Discussion article for the meetup : Tel Aviv Meetup WHEN: 27 January 2015 07:00:00PM (+0200) WHERE: Google, Electra Tower 29th Floor, Yigal Alon Street 98, Tel Aviv. This meeting we're going to try something a little different. Instead of having a formal lecture given by one of us we're going...
At the recent Tel Aviv meetup, after a discussion of the open problems in the field of FAI, we reached the conclusion that the problem of logical uncertainty is one of the most major of the problems open today. In this post I will try to give a few insights...
This meeting we're going to try something a little different. Instead of having a formal lecture given by one of us we're going to split into several small groups such that each group has its own conversation. This is the first time we're doing something like this so it's a bit experimental, come with open minds!
We'll start the meetup at 19:00, and we'll go on as much as we like to. Feel free to come a little bit later. We'll meet at the 29th floor of the building. (Note: Not the 34th where Google Campus is.) If you arrive and can't find your way around, call Anatoly who is very graciously hosting us at 054-245-1060 or Benjamin at 058-507-6543.
Nico Roos. A logic for reasoning with inconsistent knowledge. Artificial Intelligence Volume 57, Issue 1, September 1992, Pages 69–103.
That's a good point, and I concede that you are right. At the moment, it's more of a "probability assignment", as you said, rather than a probability measure. More work needs to be done on the subject, and hopefully we will progress along these lines at the MIRIx workshop.
I appreciate the links. I haven't read Gaifman's paper before, so I'll go ahead and read that.
Anyhow, I won't cotton to any method of assigning a logical probability that takes longer than just brute-forcing the right answer. For this particular problem I think a bottom-up approach is what you want to use.
I see the sentiment there, and that too is a valid approach. That said, after trying to use the bottom-up approach many times and failing, and after seeing others fail using bottom-up approaches, I think that if we can at least build a nonconstructive top-down theory, that would be a starting point. After all, Solomonoff Induction is completely top down, yet it's a very powerful theoretical tool.
Thanks for those links! They both look very intresting, and I'll read them in depth.
As you mention, you are doing something slightly diffrent. You are assigning probability 1 to all the provable sentances, and then trying to investagate the unprovable ones. I, on the other hand, am taking the unprovable ones as just that, unprovable, and focusing on assigning probability mass to the provable ones.
I think the question of how to assign probability mass to provable, yet not yet proven, statments is the really important part of logical uncertanty. That's the part that is handwaved away in discussions of, say, UDT, and so is the part that I want to focus... (read more)
At the recent Tel Aviv meetup, after a discussion of the open problems in the field of FAI, we reached the conclusion that the problem of logical uncertainty is one of the most major of the problems open today. In this post I will try to give a few insights I had on this problem, which can be thought of as the problem of constructing a (non-degenerate) probability measure over the set of the statements of an arbitrary logical system.
To clarify my goal: I'm trying to make a Solomonoff-like system for assigning probabilities to logical statements. For reasons much like the reasons that Solomonoff Induction is uncomputable, this system will be uncomputable... (read 1041 more words →)
I am a long time LessWronger (under an anonymous pseudonym), but recently I've decided that it is finally time to bite the bullet, abandon my few thousand karma, and just move over to my real name already.
Back in the day, when I joined LessWrong for the first time, I followed my general policy of anonymity on the Internet. Now, I'm involved with the Less Wrong community enough that I find this anonymity holding me back. Thus the new account.
Edit: For my first post on this new account, I posted a few of my thoughts on logical uncertainty.