Inference Methods

Full posterior distributions

The following algorithms compute the full posterior distribution over a set of variables Q given the evidence E, P(Q|E).


Performs exact inference by enumerating all possible worlds x\in\mathcal{X} that are consistent with the evidence E, i.e.

P(Q|E) = \frac{\sum_{x \models E\land Q}^{} \phi(x)}{\sum_{x'\models E}{\phi(x')}}


This is intractable for all but the smallest reasoning problems.


Performs approximate inference using the MC-SAT algorithm.

Gibbs Sampling

Performs Gibbs sampling on the ground MRF.

Most Probable Explanation (MPE)

In some cases, one is not interested in the full posterior distribution P(Q|E) over query variables Q given evidence E, but only in the most probable variable assignment of Q, \text{arg max}_QP(Q|E) pracmln provides two algorithms to perform this kind of MPE inference (which is sometimes also referred to as maximum a-posteriori (MAP) inference.


A randomized weighted satisfiability solver that performs simulated annealing.


  • maxsteps: the maximum number simulated annealing steps
  • thr: the threshold for the sum of unsatisfied weighted formulas that needs be undercut for the algorithm to terminate
  • hardw: a constant weight that will temporarily be attached to hard logical formulas.


Performs exact MPE inference by converting the ground MRF into an equivalent weighted constraint satisfaction problem (WCSP) and solving it using the toulbar2 [AdGS10] solver. For more details, see [JMW09].

[AdGS10]D Allouche, S de Givry, and T Schiex. Toulbar2, an open source exact cost function network solver. Technical Report, Technical report, INRIA, 2010.
[JMW09]Dominik Jain, Paul Maier, and Gregor Wylezich. Markov Logic as a Modelling Language for Weighted Constraint Satisfaction Problems. In Eighth International Workshop on Constraint Modelling and Reformulation, in conjunction with CP2009. 2009.