Can you hear the microphone?

Excellent.

So now we are rebooted.

So we are, as I said, in an experiment of logic engineering, right?

We had talked about propositional logic, which is wonderful because we have decision procedures

for it, which means we have algorithms that are guaranteed to terminate after a finite

time and they tell us this is satisfiable or not, right?

Which also gives us that the entailment relation is decidable, right?

We have an A and we want to know if in all situations that make A true, B is also true,

we can decide this.

Unfortunately, as a world description language, propositional logic is very, very basic.

There are many things we want to say and we cannot directly say in propositional logic.

We can do the usual trick we did with the wumpus by basically saying, oh yes, we have

a finite number of things here and I can basically, instead of saying, well, whenever there's

a wumpus in this cell, it stinks in that cell, we can say basically that on a cell by cell

basis, which is fine if we have a finite number, right?

But this is extremely tedious.

On the other hand, we had a very expressive logic, first order logic, where we can say

most of the things we want to say.

There's a couple of things we can't say in math and even in ordinary English, there's

a couple of things we cannot say.

We can say every student is wide awake and interested in AI.

Those things we can say or there is a student who's sleeping under the seats or something

like this.

We can't say most students funnily enough.

That's not something we can say in first order logic.

But that's okay.

The punishment for this expressive logic, first order logic, is that we're losing decidability.

We no longer have an algorithm that will terminate in finite time and say this formula is satisfiable

or not or this formula is entailed by that formula.

We don't have that anymore.

So it's kind of a, we're in a bad situation either way, right?

Either we can't say what we want to say or we can't decide what we want to decide.

So the idea is can't we just engineer logics?

We're just kind of in the middle, the best of both worlds.

And I've started showing you one of these logics.

And before we go into the details of this, I want to kind of restart and show you the

stuff that I've skipped over.

Classically, in philosophy, we use the word ontology for a representation of the kind

of types of objects, their properties, their interrelationships, and so on, for some universe

of discourse.

This is exactly what, if you think about it, our agents need.

We have a universe of discourse that's philosophy for the environment that we talked about.

We have an environment which is not the whole world, but basically some part of the whole

world.

And we want to worry about what are the objects in the environment?

Are they related?

Maybe we can save some time by classifying the objects.

We have students, we have blackboards, we have computers, and often we want to say something

about all the students or all the computers or all the blackboards or something like this.