Just for your orientation, we have started, well, we've completed First Order Logic last week and

we're starting on planning. Planning is essentially the topic that you'll get into when you try to

solve the search problems we started off with at the inference level. Remember, we started off with

search problems where we had black box representations. And that makes it very easy, but also keeps us

from reaping the benefits of a good representation of the world. Good world representations are

typically language level things, where instead of saying, oh, I just have this mass of millions of

states that describe each of them kind of stand for a state of the world and I have this mass of

actions I can do to get from one state to the other, which is the black box description,

which is easy. We go to language level descriptions of the world, which is what we actually looked at

with Logix. And the great thing about Logix is that you have single descriptions about what you

would otherwise have to reserve lots and lots and lots of states for. If I have the description,

Miko is in Erlangen, a tiny little thing, describes millions of states. This guy is in Erlangen too,

that is described. Obama isn't and Trump isn't and 1.4 billion of Chinese aren't in Erlangen.

We could describe where they are and where they aren't and so on. So we have just one little

partial world description describes something that would have to occupy different states. And that's

good. And inference really goes between kind of descriptions of multiple quote unquote states.

The problem when you start doing the old problems again is that your actions have to become more

complex. The idea behind planning is that you describe the world by propositions. Somebody is

in Erlangen, I don't know, the blue block is on the white table and so on. And when you do that,

you have to make sure that you have meaningful operators. And the upshot of all of planning is

really that if you use sets of propositions for describing the worlds, then you have to somehow

delete things you thought of as true, but in terms of the actions. Very simple idea. And it comes from

the fact that we're lifting the search to the description level space, which saves us work,

but also adds new complications. And that's exactly what planning is dealing with. And once

you understand that, planning is easy. So these are the kind of problems. We describe it by things

like spades six is the top level card in column one. And then we do something, right? We take the

five here, put it down here, and the proposition six of spades is the top level card in the first

column becomes untrue. Untrue means we have to delete it from the sets of propositions that

describe the world. So in one way you can think of this as involving time. It's not quite right,

but not quite wrong either. Because in your plans you have time in there. Usually the outcomes are

plans that have time in it. But it's really about description level search, which is a multi-state

operations search. Good. And it's really all that we go from a black box description to a white box

or declarative description. Given that, this idea that we're kind of using description level

operations here, that gives us a very general way of defining the semantics of these description

levels. Namely, we're lifting the operations, we define the semantics by dropping it down again.

Okay, so what we've done is we've looked at basically again the descriptions of planning level languages,

which means description level operations, and what they mean. And really the key idea here is that

the states are actually all the states of the world described by sets of propositions, and then

we can build everything on that. There's a couple of applications we went over and convinced ourselves

that planning really the main, the kind of iconic example is Box World. How do I make a plan to go

from this state to some kind of a state where say everything is unstacked or they're stacked in the

other order. And so we're going to look at Box World, but also traveling salesman's problems and so on.

You shouldn't be shocked that of course this is an exponential problem, and exponential means you

kind of have, if you write it down in numbers, which are a logarithmic representation of sizes,

then you'll see kind of a linear growth of a length of numbers that means it's exponential.

Right.