CS.462 Artificial Intelligence SOMCHAI THANGSATHITYANGKUL Lecture 05 : Knowledge Base & First Order...
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Transcript of CS.462 Artificial Intelligence SOMCHAI THANGSATHITYANGKUL Lecture 05 : Knowledge Base & First Order...
CS.462Artificial Intelligence
SOMCHAI THANGSATHITYANGKUL
Lecture 05 : Knowledge Base & First Order Logic
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Knowledge base• A knowledge base KB is a set of sentences. Ex
ample KB: JerryGivingLecture (TodayIsTuesday TodayIsThursday) JerryGivingLecture• It is equivalent to a single long sentence: the conjunction of all sentences ( JerryGivingLecture (TodayIsTuesday TodayIsThursday)) JerryGivingLecture
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Entailment
• Entailment is the relation of a sentenc e logically
follows from other sentences. |= |= if and only if, in every interpreta
tion in which is true, is also true• Deduction theorem: |= if and only
if is valid (always true)
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Natural Deduction • Proof is a sequence of sentences First ones are premises (KB) Then, you can write down on line j the result of
applying an inference rule to previous lines When is on a line, you know KB If inference rules are sound, then KB
Modus
ponens
And-introduct
ion
And-eliminat
ion
Modus
tolens
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Natural deduction example
Step Formula Derivation
1 P Q Given
2 PR Given
3 (Q R) S Given
Prove S
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Natural deduction example• KB:
1. JerryGivingLecture (TodayIsTuesd ay TodayIsThursday)
2. JerryGivingLectureProve: TodayIsTuesday
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Step Formula Derivation
1 JerryGivingLecture (TodayIsTuesday TodayIsThursday)
Given
2 JerryGivingLecture Given
3 JerryGivingLecture (TodayIsTuesday TodayIsThursday)
Biconditional elimination to 1.
4 (TodayIsTuesday TodayIsThursday) JerryGivingLecture
Biconditional elimination to 1.
5 JerryGivingLecture (TodayIsTuesday TodayIsThursday)
Contrapositive to 4.
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Propositional Resolution
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Propositional Resolution Example
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Resolution tree• KB : (A CD) (ADE) (A C)• Prove : (DE)• Negated conclusion : (DE)• Convert KB in the CNF, So we have
KB:1. (A C D)2. (A D E)3. (A C)4. D5. E
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Resolution tree
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Try this (P → Q) → Q , (P → P) → R , (R → S) → ¬(S → Q) Prove R
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