Analogical thinking


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A presentation about two theories of analogical reaoning.

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Analogical thinking

  1. 1. Analogical Thinking 5
  2. 2. A Wise Man Once Said Shore, Bradd. Culture in mind: Cognition, culture, and the problem of meaning. Oxford University Press, USA, 1996.
  3. 3. Do you see something funny here?“That’s a really small slice you have there.”“Oh boy! That dinosaur exhibit was huge !”“Yeah I guess you are right.”“The referee made a terribly wrong decision.”Why does green signal mean let’s go ahead with something? And whydoes someone give you a red flag to warn about a potential danger? “Lakoff, George, and Mark Johnson. Metaphors we live by. Vol. 111. London: Chicago, 1980.”
  4. 4. What is an Analogy?• It is not a mere numerical count of the number of features/attributes which map from a source concept to a target concept.• It is not a general account of relatedness.“An analogy is an assertion that a relational structure that normally applies in one domain can be applied in another domain”
  5. 5. Preliminary Assumptions• Domains and situations are a system of objects, object Street Domain MOTION(Vehicle attributes and relations between , Stop) objects• Knowledge = Propositional Network of nodes+predicates CAUSES[COLOR(Signal, Red), Start MOTION(Vehicle, Stop)]• Attributes vs. Relations; First- Order vs. Second-Order Predicates MOTION(Vehicle , Start)• Representations mirror cognitive constructs Causal Relations
  6. 6. The next time your advisor Red Flags you… Academic Domain PROGRESS(Research, Halted) RESULTS[PROGRESS(Research, Halted), Stop RED_FLAG(Professor, Student)] PROGRESS(Research, Smooth) Diagnostic Relations
  7. 7. Structure Mapping: Interpretation Rules for Analogy Class Hierarchy Analogy A T(Target) is (like) a B(Base) Vehicle Target Is-a Is like-a Car Truck Base Is this a meta-analogy?!
  8. 8. Let’s take an example“…What light from yonder window breaks?/It is the east, and Juliet is thesun!...”I bet you would know this: “Twinkle, twinkle little star, How I wonder what you are Up above the world so high, Like a diamond in the sky.”
  9. 9. Rule 1: Discard Attributes of ObjectsStar Diamond• BRIGHTNESS: An absolute measure in • BRIGHTNESS lumens. BRIGHTNESS(Star) = x lm• DISTANCE: Distance from Earth (or some • RADIUS (?) other referential celestial object). DISTANCE(Star, Earth) = y x 10z km • CHEMICAL COMPOSITION: Cannot obviously have a 1:1 match with a star• LUMINOSITY. This is the amount of energy generated in the star and released as electromagnetic radiation. • TEMPERATURE• RADIUS • Moh’s Scale of HARDNESS• CHEMICAL COMPOSITION • COST CARBON_CONTENT(Star) = k NITROGEN_CONTENT(Star) = l • VALUE AS GIFT• TEMPERATURE
  10. 10. Rule 2: Preserve Relations Between Objects Star Diamond • Covered by several layers of thick, highly • Covered by several layers of thick, highly carbon-dense gaseous layers. carbon-dense layers. SURROUNDS(Diamond, SURROUNDS(Star, Carbon Layers) Carbon Layers) • Appears to twinkle when viewed from a • Appears to twinkle when viewed from a distance. APPEARANCE(Twinkles, Distance) distance. APPEARANCE(Twinkles, Distance) • Twinkling is caused by multiple refractions of • Twinkling is caused by multiple refractions of light in differently dense layers of the light in differently dense (solid) layers of the atmosphere, eventually leading to total internal diamond, eventually leading to total internal reflection. reflection. 1. CAUSES[SURROUNDS(Star, Carbon Layers), 1. CAUSES[SURROUNDS(Diamond, Carbon MULTIPLE_REFRACTIONS(Light)] Layers), MULTIPLE_REFRACTIONS(Light)] 2. CAUSES[MULTIPLE_REFRACTIONS(Light), 2. CAUSES[MULTIPLE_REFRACTIONS(Light), APPEARANCE(Twinkles, Distance)] APPEARANCE(Twinkles, Distance)]Rule 3: The Systematicity Principle (aka more interesting = more appropriate) [Isomorphism Constraint]
  11. 11. Noteworthy Points• Rules are purely based on the structural representations of knowledge.• Content plays a limited role.• Need to express representations consistently across domains.• Establishing “seemingly correct” relationships does NOT ensure an instantiation of the concept mapping in the target.• Technique can be used to generate hypotheses in a semi-automated manner. No scope for verification of the hypothesis.• Experiments/observations/methods exist for generating such candidate relations for analogy mapping (e.g.., mass spectrometry in the case of an atom to estimate weight of the nucleus and electrons)
  12. 12. Domain Comparisons – A Continuum of Categories • Literal Similarity: A large subset of attributes as well as relations match between the source andAnalogy the target. “The sun is a star like Attribute Matches the Alpha Centauri”. few many • Analogy: There is a low attribute match, but it is possible to Abstraction establish a high relation match. “The structure of the atom is Relation Matches similar to the solar system”. few many • Abstraction: Source and Target concepts are not instantiated. “The main driving force in an atom is the centrifugal force of rotation along a fixed orbit”. Literal Similarity
