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

Agenda Knowledge Representation: Knowledge Manipulation: 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 Antecedent Then B1, B2 Consequent

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)

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 Rules Contrast from typical programming: Integrated Add consequent Assertions Rules Rule Interpreter 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)) (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)

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

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

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

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:

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