PASTA: Probabilistic Answer Set programming for STAtistical probabilities

This software allows to perform inference in probabilistic answer set programs under the credal semantics and with statistical statements.

Installation

Requirements: clingo, see install clingo.

python3 -m pip install clingo

Then, clone this repository

git clone git@github.com:damianoazzolini/pasta.git

Finally, move into the pasta folder and you are ready to go

cd pasta
python3 pasta_solver.py --help

See below for some example programs.

You can also use Docker (image on Dockerhub) to test the application:

docker pull damianodamianodamiano/pasta
docker container run -it pasta bash

then you are ready to go (follows the nex instructions to run an example). However, the image is not always updated.

Usage

Use

cd pasta
python3 pasta_solver.py --help

to see the various available options.

You can also use it as a library

import pasta_solver

filename = "../examples/inference/bird_4.lp"
query = "fly(1)"
solver = pasta_solver.Pasta(filename, query)
lp, up = solver.inference()

print("Lower probability for the query " + query + ": " + str(lp))
print("Upper probability for the query " + query + ": " + str(up))

where filename and query are the name of the file and the query to ask.

You can also pass the file as a string, in this way:

query = "fly(1)"
solver = pasta_solver.Pasta("", query)  # leave the filename as ""
lp, up = solver.inference(program)

print("Lower probability for the query " + query + ": " + str(lp))
print("Upper probability for the query " + query + ": " + str(up))

where program is a string containing your program.

You can find more information about the API documentation in the html/pasta folder.

Options

python3 pasta_solver.py --help
usage: pasta_solver.py [-h] [-q QUERY] [-e EVIDENCE] [-v] [--pedantic] [--approximate] [--samples SAMPLES] [--mh] [--gibbs] [--block BLOCK] [--rejection] [--pl] [--abduction] [--map] [--upper]                        [--no-minimal] [--normalize] [--stop-if-inconsistent] filename

PASTA: Probabilistic Answer Set programming for STAtistical probabilities

positional arguments:
  filename              Program to analyse

optional arguments:
  -h, --help            show this help message and exit
  -q QUERY, --query QUERY
                        Query
  -e EVIDENCE, --evidence EVIDENCE
                        Evidence
  -v, --verbose         Verbose mode, default: false
  --pedantic            Pedantic mode (prints the converted program and all the worlds), default: false
  --approximate         Compute approximate probability
  --samples SAMPLES     Number of samples, default 1000
  --mh                  Use Metropolis Hastings sampling
  --gibbs               Use Gibbs Sampling sampling
  --block BLOCK         Set the block value for Gibbs sampling
  --rejection           Use rejection Sampling sampling
  --pl                  Parameter learning
  --abduction           Abduction
  --map                 MAP (MPE) inference
  --upper               Select upper probability for MAP and abduction
  --no-minimal, -nm     Do not compute the minimal set of probabilistic facts
  --normalize           Normalize the probability if some worlds have no answer sets
  --stop-if-inconsistent, -sif
                        Raise an error if some worlds have no answer sets (and lists them)

Exact inference

cd pasta
python3 pasta_solver.py ../examples/conditionals/bird_4_cond.lp --query="fly"

Asks the query fly for the program stored in ../examples/conditionals/bird_4_cond.lp. Expected result:

Lower probability for the query: 0.7
Upper probability for the query: 1.0

You can specify evidence with --evidence.

Abduction

cd pasta
python3 pasta_solver.py ../examples/abduction/bird_4_abd_prob.lp --query="fly(1)" --abduction

MAP/MPE inference

cd pasta
python3 pasta_solver.py ../examples/map/color_map.lp --query="win" --map

Approximate inference

Available: sampling (--approximate), gibbs sampling (--gibbs), metropolis hastings sampling (--mh), rejection sampling (--rejection).

cd pasta
python3 pasta_solver.py ../examples/inference/bird_4.lp --query="fly(1)" --approximate

Handling Inconsistent Programs

The credal semantics requires that every world has at least one answer set. These programs are called consistent. Here, we make the same assumption. Note that the minimal set of probabilistic facts is correct only if the program satisfies this requirement. If you don't want to compute this set, use the flag --no-minimal or -nm. If you ask a query on a program that is not consistent, you should get a warning. For example,

% file temp.pl
0.5::a.
0.5::b.
qry:- a.
qry:- b.
:- a, b.

> python3 pasta_solver.py temp.pl --query="qry"
Warning: This program is inconsistent.
You should use --normalize or --stop-if-inconsistent.
Lower probability == upper probability for the query: 0.5

The computed probability is likely to be incorrect. There are two options: you can use the flag --stop-if-inconsistent or -sif that halts the computations (note that the consistency of the program is checked after the computation of all the projected answer sets, so it requires the same time as exact inference) and prints the unsatisfiable worlds

> python3 pasta_solver.py temp.pl --query="qry" -sif
Error: found 1 worlds without answer sets: [3]
11{ a b } % the world where both a and b is unsatisfiable

or you can use the --normalize flag, that normalizes the computed probability

> python3 pasta_solver.py temp1.pl --query="qry" --normalize
Lower probability == upper probability for the query: 0.6666666666666666

Syntax

Basically, PASTA (PASP) programs are ASP programs plus probabilistic facts. Probabilistic facts can be added with the syntax: prob::atom. where prob is a floating point number (0 < number <= 1) and atom is a standard ASP fact. For example, 0.5::a. states that a has probability 0.5.

For more examples, see the examples folder.

Using exact inference, you can also express statistical statements (x% of the y elements share the same behavior) with the syntax: (A | B)[LP,UP]. For example, "at least 60% of the birds fly" can be expressed with

(fly(X) | bird(X))[0.6,1].

See examples/conditionals/bird_4_cond.lp for an example.

Note: be super careful when using rules with disjunction in the head. You should replace them with choice rules.

Description and How to Cite

The system is currently described in:

• Abduction (preliminary): Damiano Azzolini, Elena Bellodi, and Fabrizio Riguzzi. Abduction in (probabilistic) answer set programming. In Roberta Calegari, Giovanni Ciatto, and Andrea Omicini, editors, Proceedings of the 36th Italian Conference on Computational Logic, volume 3204 of CEUR Workshop Proceedings, pages 90--103, Aachen, Germany, 2022. Sun SITE Central Europe.
• Exact inference and statistical staments: Damiano Azzolini, Elena Bellodi, and Fabrizio Riguzzi. Statistical statements in probabilistic logic programming. In Georg Gottlob, Daniela Inclezan, and Marco Maratea, editors, Logic Programming and Nonmonotonic Reasoning, pages 43--55, Cham, 2022. Springer International Publishing.