Yesterday we talked about first-order logic and the idea was that we design agents, in

this case logic-based agents, that use some kind of a formal language and formal inference

procedure for their world modeling and maintaining the world model. We have the choice of which

language to take and normally if you do these things you will actually design a logic and

an inference system for the particular world that is well adapted to that. And the inference

system has the characteristics you need. Of course I cannot show you every logic, especially

the ones we still have to invent, but I can show you two paradigmatic logics. One is propositional

logic which is designed to be extremely simple, to have decision procedures for satisfiability

and to be very efficiently handleable by algorithms. First-order logic is kind of at the other

extreme, it's in a way the most expressive logic. Expressivity is good because it allows

us to describe complex things in the world compactly. And if our formulae are compact

that's good for inference because dealing with small things is much better than dealing

with big things. And so logic is at the other extreme, it's kind of the strongest logic

that we can use without losing certain properties. And those properties are that we have sound

and complete calcali and when we have sound and complete calcali that means we can have

semi-decision procedures for satisfiability. Semi-decision procedure means if a set is

satisfiable then we can find out in finite time. If it's not it might run forever. So

that's kind of undecidability is a fact of life for strong logics. We're losing the good

property of decidability we had for propositional logic but we can express things much more

succinctly and in a much more structured way and more structure in your expression often

means more guided inference. So there's a trade-off and sometimes first-order logic

wins and sometimes propositional logic wins depending on what kind of an agent you want

to do. And there's all kinds of logics in between. There are logics which are decidable

like propositional logic but look very much like first-order logic. You're just leaving

out the stuff that causes you pain and suffering and you have to decide can I express the world

I want to talk about in that decidable fragment or not as an agent designer. So I want to

show you the kind of extreme and we'll go over it relatively quickly because you've

already seen it. We've made this experiment talking about blocks and that was mainly to

show you we need to say something like all blocks and this doesn't move anymore why not

well okay probably need new batteries right we need to say something all blocks are something

or the other red on the table clear on the top next to each other and so on. And if we

have that that's the main motivation for having propositions propositions meaning things that

are either true or false where you can that have internal structure that's the main thing

we have propositions with internal structures just like we had states with internal structure

we now have propositions with internal structure and that gives us a lot of power. Very simple

idea and gets you quite a long way right you have to you can explain in the line in your

modeling language you can explain the wumpus in five or six sentences rather than thousands

of propositional formulae you can talk about infinite things

you can talk about the semantic web you can do jeopardy which is classical AI topic of

course and all kinds of things context aware apps so on right yeah you think about having

a an app that is context aware that really has to be able to talk in a way about all

the locations on the globe they're quite there are only finitely many arguably but still

quite a lot so you want to have techniques that can actually deal with infinite sets

there.