Transcript Rules: Knowledge Representation & Manipulation

Rules:
Knowledge Representation &
Manipulation
Artificial Intelligence
CMSC 25000
January 8, 2002
Agenda
• Knowledge Representation:
– Assertions & Rules
• Knowledge Manipulation:
– Forward & Backward Chaining
– Deduction & Reaction Systems
• Costs, Choices, and Mechanisms
Representing Knowledge
• Assertion:
– Statement that something is true
• “Stretch is a giraffe”,”The sky is blue”
– Collection of assertions: “Working Memory”
Representing Knowledge: Rules
• If - then rules
If
A1,
A2
Then
B1,
B2
Antecedent
Consequent
Representing Knowledge: Rules
• May include variables, e.g.
If (parent-of ?x ?y),
(parent-of ?y ?z),
then (grandparent-of ?x ?z)
• Variables: ?x,?y,?z
– Same name => same value
Knowledge Manipulation
• Forward chaining:
– Reason from “if” antecedents to “then” consequents
• Backward chaining:
– Confirm hypothesis matching “then” patterns by
verifying “if” patterns
Rule-based Systems
• Separate knowledge from control
– Contrast from typical programming: Integrated
Add
consequent
Assertions
Rule
Interpreter
Rules
Select rule
Match antecedent
Forward Chaining
• Identify triggered rules
– Antecedents match assertions
– Match variables -> rule instances
• Select a triggered rule to fire
– Conflict resolution strategy: first, random, LRU,
combination
• Fire a rule
– Add consequents to list of assertions (deduction)
– Perform action(s) in consequent (reaction)
Forward Chaining Example
R1: if (signs (nasal congestion))
R4: if (temp >100)
(signs (viremia))
then (signs (fever))
then (diagnosis influenza)
R5: if (headache)
R2: if (runny nose)
then (signs (achiness))
then (signs (nasal congestion))
R6: if (signs (fever))
R3: if (body-aches)
(signs (achiness))
then (signs (achiness))
(cough)
Assertions:
then (signs (viremia))
F1: runny nose
Execution:
F2: temp = 101.5
R2 Fires: Asserts (signs (nasal congestion))
F3: headache
R4 Fires: Asserts (signs (fever))
R5 Fires: Asserts (signs (achiness))
R6 Fires: Asserts (signs (viremia))
R1 Fires: Asserts (diagnosis influenza)
Forward Chaining with variables
IF
(parent ?x ?y)
(parent ?y ?z)
THEN (grand-parent ?x ?z)
(parent
(parent
(parent
(parent
A
A
B
C
B)
C)
D)
E)
(parent ?x ?y) (parent ?y ?z) (grand-parent ?x ?z)
(x:A y:B)
(y:A z:B)
(y:A z:C)
(y:B z:D)
(y:C z:E)
conflict
conflict
(x:A y:B
conflict
in y
in y
z:D)
in y
(x:A y:C)
(y:A z:B)
(y:A z:C)
(y:B z:D)
(y:C z:E)
conflict
conflict
conflict
(x:A y:C
in y
in y
in y
z:E)
(x:B y:D)
(y:A
(y:A
(y:B
(y:C
z:B)
z:C)
z:D)
z:E)
conflict
conflict
conflict
conflict
in
in
in
in
y
y
y
y
(x:C y:E)
(y:A
(y:A
(y:B
(y:C
z:B)
z:C)
z:D)
z:E)
conflict
conflict
conflict
conflict
in
in
in
in
y
y
y
y
Forward Chaining: Analysis
• Reason from antecedents to consequents
– Trigger rules if all antecedents match assertions
– Add assertions or do actions in consequents
• May be computationally expensive
– Many possible deductions to make
– Brute force approach: k antecedents, N assertions
• N^k!!
– Rete method
Backward Chaining
• Test hypothesis
– Reason from consequents to antecedents
– Use assertions and rules
– If no assertions or rules give evidence, ask
questions
Backchain(G) - Rule interpreter
If G matched assertion in database, then return True
Else
If there are rules whose consequent matches G
For each matching rule R
For each antecedent C of R
If Backchain(C) is true, proceed
Else go to next rule.
Return True /* when all antecedents are true */
Return False /* when no matching rule succeeds */
Else, ask user if G is true.
If answer is “yes” return True,
Else return False.
From Lozano-Perez, April 00
Backward Chaining Example
R1: if (signs (nasal congestion))
(signs (viremia))
then (diagnosis influenza)
R2: if (runny nose)
then (signs (nasal congestion))
R3: if (body-aches)
then (signs (achiness))
R4: if (temp >100)
then (signs (fever))
R5: if (headache)
then (signs (achiness))
R6: if (signs (fever))
(signs (achiness))
(cough)
then (signs (viremia))
Backward Chaining Example
Hypothesis: (diagnosis influenza)
Diagnosis Influenza
AND
(Signs (nasal congestion))
(Signs (viremia)
AND
(Runny nose) (Signs (fever)) (Signs (achiness))(cough)
Ask
Ask
OR
Yes
Yes
(Temp > 100)
Ask
Yes
(Body-ache) (Headache)
Ask
Ask
No
Yes
Reaction Systems
• Deduction systems
– Produce new assertions
– Keep firing all triggered rules
• Order less important
• Reaction systems
– Produce arbitrary actions: assertions, printing,
moving, bagging
– Side effects -> Order important
Reaction System: Example
• For example,
IF
(at ?x ?y)
(move ?x to ?z)
ADD
(at ?x ?z)
DELETE (move ?x to ?z)
(at ?x ?y)
• Assume an initial database:
– (at A room1) (move A room2)
• Then the rule would add: (at A room2)
• And, delete:
– (at A room1) (move A room2)
Conflict Resolution
•
•
•
•
•
When >1 rule is triggered, which fires??
First: Rules are ordered. Fire first triggered.
Random: Randomly select a rule to fire
Most specific: Fire rule with most antecedents
Least recently fired: Avoids rule starvation.
– Combination
• Design rule set wrt conflict resolution strategy
Conflict Resolution: Deduction
• Generally, less important,but
• Possible to create infinitely recursive rule
– if ?x, (not (not ?x))….
• Need conflict resolution
– Allow other rules to fire
• E.g. stop rule