Predicate Logic

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Existential instantiation (EI) For any sentence α, variable v, and constant symbol k that does not appear elsewhere in the knowledge base: ∃v α Subst({v/k}, α ) E.g., ∃x Crown(x) ∧ OnHead(x,John) yields: Crown(C1) ∧ OnHead(C1,John ) provided C 1 is a new constant symbol, called a Skolem constant Artificial Intelligence: Predicate Logic Slide: 44
Reduction to propositional inference Suppose the KB contains just the following: ∀x King(x) ∧ Greedy(x) ⇒ Evil(x) King(John) Greedy(John) Brother(Richard,John) Instantiating the universal sentence in all possible ways, we have: King(John) ∧ Greedy(John) ⇒ Evil(John) King(Richard) ∧ Greedy(Richard) ⇒ Evil(Richard) King(John) Greedy(John) Brother(Richard,John ) The new KB is propositionalized : proposition symbols are King(John), Greedy(John), Evil(John), King(Richard ), etc. Artificial Intelligence: Predicate Logic Slide: 45
Page 1 and 2: Chapter 08 Predicate Logic Instruct
Page 3 and 4: Acknowledgment The slides in this P
Page 5 and 6: Why FOL? Pros and cons of propositi
Page 7 and 8: Prepositional Logic: Examples Sente
Page 9 and 10: Predicate Logic: Examples Ability o
Page 11 and 12: Syntax of FOL: Basic elements Cons
Page 13 and 14: Complex sentences Complex sentence
Page 15 and 16: Universal quantification ∀ Ever
Page 17 and 18: Existential quantification ∃ S
Page 19 and 20: Properties of quantifiers ∀x ∀
Page 21 and 22: The kinship domain: Brothers are
Page 23 and 24: Predicate Logic: Representation 1.
Page 25 and 26: Predicate Logic: Representation 6.
Page 27 and 28: Predicate Logic: Representation Gi
Page 29 and 30: Predicate Logic: Proof ¬loyalto(Ma
Page 31 and 32: Predicate Logic: Exception Excepti
Page 33 and 34: Predicate Logic: Exception Excepti
Page 35 and 36: Predicate Logic: Function + Computa
Page 43: Universal instantiation (UI) Every
Page 47 and 48: Resolution Convert to clause form,
Page 49 and 50: Resolution 1. Remove using the equ
Page 51 and 52: 2. Move ¬ next to terms: Resolutio
Page 53 and 54: Resolution 4. Move qualifier to lef
Page 55 and 56: Resolution 6. Remove every qualifie
Page 57 and 58: 7. Convert to CNF. = Resolution [¬
Page 59 and 60: Resolution 9. Add every qualifier t
Page 61 and 62: Substitution and Unification X: Va
Page 63 and 64: Substitution and Unification Union
Page 65 and 66: Substitution and Unification Union
Page 67 and 68: Substitution and Unification mgu:
Page 69 and 70: Dis-set: Example: Substitution and
Page 71 and 72: Substitution and Unification Claus
Page 73 and 74: Substitution and Unification Resol
Page 75 and 76: Substitution and Unification Proof
Page 77 and 78: # 1 2 3 4 5 6 7 8 9 10 11 Clauses m
Page 79 and 80: Homeworks Prove: ¬alive(Marcus, no

Predicate Logic

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