Knowledge Representation: Production Systems II

Transcription

1 Knowledge Representation: Production Systems II References: Rich and Knight, Artificial Intelligence, 2nd ed. McGraw-Hill, 1991 Russell and Norvig, Artificial Intelligence: A modern approach, 2nd ed. Prentice Hall,

2 Outline The RETE matching algorithm Conflict resolution strategies 2

3 Matching Let us recall the raining example and add a new fact to the WM New fact: State(Dry) Initial facts: [Raining, Outside] + [State(Dry)] Inference According to the given rules, we may assert that: State(Wet), Develop(Cold) Now known facts are: State(Dry), Raining, Outside, State(Wet), Develop(Cold) The WM is inconsistent! --- as State(Wet) and State(Dry) are asserted at the same time. 3

4 Matching How can we check that with thousands of rules and facts? Using a truth maintenance system Issues: Which global strategy to apply? Forward chaining or backward chaining? Which local strategy to apply? [i.e. which rule should be selected in a recognize-act cycle?] How to deal with the complexity of matching? 4

5 Matching Let us recall that the naïve approach aimed at dealing with matching: in order to find all applicable rules try to match all elements of the working memory against all premises in all rules But... n rules with m premises, on average, and k elements in the working memory lead to nmk possible matches at each cycle Improvement: RETE algorithm 5

6 RETE: System architecture Initial facts WM Rule execution Changes in facts Conflict resolution RETE net Changes in conflict set 6

7 RETE: Algorithm General procedure: Represent all rules in one net Newly generated working memory elements infiltrate the net from above. If they arrive at the bottom, they enlarge the conflict set with the rule instance; else they are added to internal nodes memory Newly deleted working memory elements are treated analogously, but used to narrow the conflict set By sharing and considering updates of the working memory elements only, efficiency can be improved 7

8 RETE: Algorithm Observations Rules have parts of the conditions in common (structural similarity) When a rule is applied the working memory remains almost unchanged (temporal redundancy) Method: compile condition parts of the rule(s) in a net remember previous results and change only those matches that rely on facts that changed 8

9 RETE: Algorithm The net encodes the condition parts (LHS) of the rules Inputs: changes of the working memory (new elements, deleted elements, modified elements) Output: the conflict set (i.e. the applicable rules) 9

10 RETE: Algorithm modified elements are simulated by a deletion The net encodes the condition and parts an addition (LHS) of the rules Inputs: changes of the working memory (new elements, deleted elements, modified elements) Output: the conflict set (i.e. the applicable rules) 10

11 RETE: Algorithm Network of interconnected nodes: input nodes are at the top, output nodes at the bottom Each node represents one or more tests on the LHS of a rule Pattern nodes have one input, and check the names of facts Join nodes have two inputs, and combine facts Terminal nodes at the bottom of the network represent individual rules 11

12 RETE: Network RULE1: IF: (fact1 (atr1?x) (atr2 b)) (fact2 (atr1 c) (atr2?x)) THEN tokens fact1? fact2? atr2 =? b atr1?= c Left.atr1 =? Right.atr2 Join node Activate RULE1 12

13 RETE: Network Some facts (fact1 a b) (fact2 c a) tokens RULE1: IF: (fact1 (atr1?x) (atr2 b)) (fact2 (atr1 c) (atr2?x)) THEN fact1? fact2? atr2 =? b atr1?= c Left.atr1 =? Right.atr2 Join node Activate RULE1 13

14 RETE: Network RULE1: IF: (fact1 (atr1?x) (atr2 b)) (fact2 (atr1 c) (atr2?x)) THEN tokens fact1? fact2? atr2 =? b atr1?= c +(fact1 a b) +(fact2 c a) Left memory Left.atr1 =? Right.atr2 Right memory Join node Activate RULE1 14

15 RETE: Network RULE1: IF: (fact1 (atr1?x) (atr2 b)) (fact2 (atr1 c) (atr2?x)) THEN tokens fact1? fact2? atr2 =? b atr1?= c +(fact1 a b) +(fact2 c a) Left memory Left.atr1 =? Right.atr2 Right memory +((fact1 a b),(fact2 c a)) Activate RULE1 +(R1,(fact1 a b),(fact2 c a)) 15

