Logical Inference Algorithms and Matrix Representations for
  Probabilistic Conditional Independence
  Logical inference algorithms for conditional independence (CI) statements
have important applications from testing consistency during knowledge
elicitation to constraintbased structure learning of graphical models. We prove
that the implication problem for CI statements is decidable, given that the
size of the domains of the random variables is known and fixed. We will present
an approximate logical inference algorithm which combines a falsification and a
novel validation algorithm. The validation algorithm represents each set of CI
statements as a sparse 0-1 matrix A and validates instances of the implication
problem by solving specific linear programs with constraint matrix A. We will
show experimentally that the algorithm is both effective and efficient in
validating and falsifying instances of the probabilistic CI implication
problem.
