Comment by aphyr

15 years ago

Has anyone created a probabilistic language akin to Prolog? I feel like confidence interval propagation, with appropriate notions of covariance and error distributions, could be really useful for hypothesis testing.

10 comments

aphyr

rdtsc 15 years ago

I beleive what you are looking for is Fril:

http://en.wikipedia.org/wiki/Fril

It is a lisp-y prolog that supports fuzzy relations (confidence interval for predicates).

It is not bad if fuzzy logic is your cup of tea.

Here is the reference:

http://www.enm.bris.ac.uk/ai/martin/FrilManual/index.html

Code example (from reference doc of goal set (gs) predicate):

   ((test a)) : (0.5 0.8) 
   ((test b)) : (0.7 0.9) 
   qs ((test X) (test Y)) 
   ((test a) (test b)) : (0.25 0.64) 
   ((test a) (test b)) : (0.35 0.72) 
   ((test b) (test a)) : (0.35 0.72) 
   ((test b) (test b)) : (0.49 0.81) 
   no (more) solutions 
   yes

EDIT: more examples and explanation by its author, Trevor Martin from Bristol Univ.

ftp://ftp.cs.cmu.edu/user/ai/areas/fuzzy/com/fril/fril.txt

jimbokun 15 years ago

I believe the term you are looking for is Statistical Relational Learning.

One formalism for this is Markov Logic.

http://www.cs.washington.edu/homes/pedrod/papers/pilp.pdf

Alchemy is an implementation of Markov Logic.

http://alchemy.cs.washington.edu/

Both of these are from Pedro Domingos, who does a lot of research in this area.

nathanmarz 15 years ago

There's PRISM, which is used for analyzing probabilistic systems: http://www.prismmodelchecker.org/

aphyr 15 years ago

Oh my god. I have dreamed of, and half-implemented badly, exactly this. Not quite what I was thinking of, but still quite useful for that class of problem.
You should submit this as an HN post too. Thanks!
tel 15 years ago

There's also TreeAge which is popular in health informatics (the name is a pun off of "triage") and, perhaps more generally, BUGS/JAGS which can be used to build and test arbitrary Bayesian network models.

brendano 15 years ago

There have been several systems that probabilistically extend Prolog or do something similar. I'm not aware of any that do those things specifically, though. Here's a list of some that I made a bit ago:: http://anyall.org/blog/2009/12/list-of-probabilistic-model-m...

jules 15 years ago

Can you elaborate? Do you mean something like the probability monad?

aphyr 15 years ago
Specifically, I want to express a model in analytic terms:
x = 2y + z^2
provide a dataset of x, y, and z tuples with associated error distributions, and ask questions like "what is three-sigma confidence interval for the model given this dataset", and "what would tunable parameters a and b have to be for the most consistent account".
Ideally, it'd be able to take into account convolutions, as well.
- silentbicycle 15 years ago
  
  _The Art of Prolog_'s chapter on meta-interpreters* includes an interpreter with uncertainty thresholds. It's about a quarter-page of code - It's on page 318, in the first edition (what I have on hand). Extending it to support statistical significance rather than just a 0-1.0 confidence interval shouldn't be too hard. Combining that with constraint programming would probably suffice.
  * Rather like chapter 4 of SICP, on making metacircular evaluator Prologs.