Probabilistic extension for clingo
Project description
Plingo
A system for probabilistic reasoning in clingo.
The system is based on LP^MLN, and provides frontends for different probabilistic logic languages:
While the basic syntax of plingo is the same as the one of clingo, its semantics relies on reinterpreting 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 subdirectories containing examples using our frontends 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
,lpmlnalt
,problog
,plog
). Modelpmlnalt
is the alternative definition where hard rules have to be satisfied. When using modelpmln
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
,lpmlnalt
,problog
,plog
). 
query='atom'
Adds a query atom
atom
, e.g. using the example from abovequery='bird(jo)'
. The argument has to be inside single quotation marks (otherwise the commandline might not be able to parse it correctly). 
twosolvecalls
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 lpmlnalt
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 lpmlnalt
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 optenum
option together with balanced=N
.

optenum
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! 
usebackend
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/MLKULeuven/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=lpmlnalt 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/(1p)
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 Plog
[5] J. Pajunen and T. Janhunen. (2021). Solution Enumeration by Optimality in Answer Set Programming. Theory and Practice of Logic Programming, 21(6), 750767.
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