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Chapter 4

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Chapter 4

1. 1. Dependencies in knowledge Chapter 4
2. 2. Contents <ul><li>Introduction </li></ul><ul><li>Dependency of knowledge </li></ul><ul><li>Partial Dependency of Knowledge </li></ul>
3. 3. 1.Introduction <ul><li>P Q : </li></ul><ul><ul><ul><li>Q is derivable from P , </li></ul></ul></ul><ul><ul><ul><li>Q depends on P </li></ul></ul></ul><ul><li>Developing theories can be is based on discovering inference rules of the form “if…then…” </li></ul><ul><li>Knowledge Q is derivable from Knowledge P , if all elementary categories of Q can be defined in terms of some elementary categories of P </li></ul>
4. 4. 2.Dependency of knowledge <ul><li>Let K=( U ,R) be a knowledge base and let </li></ul><ul><ul><ul><li>Knowledge Q depends on Knowledge P iff </li></ul></ul></ul><ul><ul><ul><li>Knowledge P and Q are equivalent ( ), iff and </li></ul></ul></ul><ul><ul><ul><li>Knowledge P and Q are independent ( ), iff neither nor hold. </li></ul></ul></ul>iff
5. 5. <ul><li>Example 1: </li></ul><ul><ul><li>Given knowledge P, Q </li></ul></ul><ul><ul><li>U/P= {{1,5}{2,8}{3}{4}{6}{7}} </li></ul></ul><ul><ul><li>U/Q= {{1,5}{2,7,8}{3,4,6}} </li></ul></ul>U|P U|Q then
6. 6. Proposition
7. 7. Proposition
8. 8. Proposition
9. 9. 3.Partial Dependency of Knowledge <ul><li>Definition : </li></ul><ul><li>When only part of knowledge Q is derivable from knowledge P, the derivation become partial . </li></ul><ul><li>Let K=( U ,R) be a knowledge base and . Knowledge Q depends in a degree k (0 ≤ k ≤ 1 ) from knowledge P(P ⇒ k Q) iff </li></ul>
10. 10. <ul><li>If k = 1 we say that Q depends totally on P. </li></ul><ul><li>If k < 1 we say that Q depends partially ( in a degree k ) on P. </li></ul><ul><li>Example 2: </li></ul><ul><li>U/Q= {{1}{2,7}{3,6}{4}{5,8}} </li></ul><ul><li>U/P= {{1,5}{2,8}{3}{4}{6}{7}} </li></ul><ul><li>POS P (Q) = {3,4,6,7} </li></ul><ul><li>the degree of dependency between Q and P </li></ul><ul><li>(P⇒ 0.5 Q ) </li></ul>
11. 11. Propositions