Holyoak, K. J., & Thagard, P. (1989). A computational model of analogical problem solving. In S. Vosniadou & A. Ortony (Eds.), Similarity and analogical reasoning (pp. 242-266). Cambridge: Cambridge University Press.

Author of the summary: Jim R. Davies, 2000, jim@jimdavies.org

Cite this paper for:

• SYSTEM:PI (process of induction)
• since analogical processing is more expensive, it is expected to be a backup measure when you don't have rules to fire. In consequence, we would expect novices in a domain to make more use of analogy.

[p244] Duncker 1945: People search from the goal or from the solution.
The PI system (process of induction) does both using condition/action rules.

[p245] It uses spreading activation for retrieval.It is spread as a side effect of rule activity (unlike ACT*). I.e. when a rule fires, it activates the concepts in the rule. Activated concepts activate new rules.

[p249] Rules can fire in parallel, but this is limited by which are activated.

Ontology of PI: [p252] (also abstract schemata and analogies; see control)

• messages:
  E.g. (army (obj1) true) means obj1 is an army. Messages can be [true, projected to be true, false, projected to be false].
• concepts:
  Concepts are represented as frames such as:

  ARMY
    data type:		concept
    superordinates:	organization
    subordinates:		
    instances:		(army (obj1) true)
    activated by:		
    rules:		R1, R2, R3
  

• rules:
  Rules look like this:

  R1
    data type:		rule
    attatched concepts:	army
    activation:		1
    status:		default
    strength:		0.8
    topic:		movement
    conditions:		(army ($x) true)
  			(between ($y $x $z) true)
  			(road ($y) true)
    actions:		(move-to ($x $y) true effect)
  

• problems:
  A sample problem looks like this:

  DESTROY TUMOR
    data type:       problem
    start:           (radiation (obj4) true)
  		   (tumor (obj5) true)
  		   (flesh (obj6) true)
  		   (patient (obj7) true)
                     (alive (obj7) true)
                     (between (obj6 obj4 obj5) true)
                     (inside (obj5 obj7) true)
    goals:           (alive (obj7) true)
                     (destroy (obj4 obj5) true)
  

[p255] a list of "effectors" are kept with the problem solution, telling what was done to solve it.

PI solves the symbol mismatch problem by having spreading activation between similar concepts like "destroy" and "overcome."

[p256] PI only generates a schema when the new target problem is solved by analogy. In the tumor/fortress problem, the schema looks like "if you want x to overcome z, and some y is between the two, then you might try splitting x."

Control:

1. try to solve fortress by direct attack
2. inference rule shows army destroyed
3. punish rule for direct attack
4. try splitting army
5. the problem "capture fortress" is associated with the concepts that solve the problem under slot "problem solutions."
6. Bi-directional attempt to solve tumor prob
7. try to solve with rules.
8. direct attack inferrs as unsuccessful; punish.
9. the rule firing activates concepts that are attatched to "capture fortress" e.g. "between"
10. detects relevance because of an association between "destroy" and "capture" ("destroying can be brought about my overcoming, which can be brought about by seizing, which can be brought about my capturing." [p254] using rules that produce a chain of subgoals.)
11. mapping based on what caused the activation in the first place. between :: between, capture :: destroy, etc.
12. mapping continues based on the constraints of the initial, activation-based mapping.

    Analogy found between CAPTURE FORTRESS and DESTROY TUMOR
    
      analogous concepts: (capture destroy) (between between)
      analogous objects:  (obj1 obj4) (obj2 obj5)
      source effectors:   (split (obj1) true)
                          (move-serarately-to (obj1 obj2) true)
      new subgoals:       (split (obj4) true)
                          (move-serarately-to (obj4 obj5) true)
    

13. Perform analogous actions on target problem.
14. If the analogy leads to the solution, create an abstract problem schema: "using a force to overcome a target" [p256] This is done by seeing if the rules have a higher order concept in common. There is evidence (Gick & Holyoak 1983) that people do this.

    CAPTURE FORTRESS/DESTROY TUMOR
    
      data type:                  problem
      start:                      (between ($y $x $z) true)
      goals:                      (overcome ($x $z) true)
      effectors used in solution: (split ($x) true effect) 
    

Summary author's notes:

• Differences between this and Galatea:
  
  • bi-directional search
  • inference from rules
  • spreading activation
  • has both analogy and rule inference
  • frames that contain declarative knowledge (called messages) and organizes rules. [p249]
  • production rules that can fire in parallel, but only those attatched to active concepts are candidates.
  • does retrieval
• Similarities between this and Galatea:
  
  • abstract schema :: visual representation