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# Chapter 4

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• 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