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This section presents an algorithm called PROLOG-EBG (Kedar-Cabelli and McCarty 1987) that is representative of several explanation-based learning algorithms PROLOG-EBG a sequential covering algorithm (see 10) In other is words, it operates by learning a single Horn clause rule, removing the positive training examples covered by this rule, then iterating this process on the remaining positive examples until no further positive examples remain uncovered When given a complete and correct domain theory, PROLOG-EBG guaranteed to output is a hypothesis (set of rules) that is itself correct and that covers the observed positive training examples For any set of training examples, the hypothesis output by PROLOG-EBG constitutes a set of logically sufficient conditions for the target concept, according to the domain theory PROLOG-EBG a refinement of the EBG is algorithm introduced by Mitchell et al (1986) and is similar to the EGGS algorithm described by DeJong and Mooney (1986) The PROLOG-EBG algorithm is summarized in Table 112

To illustrate, consider again the training example and domain theory shown in algorithm is a seTable 111 As summarized in Table 112, the PROLOG-EBG quential covering algorithm that considers the training data incrementally For each new positive training example that is not yet covered by a learned Horn clause, it forms a new Horn clause by: (1) explaining the new positive training example, (2) analyzing this explanation to determine an appropriate generalization, and (3) refining the current hypothesis by adding a new Horn clause rule to cover this positive example, as well as other similar instances Below we examine each of these three steps in turn

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The first step in processing each novel training example is to construct an explanation in terms of the domain theory, showing how this positive example satisfies the target concept When the domain theory is correct and complete this explanation constitutes a proof that the training example satisfies the target concept When dealing with imperfect prior knowledge, the notion of explanation must be extended to allow for plausible, approximate arguments rather than perfect proofs

PROWG-EBG(TargetConcept, TrainingExamples, DomainTheory) 0 LearnedRules c (1 0 Pos c the positive examples from TrainingExamples 0 for each PositiveExample in Pos that is not covered by LearnedRules, do I Explain: Explanation c an explanation (proof) in terms of the DomainTheory that PositiveExample satisfies the TargetConcept 2 Analyze: SufJicientConditions t the most general set of features of PositiveExample sufficient to satisfy the TargetConcept according to the Explanation 3 Rejine: 0 LearnedRules c LearnedRules NewHornClause, where NewHornCIause is of

NSString * consultantOfficePhone; NSString * consultantFirstName; NSString * consultantStreetAddress; NSString * consultantLastName; NSString * consultantMobilePhone; NSNumber * consultantDayRate; NSSet* entriesForConsultant; *fullName;

TABLE 112 The explanation-based learning algorithm PROLOG-EBG each positive example that is not yet For covered by the set of learned Horn clauses (LearnedRules), a new Horn clause is created This new Horn clause is created by (1) explaining the training example in terms of the domain theory, (2) analyzing this explanation to determine the relevant features of the example, then (3) constructing a new Horn clause that concludes the target concept when this set of features is satisfied

The explanation for the current training example is shown in Figure 112 Note the bottom of this figure depicts in graphical form the positive training example SafeToStack ( O b j l , 0 b j 2 ) from Table 111 The top of the figure depicts the explanation constructed for this training example Notice the explanation, or proof, states that it is SafeToStack O b j l on 0 b j 2 because O b j l is Lighter than O b j 2 Furthermore, O b j l is known to be Lighter, because its Weight can be inferred from its Density and Volume, and because the Weight of 0 b j 2 can be inferred from the default weight of an Endtable The specific Horn clauses that underlie this explanation are shown in the domain theory of Table 111 Notice that the explanation mentions only a small fraction of the known attributes of O b j l and 0 b j 2 (ie, those attributes corresponding to the shaded region in the figure) While only a single explanation is possible for the training example and domain theory shown here, in general there may be multiple possible explanations In such cases, any or all of the explanations may be used While each may give rise to a somewhat different generalization of the training example, all will be justified by the given domain theory In the case of PROLOG-EBG, explanation the is generated using a backward chaining search as performed by PROLOG PROLOGEBG, like PROLOG, halts once it finds the first valid proof

Take a moment to look over this header file. It contains property declarations for all of the attributes and the relationship defined for the Consultant entity in your data model. You have just added one to handle the read-only property fullName. Now implement the getter method in the counterpart file consultant.m (Listing 9 3):