16 RETE: An example (8-puzzle) RULE-MOVE-RIGHT If cell(x,y,0),cell(x1,y,z), x=x1+1 Then cell(x1,y,0),cell(x,y,z),~cell(x,y,0),~cell(x1,y,z) RULE-MOVE-LEFT If cell(x,y,0),cell(x1,y,z), x=x1-1 Then cell(x1,y,0),cell(x,y,z),~cell(x,y,0),~cell(x1,y,z) RULE-MOVE-UP If cell(x,y,0),cell(x,y1,z), y=y1+1 Then cell(x,y1,0),cell(x,y,z),~cell(x,y,0),~cell(x,y1,z) RULE-MOVE-DOWN If cell(x,y,0),cell(x1,y,z), y=y1-1 Then cell(x,y1,0),cell(x,y,z),~cell(x,y,0),~cell(x,y1,z) 16

17 RETE: An example (8-puzzle) RULE-MOVE-RIGHT If cell(x,y,0),cell(x1,y,z), x=x1+1 Then cell(x1,y,0),cell(x,y,z), ~cell(x,y,0),~cell(x1,y,z) tokens Fact =? cell atr3 =? 0 Left memory Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Activate RULE-MOVE-RIGHT 17

18 RETE: An example (8-puzzle) RULE-MOVE-RIGHT If cell(x,y,0),cell(x1,y,z), x=x1+1 Then cell(x1,y,0),cell(x,y,z), ~cell(x,y,0),~cell(x1,y,z) tokens Fact =? cell atr3 =? 0 Left memory Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Activate RULE-MOVE-RIGHT Left memory Right memory Left.atr1 =? Right.atr1 Left.atr2 =? Right.atr2+1 Activate RULE-MOVE-UP 18

19 RETE: An example (8-puzzle) tokens T1=+ (cell (1,1,1)) Fact =? cell T1 atr3 =? 0 Left memory T1 Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Activate RULE-MOVE-RIGHT Left memory T1 Right memory Left.atr1 =? Right.atr1 Left.atr2 =? Right.atr2+1 Activate RULE-MOVE-UP 19

20 RETE: An example (8-puzzle) T1=+ (cell (1,1,1)) tokens Fact =? cell T1 disappears atr3 =? 0 Left memory T1 Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Activate RULE-MOVE-RIGHT Left memory T1 Right memory Left.atr1 =? Right.atr1 Left.atr2 =? Right.atr2+1 Activate RULE-MOVE-UP 20

21 RETE: An example (8-puzzle) T1=+ (cell (1,1,1)) tokens Fact =? cell T2 = + (cell (1,2,0)) atr3 =? 0 Left memory T1 Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Activate RULE-MOVE-RIGHT Left memory T1 Right memory Left.atr1 =? Right.atr1 Left.atr2 =? Right.atr2+1 Activate RULE-MOVE-UP 21

22 RETE: An example (8-puzzle) T1 = + (cell (1,1,1)) T2 = + (cell (1,2,0)) tokens Fact =? cell T2 atr3 =? 0 T1 T1 T2 T2 T2 T2 Left memory Right memory Left memory Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Left.atr1 =? Right.atr1 Left.atr2 =? Right.atr2+1 Activate RULE-MOVE-RIGHT Activate RULE-MOVE-UP 22

23 RETE: An example (8-puzzle) T1 = + (cell (1,1,1)) T2 = + (cell (1,2,0)) tokens Fact =? cell atr3 =? 0 T1 T1 T2 T2 T2 T2 Left memory Right memory Left memory Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Activate RULE-MOVE-RIGHT Left.atr1 =? Right.atr1 Left.atr2 =? Right.atr2+1 Activate RULE-MOVE-UP T2 & T1 Rule effect is deleting cell(1,2,0) 23

24 RETE: An example (8-puzzle) T1 = + (cell (1,1,1)) T2 = + (cell (1,2,0)) tokens Fact =? cell T3 = - (cell (1,2,0)) T3 atr3 =? 0 T1 T1 T2 T2 T2 T3 T3 T3 T2 T3 Left memory Right memory Left memory Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Activate RULE-MOVE-RIGHT Left.atr1 =? Right.atr1 Left.atr2 =? Right.atr2+1 Activate RULE-MOVE-UP T2 & T1 24

