### Table 4: Algorithm for induction

"... In PAGE 4: ... Then it invokes the induction process and either returns back with the induced definition or fails if the induction fails. Table4 outlines the algorithm for induction. During in- duction, an agent first induces any undefined predicates be- fore using them as background knowledge.... ..."

### Table 9: Induction variables

"... In PAGE 23: ...Table 9: Induction variables Table9 displays the variables which have been analysed during the inductive analysis. (Nu- merical variables are represented by numbers and logical variables are represented by combining similar data into groups, e.... ..."

### Table 1: Induction Variables

"... In PAGE 12: ... Also, parts of induced rules rather than whole induced rules may suggest patterns worthy of closer examination. The variables used are summarised in Table1 and the nal induction database with the logical groupings implemented is shown in Table 2 It is important when applying techniques such as rule induction to plan in advance which data needs to be collected. Traditional statistical approaches demand values for dependent and independent variables, but these alone are frequently inadequate for the successful application of classi cation approaches.... ..."

### Table 3: Inductive conditions

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### Table II: Inductive Rules

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### Table 1 Induction Results

"... In PAGE 10: ... The predictive accuracy for a given run is the average of the 10 corresponding trials and the predictive accuracy for the dataset is the average of the 10 runs. Results are shown in Table1 . In the second and third columns, the first number represents predictive accuracy on the test set and the second number represents the ratio of the size (in number of rules) of the final knowledge base to the number of examples used in learning.... ..."

### Table 4: A Semantics for CTRSs as ordered -algebra-transformers The carrier set of [[ ]](A) is the carrier of A. The order of [[ ]](A) is de ned inductively by

"... In PAGE 6: ... In addition, we take the many-step reduction relation as being of primary importance since it is usually this relation that one wants to reason about. Thus we de ne a term reduction algebra in Table4 which takes a pre-order P of variables and rewrites between them and returns a pre-order T (P) of terms and rewrites between them. This term reduction algebra is the direct generalisation of the term algebra construction of section ?? which takes a set of variables X and returns a set of terms T (X).... ..."