Inference and Resolution
嚜澠nference and Resolution
Introduction to Artificial Intelligence
CS/ECE 348
Lecture 15
October 11, 2001
CS348, Fall 2001
? David Kriegman, 2001
Outline
Last Lecture
每 Wumpus in FOL
每 Inference rules of FOL
每 Unification
This Lecture
每 Generalized Modus Ponens
每 Forward and backward chaining
每 Resolution
Reading
? Chapter 7, 9
CS348, Fall 2001
? David Kriegman, 2001
Upcoming Dealdines
? HW2 has been assigned
每 Due Tuesday, October 16
每 No late assignments
? Midterm:Thursday, October 18, in class.
? Projects for 1 Unit grad students: Available on web.
每 Proposal: Due October 25
CS348, Fall 2001
? David Kriegman, 2001
Deducing Hidden Properties
? ※Squares are breezy near a pit.§
? Diagnostic rule 每 infer cause from effect
?y Breezy(y) ? [?x Pit(x) ＿ Adjacent(x,y)]
? Causal rule 每 infer effect from cause
?x,y Pit(x) ＿ Adjacent(x,y) ? Breezy(y)
? Neither of these is complete 每 e.g. diagnostic rule doesn＊t
tell us that if there is no breeze then there isn＊t a pit nearby.
? Definition of Breezy predicate:
?y Breezy(y) ? [?x Pit(x) ＿ Adjacent(x,y)]
CS348, Fall 2001
? David Kriegman, 2001
Combining Diagnostic & Causal Rules
Diagnostic: ?y Breezy(y) ? [?x Pit(x) ＿ Adjacent(x,y)]
Causal: ?x,y Pit(x) ＿ Adjacent(x,y) ? Breezy(y)
= ?y,x Pit(x) ＿ Adjacent(x,y) ? Breezy(y)
= ?y [? ?x ?(Pit(x) ＿ Adjacent(x,y) ? Breezy(y))]
Duality
= ?y [? ?x ?(? (Pit(x) ＿ Adjacent(x,y)) ˍ Breezy(y))]
Rewrite ?
= ?y [? ?x (Pit(x) ＿ Adjacent(x,y)) ＿ ? Breezy(y)]
DeMorgan
= ?y [? ( [?x (Pit(x) ＿ Adjacent(x,y))] ＿ ? Breezy(y))]
Breezy doesn＊t contain existential variable x
= ?y [? (?x Pit(x) ＿ Adjacent(x,y)) ˍ Breezy(y)]
DeMorgan
= ?y [?x (Pit(x) ＿ Adjacent(x,y))] ? Breezy(y)]
Rewrite as ?
Take conjunction of diagnostic and causal rules to get definition:
?y Breezy(y) ? [ ?x Pit(x) ＿ Adjacent(x,y) ]
P ? Q √ ? Pˍ Q
?(PˍQ) √ (?P) ＿ (?Q)
CS348, Fall 2001
(P＿Q)ˍ(P＿R)
√ P＿(QˍR)
? David
Kriegman, 2001
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