Predicate Logic

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Substitution and Unification Union of θ and δ: θδ is calculated as follows: 1. Apply δ to denominator of θ: {x 1/t 1δ, x 2/t 2δ, .., x n/t nδ} 2. Remove all the form: x i /x i from 1. 3. Remove from δ the form: y i /s i if y i ∈ {x 1 ,x 2 , .., x n } 4. θδ = union( line 2 and 3) Artificial Intelligence: Predicate Logic Slide: 64
Substitution and Unification Union of θ and δ: θ , δ : substitution. ε : empty substitution. E: Expression. Properties: 1. E(θδ) = (Eθ)δ. 2. Eε = E 3. θε = εθ = θ Artificial Intelligence: Predicate Logic Slide: 65
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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 and 44: Universal instantiation (UI) Every
Page 45 and 46: Reduction to propositional inferenc
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: 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
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Predicate Logic

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