics that are kind of tailored to the world they live in.

And yesterday I mainly tried to kind of teach you logic, independent logic.

What are the things we'll see every time?

We'll see a formal language and no matter how we do it, there will be a formal language

which we can decide well-deformedness in.

There will be a semantics which is just essentially a mapping from that language into the world.

That's what we need.

That's kind of the reverse of the sensory mapping.

The sensory mapping, you see something in the world and map it into your language, whereas

the semantics should be the inverse or at least partial inverse to that.

And the last thing is we need a calculus.

A way of taking world models and deriving better world models out of that.

So the first thing you should realize is this is a description layer process just like we

learned in constraint propagation, where we took constraint descriptions and made tighter

equivalent constraint descriptions out of it.

This is exactly what we're going to, what we're doing with the calculus.

We take a world model and make a quote unquote tighter world model.

Something where we can see directly what the consequences are.

Without changing the meaning, that's the important thing, which is why we're studying meaning,

but we're really interested in these calculus here.

Okay.

I could directly stop now.

That's all you really have to know about logic.

Except of course, there are many calcali and some of them are better for some things and

other are better for other things.

So we're going to learn a couple of calcali and we're going to learn a couple of calcali,

I hope we can get to them, which are very suited for implementing on the machine.

We're doing not philosophy, but AI after all.

So it's always also the question is, can we engineer this so that we can actually build

it?

Good.

Okay.

So let's start.

And we've looked at two logics actually.

One is called propositional logic, is very important logic.