This kind of assessing operationality is dynamic It depends on the current

# This kind of assessing operationality is dynamic it

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also illustrate if the searching direction is right. This kind of assessing operationality is dynamic. It depends on the current status and the current goal of performance. What is more, this assessment can generate measurement and efficiency. But this cost much for the system must be tested once operationality is assessed. The operationality is vital to EBL system. However, current methods to detect operationality depend on whether the performance hypothesis can be simplified (these hypothesis are easy to be broken). Though researchers from home and abroad are seeking for effective methods for dealing with simplification, most of the research only treats with theory application while in real applications it is hard to get a satisfied answer. There is still a long way to go for investigation. 9.9 EBL with imperfect domain theory 9.9.1 Imperfect domain theory One of the most important problems in EBL is domain theory. As the premise of EBL, domain theory should be complete and correct. These demands are often hard to meet in real applications and in reality domain theory is always incomplete and incorrect. If the domain theory can not explain the training example, the existing EBG will be invalid.
Explanation-Based Learning 357 The imperfect of domain theory may involve the following conditions: (1) Incomplete Lack of rules and knowledge in the domain theory thus no explanation of training example can be given. (2) Incorrect Some rules in the domain theory is unreasonable thus incorrect explanation might be created. (3) Intractable Domain theory is too complex; the existing resource can not afford to create an explanation tree for training examples. In order to solve the problem of imperfect domain theory, we make some attempts in inverting resolution and deep knowledge based approach. 9.9.2 Inverting Resolution Resolution theorem in first order logic is the foundation of machine theorem proving and the main way to construct explanation in EBL(Muggleton etal., 1988). Resolution theorem Let C 1 ,C 2 be two clauses without any common variables. L 1 , L 2 are two literals of C 1 and C 2 respectively, if there is a most general unifier σ , then clause C= (C 1 - {L 1 }) σ (C 2 - {L 2 }) σ (9.2) is the resolution clause of C 1 and C 2 . Inverting resolution deals with that given C and C 1 how to obtain C 2 . In propositional logic, σ Φ , so the inverting clause (9.2) can be converted into: C =(C 1 C 2 ) - {L 1 ,L 2 } (9.3) From formula (9.3), the following formulas can be concluded (1) if C 1 C 2 = , then C 2 = (C-C 1 ) {L 2 } (2) if C 1 C 2 , C 2 needs to contain the arbitrary sub-set of C 1 -{L 1 }, therefore, generally speaking: C 2i = (C - C 1 ) {L 2 } S 1i (9.4) Here, S 1i P (C 1 -{L 1 }, P( x ) represents the power set of set x. It is obvious if there are n literals in C 1 , the number of solution for C 2 is 2n-1.

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