Lecture-11

# Lecture-11 - Artificial Intelligence CS 165A 165A Tuesday...

This preview shows pages 1–10. Sign up to view the full content.

Artificial Intelligence S 165A CS 165A Tuesday, Feb 8, 2011 ference (Ch 9) Inference (Ch. 9) 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Notes • Midterm, this Thursday –O n e H o u r – Close Book 2
What we’ve been talking about Complete and sound inference procedures ew inference rules: New inference rules: – Universal Instantiation (gets rid of ) – Existential Instantiation (gets rid of ) – Existential Introduction (adds ) • Generalized Modus Ponens • Generalized (First-Order) Resolution – Complete but semidecidable nification Unification – Finds the substitution(s) necessary to make two sentences match •C o n junctive normal form (CNF) 3 j( )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Generalized Modus Ponens • For atomic sentences p i , p i ', and q , where there is a substitution such that S UBST ( , p ' ) = S UBST ( , p ) for all i i i , then Specific facts General rule ) , ( ) ( , , , , 2 1 2 1 q SUBST q p p p p p p n n • How to prove this? Instantiated conclusion 4
Unification Unification takes two atomic sentences p and q and returns a substitution that would make p and q look the same (or else it fails) U NIFY ( p, q ) = where S UBST ( , p ) = S UBST ( , q ) is the unifier of the sentences p and q •E x a m ples p = Knows(John, x ) q = Knows(John, Jane) = { x /Jane} p = Knows(John, x ) q = Knows( y , Fred) = { x /Fred, y /John} p = Knows(John, x ) q = Knows( y , MotherOf(y)) = { x /MotherOf(John), y /John} p = Knows(John, x ) q = Knows( x , Mary) = fail p = Knows(John, x ) q = Knows( x , Mary) 5 1 2 = { x 1 /Mary, x 2 /John}

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Incompleteness of GMP x P(x) Q(x) x P(x) R(x) Q(x) (x) x Q(x) S(x) x R(x) S(x) Want to conclude S(A) S(A) is true if Q(A) or R(A) is true, and one of those must be true because either P(A) or P(A) Incomplete: there are entailed sentences that the procedure cannot infer. 6
Inference (search) strategies Forward chaining Generalized Modus Ponens ackward chaining Backward chaining 7

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Generalized Modus Ponens in Horn FOL • A Horn clause is a sentence of the form: x (P1(x) ˄ P2(x) ˄ ... ˄ Pn(x)) Q(x) – where there are 0 or more Pi 's, and the Pi 's and Q are positive (i.e., n egated) literals un-negated) literals • Horn clauses represent a subset of sentences in FOL (First Order Logic). For example, P(a) ˅ Q(a) is not a Horn clause. • Generalized Modus Ponens (GMP) is complete for KBs containing only Horn clauses – Proofs start with the given axioms/premises in KB, deriving new ntences using GMP until the goal is derived. This defines a sentences using GMP until the goal is derived. This defines a forward chaining inference procedure because it moves “forward” from the KB to the goal. 8
Example of forward chaining All cats like fish. Cats eat everything they like. Ziggy is a cat. Data-driven KB = at(x) ikes(x Fish) 1. x cat(x) likes(x, Fish) 2. x y (cat(x) ˄ likes(x,y)) eats(x,y) 3. cat(Ziggy) Goal : Does Ziggy eat fish?

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}

### Page1 / 39

Lecture-11 - Artificial Intelligence CS 165A 165A Tuesday...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online