Probability of logical propositions



Jan Ploski escribi?:
> Hello,
> 
> Having briefly checked out Alexey Beshenov's logic.mac package (discussed 
> here earlier: 
> http://www.math.utexas.edu/pipermail/maxima/2008/010825.html), I started 
> wondering how difficult it would be to implement probability theory rules 
> (sum and product rule) to allow the calculation of probabilities of 
> related logical propositions, Bayesian-style? I have absolutely no prior 
> experience with Maxima and CAS, so I can't estimate whether it is a piece 
> of cake or a big project, especially for someone who's already "been there 
> done that".
> 

I suppose the difficulty depends on the level of generality.

* Do you allow stochastic dependence among variables? in this case the 
procedures should handle multivariate distributions.

* Even if you only assume stochastic independence, you should solve 
problems like "what's the distribution of X*Y*Z, where X is binomial, Y 
is gumble and Z is chi^2 ?"

* But if you restrict your model to stochastic independence and 
bernoulli distributions, This is closer to human beings.

* Driving in another direction, I ask if something as fuzzy logic could 
be of some interest. I don't know much about that.

Forgive me if this post doesn't answer your question. I was thinking 
aloud, since this question came to my mind two or three times in the past.

-- 
Mario Rodriguez Riotorto
http://www.telefonica.net/web2/biomates