## 9 Processing of Complex Data Analysis Models Using Intelligent Methods
### Deep Knowledge Modeling and Constraint-Based Fast Preprocessing
\[B\leftarrow\Lambda_{i\in I}A_{i} \tag{7}\]  
where the form of the rule is suitable for the backward chaining. This rule is changed when an exclusion \(E(C,Ak)\) is attached to Equation (7): if \(C\) is true, the corresponding \(Ak\) is defeated, which means that its truth value is reverted Equation (8) or it disappears from the antecedent Equation (9) because its significance for '\(B\) is true' is defeated to zero. Furthermore, the variant Equation (10) is researched where the defeated value is changed by another formula. \[\frac{B\leftarrow\Lambda_{i=1}^{z}A_{i},C,E(c,A_{k}),\
eg A_{k}\gets C}{B \gets A_{1}\Lambda A_{2}\Lambda\cdots A_{k-1}\Lambda\
eg A_{k}\Lambda \cdots A_{z}} \tag{8}\]  
\[\frac{C,B\leftarrow\Lambda_{i=1}^{z}A_{i},E(C,A_{k})}{B\gets A_{1} \Lambda\cdots A_{k-1}\Lambda A_{k+1}\Lambda\cdots A_{z}} \tag{9}\]  
\[\frac{C,B\leftarrow\Lambda_{i=1}^{z}A_{i},E(C,A_{k})}{B\gets A_{1} \Lambda\cdots A_{k-1}\Lambda(A_{k}\forall C)\Lambda A_{k+1}\cdots A_{z}} \tag{10}\]  
One of the frequently used health cases is where both antecedent and consequent are changed in the defeated rule. The other frequent case produces a fact from the defeated rule, and this fact contains a non-implicative relation. The defeasible process explores non-classical rule forms, one of them is '\(Ak\) is defeated if \(C\) is true in \(E(C,Ak)\)'. Detailed information concerning this topic is given in book chapter [25]. The defeasible reasoning is applied to test the strength of the investigated process and of its significant features. The quoted binding and pointing constraints significantly improve the defeasible processes. The pointing (indicating) constraints are applied in order to determine both the distance to the goal and the direction of the research. Furthermore, the history of the research process can influence on the pointing direction. The group of pointing constraints can be considered as a generalization of the classical systems of goal/target or fitness functions. In contrast to the classical cases, pointing constraints are data-driven by nature and revert to being direction-driven with accumulated data. For example, if there is information that there was a pain, the data on its coordinates are probably no longer valid. In this case, the exact conclusion is in doubt until enough proof is accumulated. The third researched constraint is named 'crossword'. It is depicted by the triple \(\left\{A,C,E\right\}\) in Figure 10. This type models the process of reasoning on the unknown things based on the accumulated knowledge. In such a way, parts of the searched goal have been found, and by using original evolutionary Puzzle method, a trial to complete the whole solution is attempted. The internal links between the elements of \(\left\{A,C,E\right\}\) are studied using different combinations of the quoted binding and pointing modeling. Many algorithms and data-driven approaches were investigated with the aim to find any binding or pointing solution enlarging the set of the known part from \(G1\). Generally speaking, every pointing constraint was used aiming to diminish the set of selected/processed data and knowledge: the'selection focus' should be narrowed. Pointing to a certain part of the binding area improves the reasoning process. * Type 1: this pointing constraint is based on a priori given special conditions: if \(T_{1}\star T_{2}\cdots\star T_{n}\) are true, then pointing value of \(Y\) is formed, where \(\star\) denotes a logical operation conjunction or disjunction. * Type 2: this pointing constraint is based on conditions: if \(T_{1}\star T_{2}\cdots T_{n}\) are true, then pointing value of \(Y\) is formed, and \(T_{i}\) have been formed in a data-driven manner. \(Y\) is gradually changing its direction and value. On the other hand, in mobile signal processing applications, the pointing constraints show to the center of corresponding binding area. The binding cases frequently concern best signal processing practice, good medical practice, and many analogical examples.