The dPASP framework provides a high-level declarative language for describing sophisticated probabilistic reasoning tasks that can combine perception and logical reasoning. dPASP programs are made of probabilistic choices and logic rules (think of if-then rules), allowing easy specification of uncertain and logic knowledge. Notably, the probabilities in the program can arise as outputs of neural network classifiers, and both the statistical model and logic program can be jointly optimized by making use of efficient gradient-based learning libraries (e.g. PyTorch).
dPASP has both a domain-specific language (DSL) and command-line interpreter (parser) for that language, which can be used as a standalone tool. Alternatively, dPASP can be accessed as Python library or more directly through its C backend.
The easiest way to get started is by reading the tutorial Learning dPASP Through Examples.
dPASP allows for several semantics by combining logic programming semantics and probabilistic semantics:
- Stable semantics;
- Partial Stable semantics;
- L-Stable semantics;
- smProbLog semantics.
- Credal semantics;
- MaxEnt semantics.
There are two uses of the systems: learning and querying. Currently, learning is only available for the MaxEnt-Stable semantics.
Learning and querying can either be made by (highly inneficient) enumerative algorithms and (more efficient) approximate inference. Enumerative algorithms are available to all possible (logic and probabilistic) semantics, while currently only MaxEnt-Stable semantics implements all approximate algorithms. Developing more efficient and accurate approximate algorithms is a current active line of research.
Here's a simple example of dPASP for inference in probabilistic logic programs (no neural networks and no learning).
Assuming you have dPASP installed and configured (see the tutorial if not), open a Python Shell and load the Python library by:
pasp examples/earthquake.plpOne may need to manipulate output probabilities, in which case the Python API can be used instead.
import paspTo parse the program into dPASP internal's data struct we use
P = pasp.parse("examples/earthquake.plp")We can also specify a probabilistic logic program string using the dPASP DSL.
Here we have a program enconding graph 3-coloring (lines starting with % are comments):
program_str = '''
% Build a random graph with n vertices.
#const n = 5.
v(1..n).
% The choice of p reflects the sparsity/density of the random graph.
% A small p produces sparser graphs, while a large p prefers denser graphs.
0.5::e(X, Y) :- v(X), v(Y), X < Y.
e(X, Y) :- e(Y, X).
% A color (here the predicate c/2) defines a coloring of a vertex.
% The next three lines define the uniqueness of a vertex's color.
c(X, r) :- not c(X, g), not c(X, b), v(X).
c(X, g) :- not c(X, r), not c(X, b), v(X).
c(X, b) :- not c(X, r), not c(X, g), v(X).
% Produce a contradiction if two neighbors have the same color.
f :- not f, e(X, Y), c(X, Z), c(Y, Z).
#semantics lstable.
% Query the probability of vertex a being red.
#query(c(1, r)).
% Query the probability of the edge e(1, 2) existing given that the graph is not 3-colorable.
#query(e(1, 2) | undef f).
% Query the probability of the graph not being 3-colorable.
#query(undef f).'''We may then pass program_str to dPASP as a string by using the from_str=True keyword.
P = pasp.parse(program_str, from_str=True)You can check that the program was correctly parsed by inspecting the object P
>>> P
<Logic Program:
#const n = 5.
v(1..n).
e(X, Y) :- e(Y, X).
_e(X, Y) :- _e(Y, X).
c(X, r) :- not _c(X, g), not _c(X, b), v(X).
_c(X, r) :- not c(X, g), not c(X, b), _v(X).
c(X, g) :- not _c(X, r), not _c(X, b), v(X).
_c(X, g) :- not c(X, r), not c(X, b), _v(X).
c(X, b) :- not _c(X, r), not _c(X, g), v(X).
_c(X, b) :- not c(X, r), not c(X, g), _v(X).
f :- not _f, e(X, Y), c(X, Z), c(Y, Z).
_f :- not f, _e(X, Y), _c(X, Z), _c(Y, Z).
_c(X, g) :- c(X, g).
_e(X, Y) :- e(X, Y).
_c(X, b) :- c(X, b).
_f :- f.
_c(X, r) :- c(X, r).
_v(1..n) :- v(1..n).,
Probabilistic Rules:
[0.5::e(X, Y) :- v(X), v(Y), X < Y],
Queries:
[ℙ(c(1,r)), ℙ(e(1,2) | undef f), ℙ(undef f)]>To run the program:
>>> P()
ℙ(c(1,r)) = [0.000000, 1.000000]
ℙ(e(1,2) | undef f) = [0.772727, 0.772727]
ℙ(undef f) = [0.064453, 0.064453]
---
Querying: 0h00m01s
array([[0. , 1. ],
[0.77272727, 0.77272727],
[0.06445312, 0.06445312]])This software is being developed by the KAMeL group and the Center for Artificial Intelligence of the University of São Paulo. If you use this software, please acknowledge by citing the paper below: