Okay, so sorry for being so late, changing the rules on the locks without telling us

first.

How nice.

So we've been talking about logic.

Remember the idea is that we're using a formal language as a world description language and

the agent uses inference to find out more about the world than just its sensors tell

it.

So the, and we've looked at two logics.

One is propositional logic and you've looked at one inference calculus, natural deduction

in a bit of detail.

And we've shown you a little bit of a more practically useful logic, which is really

a variant of propositional logic, predicate logic without quantifiers.

And that kind of gives me the opportunity to show you little bits and pieces of a stronger

logic, first order logic, and already use in propositional logic this logic as a kind

of practical enhancement.

And this is something we often do and we're going to see that a couple of times in the

in other contexts.

So remember propositional logic, very simple.

The central idea is that of an atomic proposition, something that can be true or false.

And those are enhanced by and not or implies all of those kind of things.

And these kind of things is what the inference is always about.

Inference tells us how does A and B behave?

What can I infer from A and B?

Or what can I infer if I know that if A then B?

And Peeling Q kind of takes special care with the things that can be true or false.

And the idea is there that we, for a world description language, we need something like

talking about individuals.

There's a cow in the driveway, the cow would be an individual.

And their relations to each other.

And that is something where we're using this notion of a first order signature for.

It tells us about the individuals that are around, whether their relation is Bill married

to Jane and the functions like the father of Bob or something like this.

And that's kind of the central thing and we kind of have extend the grammar of propositional

logic which is essentially the lower part with this notion of atomic formulae which

is just a predicate applied to a bunch of terms.

And the complicated thing here is really how we make the meaning of this, the semantics.

And you've basically looked through this and mathematically this is just a homomorphism.

If we know the meanings of the functions, if we know the meanings of the predicates,

then we can homomorphically assemble the meaning of everything.

And you've looked into a particular model.

Are there any questions so far?

Yeah.

We could have an extension where every set is an individual as well.

We usually don't use it.

So this is a very simple logic.

So it has lots of deficiencies, things it cannot do.

And so the real thing would be to allow set valued functions or do a set theory where

you have kind of functionality for sets of things.

We could have done that, it would have made the whole thing much more complicated, so

we didn't.