  13. 13. Anomaly Attribute Matches “Twinkle, twinkle little star, few many How I wonder what you are Up above the world so high, Relation Matches Like an iPod Touch in the sky.” few many• Hardly any (or no) attribute as well as relational matches.• “Totally unrelatable” Anomaly• A conceptual fallacy if assumed to be true. Its ABSURD!
  14. 14. Empirical Support of the Structure Mapping Theory• Interpretation of rules = Meaning(Parti)• Rules clearly demarcate the boundaries between different categories of domain comparisons.• Semantic relationships during the mapping process are established syntactically (i.e., according to a well- defined set of rules and a consistent notation)
  15. 15. Related Research• Merlin System: Mechanism for viewing a target as a similar object to a source. Involves explicitly comparing their shared and non-shared predicates.• Winston’s propositional representation: Perform an algorithm similar to forward chaining to derive certain general (hidden) rules from established analogies.• Similar work by Gick & Holyoak: Constructing general schemas representing the transformation in problem-solving techniques in parallel to analogical matching.• Theory of Analogical Shift Conjecture: Adapting the solution of a problem in a different domain, to solve a “similar” problem in one’s domain.
  16. 16. Analogical Shift Conjecture Domain A Domain X Problem Statement Select problem from X where problem_type “LIKE” A.problem_type “Similar” Abstraction Problem Abstracted Existing Abstraction Solution Solution Solution to 1. Understand causal relations between domains Adapt/Modify Problem 2. A new relational model/data store required to store sematic relations between objects
  17. 17. Analogical Mapping by Constrain Satisfaction
  18. 18. The Mapping QuestionComponents of Analogy 1. Selecting a “feasible” source 2. Mapping 3. Analogical Inference/Knowledge Transfer 4. Learning• Correct conceptual mapping is central to the establishment of “meaningful” analogies.• Is there a common set of principles that govern mapping across different domains?• This cannot be established without taking into account goals and purposes of the cognitive system.
  19. 19. Knowledge required depends on the type of analogy Qualitative traits 1. Ruling Style 2. Control of the “parliament” 3. Popularity among people Fidel Castro Daniel Ortega Quantitative Results/ObservationsSugarcane production Sugarcane production 1. Temperature 2. Rainfall 3. Other relevant weather patterns Cuba Nicaragua
  20. 20. A Constraint-Satisfaction Theory•
  21. 21. ACME: A Cooperative Algorithm for Mapping1. Governed by two principles of information processing:(a) Graceful degradation: As input degrades, output should at least be partial (not non-existent).(b) Least Commitment: Perform lazy updates. Do not perform a mapping/update which may have to be undone. (“If it ain’t broken don’t fix it).2. It is co-operative in the sense that the algorithm can be executed parallel in scenarios where the final analogy can simply be represented as a composition of the analogies of individual sub-units of the source and target.3. Supports two distinct types of queries: (a) Cross-structure queries: Apply the inference from ACME Mapping Network. Combinatorial one model to answer a question in the other. explosion of the states is prevented by (b) Internal queries: Form a hypothesis of the source implementing correspondence model from the target’s attributes. constraints.
  22. 22. Applications of ACMEAKA Functions served by Analogical Reasoning1. Problem solving: Also in coming up with solutions to design problems in association with a TRIZ-like approach (recall the laser surgery of cancer and the army attacking a fort exercise).2. Argumentation: Argue that the likelihood of two “similar” events is pretty close. States/resources/objects true in one event are most probably true in the other.3. Understand less familiar topics by drawing a parallel with more familiar ones (teaching a KG kid laws of refraction from the nursery rhyme!)4. Explain formal analogies and proofs in mathematics. (Mathematical Induction)5. Use of metaphors to improve the aesthetic quality of language.
  23. 23. Scope for Improvement1. Richer semantic information can be built automatically into the constraint graph.2. Allow for re-representations: Different propositions can be established on the same set of predicates at different times or based on the context of knowledge transfer.3. Allow for m-to-n mapping. i.e., Allow relations from the source/target to map to more than one relation of the other.4. Flexible/dynamically modifiable set of constraints.
  24. 24. Objectives of the PresentationPresenter should have fun presenting the content of the papers.Content should be useful to the listeners.Stimulating discussions emerge from the ideas of the paper.? Listeners should have fun during the presentation.