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So, I'm seeing that my quiz questions are getting people to think and to discuss a little bit.

That's what they're for. I'm willing to spend some bonus points on getting you to think with them, so that's fine.

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Is everybody registering for the exam?

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OK. We were talking about constraint networks. If you think where we are, we've talked about atomic states.

Search problems is the only thing we can really do if we have atomic states, where we only know from the outside what the successor states are for expansion,

and what the applicable actions are, and so on, where we don't have any information about the inner structure of things, and we've graduated from that to factored representations.

And if you think about it, factored representation means that you have certain ways of measuring the outside state.

Think about maybe you have a GPS location and a thermometer, then everything you know about your state will just basically be the essentially X coordinate, Y coordinate, and temperature.

So you will have world states, or reasonably have world states that are triples of positive real numbers maybe.

OK. So, but these things have an internal structure. We know they're triples. We might even know what they mean.

If you have GPS coordinates and we have different between the states, you can actually compute the straight line distance.

Those kind of things. That is something you could not do in the search problems.

Even though we sometimes cheated and looked into the states anyway, we never were really allowed by the algorithm framework.

That's changed here. OK. So we've kind of talked about these constraint satisfaction problems, which are factored representations.

So we have what is called a variable, which is really an attribute, something we can measure about the real states, which we chose to include in our represented world knowledge.

Even if we can measure the temperature, it doesn't mean that it actually plays a role for our agent.

If it doesn't, we may decide to leave it out, which may be a good decision or it may be a bad decision, but it's a decision we as the agent designers can take.

Whatever it is, we're left with a factored state and that's what we are building on.

We've convinced ourselves that all we have to worry about are these binary constraints.

Because higher order constraints we can kind of crash down to binary constraints.

Unary constraints we can put into or move on into the domains.

And so we're left with binary constraints and that's really what we're going to work on.

And that's what we formalize in the official definition of what a, we call it, constraint network is, which is just a binary CSP.

And so a binary CSP consists of a finite set of variables, a finite set of domains, one domain per variable.

They can be different, they don't have to be different, and constraints.

And constraints are just relations on the domains, sets of pairs, sets of, in this case, allowed pairs.

And the only thing that we insist on is that the constraints read this way are the same as the constraints read that way.

The same set of pairs.

Okay? So now we know exactly what we're talking about.

And we see here a similar thing that we're seeing almost always.

We can think of constraints as kind of semantic black box things, their relations.

Or we can think of them as something we can describe in a language.

Not equal.

The not equal relation on, say, some big set A is all the sets, all the pairs AB or AA' where A and A' are different.

Huge relation. Big thing. If A is big, then this is a quadratically big object.

Which is hard to write down, maybe.

But we can just basically say the constraint is they have to be equal or one has to be bigger than the other or something like this.

Okay? So officially we're going to go with relations.

Inefficially we're going to use the language anyway.

And you in your heads silently just make not equal into a relation so that we come back into the official.

And how this stuff with the language works is something for the next chapter.

And in a way when we've done that, when we go to structured representations where the language is the primary thing, then you can kind of backport the ideas.