lec18

# Modus ponens pw qw q y s y yw pw sw true

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Canonical forms for resolution Conjunctive Normal Form (CNF) Implicative Normal Form (INF) P( w) ⇒ Q( w) True ⇒ P ( x) ∨ R ( x) Q( y ) ⇒ S ( y ) R( z ) ⇒ S ( z ) ¬P ( w) ∨ Q ( w) P( x) ∨ R ( x) ¬Q ( y ) ∨ S ( y ) ¬R ( z ) ∨ S ( z ) CS 460, Session 18 23 Inference in First-Order Logic • Resolution Proofs to show S(A) is entailed In a forward- or backward-chaining algorithm, just as Modus Ponens. P(w) ⇒ Q(w) Q( y) ⇒ S ( y) {y/w} P(w) ⇒ S(w) True ⇒ P ( x ) ∨ R ( x) {w/x} R( z ) ⇒ S ( z ) True ⇒ S ( x) ∨ R( x) {x/A,z/A} True ⇒ S ( A) CS 460, Session 18 24 Inference in First-Order Logic • Refutation proof to show S(A) is entailed P(w) ⇒ Q(w) Q( y) ⇒ S ( y) {y/w} P(w) ⇒ S(w) True ⇒ P ( x ) ∨ R ( x) {w/x} R( z ) ⇒ S ( z ) True ⇒ S ( x) ∨ R( x) {z/x} ( KB ∧ ¬P ⇒ False) ⇔ ( KB ⇒ P ) True ⇒ S ( A) S ( A) ⇒ False {x/A} True ⇒ False CS 460, Session 18 25 Example of Refutation Proof (in conjunctive normal form) (1) (2) (3) (4) Cats like fish Cats eat everything they like Josephine is a cat. Prove: Josephine eats fish. ¬cat (x) ∨ likes (x,fish) ¬cat (y) ∨ ¬likes (y,z) ∨ eats (y,z) cat (jo) eats (jo,fish) CS 460, Session 18 26 Backward Chaining Negation of goal wff: ¬ eats(jo, fish) ¬ eats(jo, fish) ¬ cat(y) ∨ ¬likes(y, z) ∨ eats(y, z) θ = {y/jo, z/fish} ¬ cat(jo) ∨ ¬likes(jo, fish) cat(jo) θ=∅ ¬ cat(x) ∨ likes(x, fish) ¬ likes(jo, fish) θ = {x/jo} ¬ cat(jo) cat(jo) ⊥ (contradiction) CS 460, Session 18 27 Forward chaining ¬cat (X) ∨ likes (X,fish) cat (jo) \ / ¬cat (Y) ∨ ¬likes (Y,Z) ∨ eats (Y,Z) likes (jo,fish) \ / ¬cat (jo) ∨ eats (jo,fish) cat (jo) \ / ¬ eats (jo,fish) eats (jo,fish) \ / CS 460, Session 18 28 Question: • When would you use forward chaining? What about backward chaining? • A: • FC: If expert needs to gather information before any inferencing • BC: If expert has a hypothetical solution CS 460, Session 18 29...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online