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Mixed mode inferencing is provided by creating an extension to a RETE network to handle both forward and backward chaining efficiently. The extended KETE network is traversed from a root node through intermediate nodes to the rules of the network. The intermediate nodes contain objects that have values assigned by rules, and the intermediate nodes are linked to those rules appropriately. When using the network in a backward chaining context, rules linked to the intermediate node of interest are checked to see if they are active and the rule is solvable. If not, the related rules are checked. Because the system takes advantage of the previously formed PETE network, these checks can be done at the rule nodes without the need to retest each condition. (FIG. - 2)