First-Order Logic and Inference - Berlin Chen

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Using First-Order Logic• Assertions and Queries– Assertions:• Sentences are added to KB using TELL, such sentencesare called assertionsTELL(KB, King(John))TELL(KB, ∀x King(x) ⇒ Person(x) )– Queries• Questions are asked using ASK, which are also called queriesor goalsASK(KB, King(John))return trueASK(KB, Person(John)return trueASK(KB, ∃x Person (x))return {x/John}A substitutionor binding list20
Using First-Order Logic• Example: The Kinship Domain– One’s mother is one’s female parent∀m,c Mother(m, c) ⇔ (Female(m) ∧ Parent(m, c))– One’s husband is one’s male spouse∀w,h Husband(h, w) ⇔ (Male(h) ∧ Spouse(h, w))– A grandparent is a a parent of one’s parent∀g,c Grandparent(g, c) ⇔ (∃p Parent(g, p)∧Parent(p, c))– A sibling is another child of one’s parents∀x,y Sibling (x, y) ⇔ x≠y ∧ ( ∃p Parent(p, x)∧Parent(p, y))– A first cousin is a child of a parent’s sibling∀x,y FirstCousin(x, y) ⇔ ∃p,ps Parent(p, x) ∧ Sibling(ps, p)∧ Parent(ps, y)21
Page 1 and 2: First-Order Logic and InferenceBerl
Page 3 and 4: Natural Languages• Natural Langua
Page 5 and 6: Logics in General5
Page 7 and 8: Models for FOL• A model contains
Page 9 and 10: Semantics of FOL• The truth of an
Page 11 and 12: Atomic Sentences• An atomic sente
Page 13 and 14: Universal Quantification• The fol
Page 15 and 16: Existential Quantification• The f
Page 17 and 18: • Nested QuantifiersProperties of
Page 19: Review: De Morgan’s Rules∀x ¬P
Page 23 and 24: KB for the Wumpus World• Percepti
Page 25 and 26: Inference Rules for Quantifiers•
Page 27 and 28: Universal/Existential Instantiation
Page 29 and 30: Reduction to Propositional Inferenc
Page 31 and 32: Reduction to Propositional Inferenc
Page 33 and 34: Generalized Modus Ponens (GMP)• F
Page 35 and 36: Standardizing Apart• Eliminate ov
Page 37 and 38: Unification AlgorithmAs matching a
Page 39 and 40: • OperationsForward Chaining- Sta
Page 41 and 42: Example KB• The law is that it is
Page 43 and 44: Example KB• West, who is American
Page 45 and 46: Example KB: FC Proof• Apply Gener
Page 47 and 48: Forward Chaining Algorithmrenaming
Page 49 and 50: Incremental Forward Chaining• Eve
Page 51 and 52: Hard Matching Example• Express a
Page 53 and 54: Example KB: BC ProofPut the query o
Page 55 and 56: Example KB: BC ProofProof Tree55
Page 61 and 62: Properties of Backward Chaining•
Page 63 and 64: Conversion to CNF• Example :Every
Page 65: 65Resolution• The binary resoluti
Page 68 and 69: Resolution: Example Proof 2Problem:
Page 70:
Resolution: Example Proof 2EFD¬Gx/
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First-Order Logic and Inference - Berlin Chen

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