Abstract: Expert systems often must be operated under constraints of time or other computer resources. In the past, this has created significant problems since conventional "depth-first" systems will often not be able to arrive at a satisfactory response, or even any response at all, within the limitations of the constraint. Accordingly, an expert system control process and an associated inference network are provided which assign merit values to each inference node (i.e. each proposition) of the inference network. These merit values reflect the processing cost of expanding a node to calculate a likelihood value for the proposition that the node represents. The merit values are then used in the control process to determine which of the nodes will be processed first to calculate likelihood values. In this way, a "best-first" control process is provided which takes account of the actual processing cost of each node in the inference network to establishing which nodes are, in fact, "best" to evaluate first.