Chapter 4
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Transcript

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