Natural extension without irrelevance relations

If no irrelevance relation is stated concerning the network, then the expressions in Figure 1 and the unitary constraint are the only restrictions on the natural extension. To generate lower and upper bounds on p(d|l), it is necessary to write these thirteen linear constraints (nine are equality constraints and four are inequality constraints) and solve a linear fractional program with the objective function p(d,l)/p(l). The solution of this program produces the lower bound 0 and the upper bound 1 for p(d|l), demonstrating that the absence of irrelevance relations can lead to inferences that are essentially vacuous.