Teach me how to read (math notation question)

General Questions
#1

I need to know how to read the notation on page three of this article: http://fitelson.org/few/few_05/egan.pdf

I know almost nothing about how to read the notation I’m looking at. The sigma has something to do with… summing something up, I think. Is that the ‘v’ of disjunction or something else? I know the probability notation in the first parentheses–but is the second parentheses enclosing a product (of H and A) or does juxtaposition not mean products here? If a product, how do you compute the product of a set of worlds and an action? Where did that random ‘c’ come from?

Thanks for any pointers…

#2

I think the ‘c’ represents something like a “credence function,” though I’d like to read a little more about how that’d be defined.

#3

I think the Sigma[sub]H[/sub] is supposed to be the sum over all the H’s (“the H’s form a partition of the worlds”). In other words, for each “world” H, evaluate c(H|A)v(HA), and add all those values together. However you do that. Dunno if that helps.

The typesetting’s a bit confusing. At first I thought the c was a superscript on the H, perhaps meaning “complement,” but seeing how it was used elsewhere in the article rules that out.

#4

I think you’re right. Now I just need to know what is meant by that “v” and that “HA”.

#5

The go-to book on causality is Judea Pearl’s Causality. This is not something that the average mathematician will be at all familiar with, so you’re best off going straight to the source.

Edit: I’m not familiar enough with this stuff to swear that what you’re looking for is in there, but it’s definitely the first place I’d look.

#6

I’ll think about taking a look at it (a lot of money to cough up though, and trips to the library these days are difficult with baby twins in tow…) but from here it looks a little more like “throw me in the deep end and yell at me to swim” than “teach me how to read” material…