Various networks have been described which will function as content addressable memories; when given an incomplete description of a stored item they will supply those features of the item which are missing from the description. In this paper we consider a more difficult problem, that of designing a network which will also accept a description to which no stored item corresponds, and will supplement such a description by inductive generalization over the items already in store. This problem is tractable only if the ensemble of possible items is restricted in some way. A reasonable restriction is to assume (i) that any item can be fully described by a binary vector of fixed length, where the value of any component indicates the value of the corresponding binary feature; (ii) that no two features are logically independent of one another. Condition (ii) implies for example, that the ensemble does not contain items answering to all four of the descriptions ++..., +-..., -+... and --.... If these conditions are satisfied, the ensemble may be represented as a tree, in which each node corresponds to a possible item and each link to the alteration of one or more features. A simple network is described, incorporating modifiable switches and threshold logic, which will supply all the inferences which could be drawn about an incompletely described item by inspecting this tree. It is possible, furthermore, to give a clear interpretation to the output of the network when the input describes an item which could not possibly belong to the same ensemble as those in store.