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All of the remaining operators are easier to describe in terms of a set of four primitive operators Therefore we next define these four primitives which are one step operators that are special cases of  change and appear at the bottom right as leaves in the hierarchy of Figure The first two primitive operators delete and add a add edges We define delete to delete edge 1 2 with the operator schema Operator Schema 2 (Odelete) Let   be an FSA with Boolean algebra   , and let  delete
' be defined with  delete 1  2   for deleted edge   1  2  of Recall that a nonexistent edge has transition condition 0. Operator  detete could therefore be considered a special case of  change that consists only of step (1) and an additional condition that must be met, namely, that delete K 1 2 = ( K 1 2 = 0.

We define add to add edge 1 3 with the operator schema Operator Schema 3 (0add) Let   be an FSA with Boolean algebra   , and let  add
' be defined with add 1 3 for added edge 1 3 of . Operator add could be considered a special case of  change that consists only of step (2) and the additional condition that x 1 3 = 0 prior to applying add The other two primitive operators are specialization spec and generalization gen Specialization and generalization are operators commonly found in the machine learning lit erature eg see Michalski            In the context of an FSA  specialization lowers the level of a particular state to state transition condition in the partial order     whereas general ization raises it  as in Mitchell s Version Spaces  Mitchell condition can be specialized with a meet and can be generalized with a join  which is analogous to adding a conjunct to specialize and a disjunct to generalize as in Michalski Formally  we define specialization and generalization  respectively  as follows Operator Schema 4 (ospec) Let    be an FSA with Boolean algebra    , and let   spec
'. Then we can define spec    K
K ' , where spec  K  1  2

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