# Generic algorithm for probability any propositional formula

Ciao all,

Is there a generic algorithm to compile the probability P(A)
of any propositional formula A (provided that we have only the probability of each atoms constituting A)?

For example, we have that A= a1 and not (a2 and a3 and ( not a4 and not a5 and not a6 ..) , or any other complicated formula.
The an are independant here!!!!

I know pr(a1), pr(a2)... and so on...

Is there an algorithm to compute pr(a1 and not (a2 and a3 and ( not a4 and not a5 and not a6 ..) ) ?????

Just repeatedly apply Bayes' rule. But you will have difficulty usually coming up with numbers for all of the required terms.

Applying Bayes.

Thank you for the advice!! I shall try it.

What did you exactly mean by:

"you will have difficulty usually coming up with numbers for all of the required terms"

???

Essentially you'll need all the cross probabilities -- all the and's and or's of the all the possible pairs of propositions. Usually, these numbers aren't easy to come up with.

I do not get it.

Could you provide an example?

or do you have a reference where that is well explained ( I am not an expert of Probabiliies)?

Any standard probabilities textbook would be a good place to start. My personal favourite is Probability Theory by E.T. Jaynes.

EnumaElish
Homework Helper
Well, if the a's are independent, that simplifies the problem considerably.

Ciao EnumaElish,

Do you have an algorithm? eventually a reference to it?

Ciao EnumaElish,

Do you have an algorithm? eventually a reference to it?

I'm fairly sure nothing beyond a textbook would even bother to spell it out:

given two independent events, A and B, pr(A and B) = pr(A) pr(B), pr(A or B) = pr(A) + pr(B). Generalise in the obvious way for more than 2 events.

EnumaElish