Why are we doing all this? Well, it's great and important and it's at the base of physics,

computer science, mathematics and everything you hold dear. And if we make calculus that

are sound and complete, meaning play nice with the semantics, then syntax and semantics

coincides and we get what I call the miracle of logic, namely, world models work. Right?

If you have observations, this is my agent here, if I have observations, in this case

two, and I have inference, I get representations that must be true in the world. It's important

that this is true in the world because that's my augmented world model as an agent and I

will be basing my actions on this. I will go right in the Wumpus cave and it better

be true that there is no pit there, otherwise, right, end of life. Not something that's very

high in the fitness function of an agent. The agent is supposed to get gold, not die

in the pit. That only works if the miracle of logic happens. Therefore, it's very important

that we have at least sound calcolate. Sound means if I derive there's no pit, there's

no pit. Complete means I actually can derive if there's no pit, then there is no, then

I can derive the information that there's no pit. Right? Completeness is something like

a guarantee against blindness. Soundness is a guarantee against hallucinations. And you

want neither. You don't want to be blind as an agent, you don't want to hallucinate because

both actually get you into trouble. Okay, that was as far as we got yesterday.