25 RETE: An example (8-puzzle) T1 = + (cell (1,1,1)) T2 = + (cell (1,2,0)) T3 = - (cell (1,2,0)) tokens Fact =? cell T3 atr3 =? 0 T1 T1 T2 T2 T2 T3 T3 X X T3 X T2 X T3 Left memory Right memory Left memory Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Activate RULE-MOVE-RIGHT Left.atr1 =? Right.atr1 Left.atr2 =? Right.atr2+1 Activate RULE-MOVE-UP T2 & T1 25

26 RETE: An example (8-puzzle) T1 = + (cell (1,1,1)) T2 = + (cell (1,2,0)) T3 = - (cell (1,2,0)) tokens Fact =? cell atr3 =? 0 T1 T1 T2 T2 X T2 X X T2 X Left memory Right memory Left memory Right memory Left.atr1 =? Right.atr1+1 Left.atr2 =? Right.atr2 Activate RULE-MOVE-RIGHT Left.atr1 =? Right.atr1 Left.atr2 =? Right.atr2+1 Activate RULE-MOVE-UP X T2&T1 26

27 Conflict resolution Important because it can affect the solution Conflict set is a set of pairs of the form <production rule, matching wm elements> CR strategy can be general or domain specific 27

28 Conflict resolution in OPS5 General strategy: Means-Ends Analysis a) Delete instantiations of rules if they have already been fired b) Try matching first against elements that have entered the WM most recently c) Prefer the most specific rules (i.e. those with more specific preconditions) d) If several rules can be fired then perform a random choice 28

29 Conflict resolution in OPS5 General strategy: MEA a) Delete instantiations of rules if they have already been fired b) Try matching first against elements that have entered the WM To avoid most endless recently loops... c) Prefer the most specific rules (i.e. those with more specific preconditions) d) If several rules can be fired then perform a random choice 29

30 Conflict resolution in OPS5 General strategy: MEA It appears reasonable that more recent elements describe better the current situation Modeled according to the behavior of human short-term memory a) Delete instantiations of rules if they have already been fired b) Try matching first against elements that have entered the WM most recently c) Prefer the most specific rules (i.e. those with more specific preconditions) d) If several rules can be fired then perform a random choice 30

31 Conflict resolution in OPS5 General strategy: MEA a) Delete instantiations of rules if they have already been fired Can be used for modeling exceptions b) Try matching first against elements that have entered the WM most recently c) Prefer the most specific rules (i.e. those with more specific preconditions) d) If several rules can be fired then perform a random choice 31

32 Conflict resolution in OPS5 General strategy: MEA a) Delete instantiations of rules if they have already been fired Can be used for modeling exceptions b) Try matching first against elements that have entered the WM most recently c) Prefer the most specific rules (i.e. those with more specific preconditions) d) If several rules can be fired then perform a random choice 32

33 Conflict resolution in OPS5 General strategy: MEA a) Delete instantiations of rules if they have already been fired b) Try matching first against elements that have entered the WM most recently Using a non-deterministic approach c) Prefer the most specific rules (i.e. those with more specific preconditions) d) If several rules can be fired then perform a random choice 33

34 Conflict resolution in OPS5 Problem specific strategies Add extra conditions to rules to avoid conflicts R1 IF [interested in starter motor] and [engine does not turn] and [battery is not flat] THEN [ask user to test starter motor] Disadvantages mixture of factual knowledge and heuristic knowledge difficult to maintain for large knowledge bases 34

35 Problem-specific conflict resolution Better to separate factual knowledge object level knowledge from from control knowledge meta-level knowledge R1 IF [engine does not turn] and [battery is not flat] THEN [ask user to test starter motor] META-RULE-R1 IF [interested in starter motor] THEN [select rule R1] 35

36 Requirements of control strategies Expressiveness Adequacy (naturalness) Modularity Independence of rule base and control strategy Sensitivity (react to dynamic changes) Stability (continuity in behavior) Compositionality (can add new rules without major unwanted effects) 36

37 Evaluation There is no single most adequate knowledge representation algorithm for everything Choose based on what should be represented and how the knowledge should be processed (inference) 37

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