Markov Logic Network (MLN)

A Markov Logic Network (MLN) is a Markov Network based on set of 2-Tuples [math]\displaystyle{ (F,w) }[/math] where [math]\displaystyle{ F }[/math] is a first-order logic sentence, and [math]\displaystyle{ w }[/math] is a real number weight (exponential).

Context:
- It can be a member of a Markov Logic Network Family.
- It can be thought of as an Undirected Par-Factor Graph.
- It can be used as a Statistical Relational Language that combines First-Order Logic and Markov Networks.
- It can support Soft Logical Constraints which become less probable given conflicting data.
- It can range from being a Tractable Markov Logic Network to being an Intractable Markov Logic Network.
Example(s):
- a Tractable Markov Logic Network.
  - [P(a,x) ∨ Q(b) ∨ ¬R(x), 0.297].
  - [P(x,a) ∨ Q(x) ∧ P(y,a) ∨ Q(b), 0.972].
- …
Counter-Example(s):
- an HMM Network.
- a First-Order Logic Formula.
- a Sum-Product Network.
See: Markov Logic; Statistical Relational Learning; Markov Random Field; Log-Linear Model; Graphical Model; Satisfiability; Inductive Logic Programming; Knowledge-based Model Construction; Markov Chain Monte Carlo; Pseudo-Likelihood;Bayesian Network; Graphical Model Learning; Markov Chain.

References

(Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Markov_logic_network
- A Markov logic network (or MLN) is a probabilistic logic which applies the ideas of a Markov network to first-order logic, enabling uncertain inference. Markov logic networks generalize first-order logic, in the sense that, in a certain limit, all unsatisfiable statements have a probability of zero, and all tautologies have probability one.