Eliminate existential quantification skolem function

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Unformatted text preview: (∀x)(¬P(x) ∨ ((∀y)(¬P(y) ∨ P(f(x,y))) ∧ (∃y)(Q(x,y) ∧ ¬P(y)))) 4. Standardize variables apart (∀x)(¬P(x) ∨ ((∀y)(¬P(y) ∨ P(f(x,y))) ∧ (∃z)(Q(x,z) ∧ ¬P(z)))) CS 460, Session 18 17 Examples: Converting FOL sentences to clause form… 5. Eliminate existential quantification – Skolem function g introduced: (∀x)(¬P(x) ∨((∀y)(¬P(y) ∨ P(f(x,y))) ∧ (Q(x,g(x)) ∧ ¬P(g(x))))) 6. Drop universal quantification symbols (¬P(x) ∨ ((¬P(y) ∨ P(f(x,y))) ∧ (Q(x,g(x)) ∧ ¬P(g(x))))) 7. Convert to conjunction of disjunctions (¬P(x) ∨ ¬P(y) ∨ P(f(x,y))) ∧ (¬P(x) ∨ Q(x,g(x))) ∧ (¬P(x) ∨ ¬P(g(x))) CS 460, Session 18 18 Examples: Converting FOL sentences to clause form… 8. Create separate clauses containing only disjunctions ¬P(x) ∨ ¬P(y) ∨ P(f(x,y)) ¬P(x) ∨ Q(x,g(x)) ¬P(x) ∨ ¬P(g(x)) 9. Standardize variables so that each clause uses different 9. variables ¬P(x) ∨ ¬P(y) ∨ P(f(x,y)) ¬P(z) ∨ Q(z,g(z)) ¬P(w) ∨ ¬P(g(w)) CS 460, Session 18 19 Resolution proof CS 460, Session 18 20 Resolution proof CS 460, Session 18 21 Resolution proof: definite clauses ¬ CS 460, Session 18 22 Inference in First-Order Logic •...
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This note was uploaded on 02/19/2014 for the course CSCI 460 taught by Professor Narayanaswamy during the Spring '08 term at USC.

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