1. Rules: Knowledge Representation & Manipulation
Artificial Intelligence
CMSC 25000
January 8, 2002

2. Agenda Knowledge Representation: Knowledge Manipulation:
Assertions & Rules
Knowledge Manipulation:
Forward & Backward Chaining
Deduction & Reaction Systems
Costs, Choices, and Mechanisms

3. Representing Knowledge
Assertion:
Statement that something is true
“Stretch is a giraffe”,”The sky is blue”
Collection of assertions: “Working Memory”

4. Representing Knowledge: Rules
If - then rules
If A1, A2
Antecedent
Then B1, B2
Consequent

5. Representing Knowledge: Rules
May include variables, e.g.
Variables: ?x,?y,?z
Same name => same value
If (parent-of ?x ?y),
(parent-of ?y ?z),
then (grandparent-of ?x ?z)

6. Knowledge Manipulation
Forward chaining:
Reason from “if” antecedents to “then” consequents
Backward chaining:
Confirm hypothesis matching “then” patterns by verifying “if” patterns

7. Rule-based Systems Separate knowledge from control Rules
Contrast from typical programming: Integrated
Add
consequent
Assertions
Rules
Rule
Interpreter
Select rule
Match antecedent

8. 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)

9. Forward 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))
Assertions:
F1: runny nose
F2: temp = 101.5
F3: headache
Execution:
R2 Fires: Asserts (signs (nasal congestion))
R4 Fires: Asserts (signs (fever))
R5 Fires: Asserts (signs (achiness))
R6 Fires: Asserts (signs (viremia))
R1 Fires: Asserts (diagnosis influenza)

10. Forward Chaining with variables
IF (parent ?x ?y) (parent A B)
(parent ?y ?z) (parent A C)
THEN (grand-parent ?x ?z) (parent B D)
(parent C E)
(parent ?x ?y) (parent ?y ?z) (grand-parent ?x ?z)
(x:A y:B) (y:A z:B) conflict in y
(y:A z:C) conflict in y
(y:B z:D) (x:A y:B z:D)
(y:C z:E) conflict in y
(x:A y:C) (y:A z:B) conflict in y
(y:B z:D) conflict in y
(y:C z:E) (x:A y:C z:E)
(x:B y:D) (y:A z:B) conflict in y
(x:C y:E) (y:A z:B) conflict in y

11. 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

12. Backward Chaining Test hypothesis
Reason from consequents to antecedents
Use assertions and rules
If no assertions or rules give evidence, ask questions

13. 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

14. 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))

15. 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
(Temp > 100)
Yes
Ask
Yes
(Body-ache)
(Headache)
Ask
Ask No
Yes

16. Reaction Systems Deduction systems Reaction 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

17. 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:

18. 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

19. 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