Plingo

A system for probabilistic reasoning in clingo.

The system is based on LP^MLN, and provides front-ends for different probabilistic logic languages:

• lpmln [1]
• p-log [2]
• problog [3].

While the basic syntax of plingo is the same as the one of clingo, its semantics relies on re-interpreting the cost of a stable model at priority level 0 as a measure of its probability.

Solving exploits the relation between most probable stable models and optimal stable models [4]; it relies on clingo's optimization and enumeration modes, as well as an approximation method based on answer set enumeration in the order of optimality [5].

The plingo system can be used to solve two reasoning tasks:

• MPE inference: find a most probable explanation (stable model)
• Marginal inference: find all stable models and their probabilities

A number of examples can be found here. There are also sub-directories containing examples using our front-ends for the other probabilistic logic languages.

Installation

With coda

conda install -c potassco plingo

With pip

pip install plingo

From source

git clone https://github.com/potassco/plingo.git
cd plingo
pip install .

Usage

plingo is an extension of clingo, therefore it counts with all of clingo's functionality with new options.

Run the following command and look at plingo's latest options under Plingo Options:

plingo -h

Command line options

• --all

  Enumerates all stable models and prints their probabilities.

• --evid=file

  Provides an evidence file to the program (.lp file with clingo syntax rules)

• --frontend=mode

  Specifies which frontend to use (lpmln, lpmln-alt, problog, plog). Mode lpmln-alt is the alternative definition where hard rules have to be satisfied. When using mode lpmln hard rules are also translated which can be useful for debugging or resolving inconsistencies in the program.

• --problog=output'

  Uses reificiation to translate a plingo program to a program which be can be given as input to the ProbLog system. The ProbLog program is saved under the path given in output. The input can also be given in any of the frontends (lpmln, lpmln-alt, problog, plog).

• --query='atom'

  Adds a query atom atom, e.g. using the example from above --query='bird(jo)'. The argument has to be inside single quotation marks (otherwise the command-line might not be able to parse it correctly).

• --two-solve-calls

  Uses two solve calls: The first one finds the minimal bound for weak constraints priorities higher than 0. The second one solves for probabilistic stable models of LP^MLN.

• --unsat

  Uses the conversion with unsat atoms

Examples

MPE

Find a most probable stable model

plingo examples/lpmln/birds.plp --frontend lpmln-alt

plingo version 1.1.0
Reading from examples/birds.lp
Solving...
Answer: 1

Optimization: 300000
Answer: 2
residentBird(jo) bird(jo)
Optimization: 100000
OPTIMUM FOUND

Models       : 2
  Optimum    : yes
Optimization : 100000
Calls        : 1
Time         : 0.005s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)
CPU Time     : 0.005s

Marginal probabilities

To list all stable models, add the flag --all.

plingo examples/lpmln/birds.plp --all --frontend lpmln-alt

plingo version 1.1.0
Reading from examples/birds.lp
Solving...
Answer: 1

Optimization: 300000
Answer: 2
residentBird(jo) bird(jo)
Optimization: 100000
Answer: 3
migratoryBird(jo) bird(jo)
Optimization: 200000


Probability of Answer 1: 0.09003
Probability of Answer 2: 0.66524
Probability of Answer 3: 0.24473


OPTIMUM FOUND

Models       : 3
  Optimum    : yes
Calls        : 1
Time         : 0.006s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)
CPU Time     : 0.006s

Approximation algorithm

For large problems it is infeasible to determine all stable models. Plingo offers an option to determine approximate probabilities using answer set enumeration by optimality (ASEO) [1].

For approximation of probabilistic queries it is recommended to use the --opt-enum option together with --balanced=N.

• --opt-enum

  Enumerates stable models by optimality. This can be used for approximating probabilities and queries. Recommended to use along with -q1 to suppress printing of intermediate models

• --balanced=N

  Approximates a query in a balanced way, i.e. it will determine N stable models containing the query, and N stable models not containing the query. This overwrites clingo's --models option. Works only for a single ground query atom!

• --use-backend

  Adds constraints for query approximation in backend instead of using assumptions.

Using ProbLog as a solver

With the --problog option it is possible to translate a plingo program to a problog program which can be solved by the ProbLog system (https://github.com/ML-KULeuven/problog). This can also be combined with using any of the frontends. The input file needs to contain at least one query when using marginal inference.

plingo examples/lpmln/birds.plp examples/lpmln/birds_query.plp --frontend=lpmln-alt --problog=problog.lp >/dev/null; problog problog.lp

show(residentBird(jo)): 0.66524095

Input Language

Syntactically, LPMLN differs between "soft" rules and "hard" rules, where "soft" rules have a (real number) weight and "hard" rules the weight "alpha".

Weights can be added by the theory atom &weight/1 to the body of a rule. The argument has to be an integer or a string containing a float or an expression like 2/3. For example

a(X) :- b(X), &weight(5).
b(X) :- &weight("-2/3").

Further it is possible to use the theory atoms &log/1 or &problog/1 which only accept strings as arguments. The atom &log/1 uses the natural logarithm log(p) of its argument p as weight. The atom &problog/1 uses the natural logarithm of p/(1-p) as its weight. Rules that do not have any weight in the body are assumed to be hard rules.

To compute LPMLN programs, a rule in an LPMLN program is converted to ASP with weak constraints

By default, only soft rules are converted. To convert hard rules as well, the --hr flag can be added on the command line. This option essentially makes hard rules optional, whereas in the default setting all hard rules have to be satisfied as usually in ASP.

References

[1] J. Lee and Y. Wang. (2016). Weighted Rules under the Stable Model Semantics

[2] C. Baral and M. Gelfond and J.N. Rushton. (2009), Probabilistic Reasoning with Answer Sets

[3] L. De Raedt and A. Kimmig and H. Toivonen ProbLog: A Probabilistic Prolog and its Applications in Link Discovery

[4] J. Lee and Z. Yang (2017). LPMLN, Weak Constraints and P-log

[5] J. Pajunen and T. Janhunen. (2021). Solution Enumeration by Optimality in Answer Set Programming. Theory and Practice of Logic Programming, 21(6), 750-767.