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# 100705 pres kr agi count montag_ahmds

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• - x: a ~ 0, - x: d steps - makes one for A too → error (A is starting point) conclusion: → discovering an analogy doesn&apos;t automatically transfer all functionality of the source domain → one has to conceive of how to transfer it explicitly (in respect to pt. 2 of the schema; building a prosthesis for the target domain)
• - “leaving one out” is prominent (and inherent to the sequence) (X) - the successor schema works very well already for this sequence; and is being parametrised to leaving one out and different starting points - such a parametrisation is a form of coord . (and as such the underlying schema has to be already encaps)
• - A-&gt;D lex. order; bA, bB → bC, bD (still lex.) - skipping A becomes important → most regular system for skipping is turntaking (for him) → generalisation to 4-letter-clusters conclusion: - there are such things as prioritised schemas (skipping), regularities are searched in respect to this (as opposed to others)
• → D is like 9 insofar as both are the highest number of one digit in their respective base systems → regularity as commonality → justification through reference to analogy
• → building succ.; alphabetic vs. numerical → in a base system digits can be calculated seperately (uses algorithmic strategy) → c ~ 2 is prominent → “ 3x4 iterations of abcd and then the first is 9 → div. by 3 because d~3 and last nmb. → in the end: analogy (BA ~ 10)
• → bag of tricks! → div&amp;conq → A-&gt;C (A is “empty”) → good application of tricks that subj knows from “normal” numbers → these tricks do essentially contribute to number understanding / competence (e.g. times BA → xxxA) → domains are smorgasbords of tricks → analogy transfer from one domain to the other might bring along tricks (question?)
• ### 100705 pres kr agi count montag_ahmds

1. 1. Psychologically Informed Aspectsof aA General Mechanism of Intelligence Presentation for Aspects of Knowledge Representation in Artificial General Intelligence 2010 Benjamin Angerer, Stefan Schneider
2. 2. A predecessor to AGI... A. Newell und H. A. Simon (1961) GPS, a program that simulates human thought idea: a general problem solver user defined rules & objects program generated heuristics … applicable to formalised problemsGeneral Mechanism of Intelligence problems: generating representations/concepts doesnt work only applicable to manually pre-formalised problems consequences: expert systems SOAR – architecture is a follower
3. 3. How we try to find this/these mechanism(s)?- Developmental psychology: - Looking at how abilities develop may give insight into how they work
4. 4. How we try to find this/these mechanism(s)?- Developmental psychology: - Looking at how abilities develop may give insight in how they work- Theoretical psychological and philosophical analysis: - What has to be possible; how cant it be under any circumstances ... - e.g. infinitely many representations of individual numbers
5. 5. How we try to find this/these mechanism(s)?- Developmental psychology: - Looking at how abilities develop may give insight in how they work- Theoretical psychological and philosophical analysis: - What has to be possible, how cant it be under any circumstances... - e.g. infinitely many representations of individual numbers- Problem-solving tasks / Interviews with students: - observing people solving problems and coming up with solutions - esp. the structure of their argumentation & justifications
6. 6. COUNTSTUDY PROJECT
7. 7. COUNTSTUDY PROJECT Sven Spöde Stefan Schneider Benjamin Angerer Alexander Blum sspoede@uos.de stefschn@uos.de bangerer@uos.de ablum@uos.de
8. 8. COUNTSTUDY PROJECT If we do not want to believe that ideas are innate or God-given, but the result of subjective thinkers conceptual activity, we have to devise a model of how elementary mathematical ideas could be constructed – and such a model will be plausible only if the raw material it uses is itself not mathematical. (Glasersfeld, 64)
9. 9. COUNTSTUDY PROJECTWhy numbers?
10. 10. COUNT STUDY PROJECT Why numbers?- development starts early, lasts long, results in complex & abstract concept
11. 11. COUNT STUDY PROJECT Why numbers?- development starts early, lasts long, results in complex & abstract concept- numbers are used in diverse contexts (without “real meaning” in themselves)
12. 12. COUNT STUDY PROJECT Why numbers?- development starts early, lasts long, results in complex & abstract concept- numbers are used in diverse contexts (without “real meaning” in themselves)- numbers are clearly definable and less fuzzy than most abstract philosophicalconcepts
13. 13. COUNTSTUDY PROJECTSome Theoretical notions
14. 14. COUNT PiagetSTUDY PROJECT sensorimotor “schemas” SENSOR SCHEMA MOTOR ORGANISM ENVIRONMENT
15. 15. COUNT PiagetSTUDY PROJECT “schemas” in general 1 2 3 situation, action, expectation context operation of result S SCH M
16. 16. COUNT PiagetSTUDY PROJECT “schemas” in general 1 2 3 situation, action, expectation context operation of result Assimilation: grasping of “new” observations as repetition of sth. already known, “Integration” through existing schemas S Accommodation: Adaptation of schemas after unsuccessful SCH assimilation, “Differentiation” M
17. 17. COUNTSTUDY PROJECT Grounding genesis of the first schemas
18. 18. COUNTSTUDY PROJECT 2 20 0 ,5 Tagging Turn-Taking 1 2 23 6 5 ,5 Objects with Distribution Slots Alignment Grounding genesis of the first schemas
19. 19. COUNT AbstractionSTUDY PROJECT psychological ideas of a general mechanism
20. 20. COUNTSTUDY PROJECT number concept
21. 21. COUNT STUDY PROJECT Clearly, in the head we do not have every number (infinite instances) reave procedures to operate with them. So whenever I face a number symbol number concept
22. 22. Abstractionpsychological ideas
23. 23. Abstraction psychological ideasWhat is being abstracted?regularities of own actions (not of individualobjects), such as repetition rhythmic order successor relations
24. 24. Abstraction psychological ideasAbstractionmechanismsExtractionCoordinationEncapsulationGeneralisationtask as scaffolding ?
25. 25. Encapsulatio Generalisatio Extraction Coordination n n extension of theextraction of applicability of aaspects schema→ assimilation compositionality principle a well-known schema might → new structures become encapsulated into composed of older ones an object (of another schema)
26. 26. Encapsulatio GeneralisatioExtraction Coordination n n the properties of some task or situation that one extracts → what can be done in a certain situation (think of functional fixedness) one understands only according to the schemas one already possesses thus, extraction is the assimilation of a context through activation of applicable schemas extraction / assimilation can take place both on external circumstances and on internal reflection an external situation is perceived as “such and such” in thinking, one realises (extracts), that for some circumstances a certain schema is applicable extraction can thus also be thought of as the discovery of an analogy
27. 27. Encapsulatio GeneralisatioExtraction Coordination n n bring schemas in a certain order possibly resulting in a coordination that solves a problem temporal order hierarchical order? compositionality principle → new schemas out of older schemas what guides coordination? task every structure might be able to guide the assembly of others
28. 28. Encapsulatio GeneralisatioExtraction Coordination n nencapsulation allows schemas to be groundedthrough generating more and more abstract schemaswhich only if necessary have to be executed (or filled with) indetail (if they still can) through encapsulation coordinated and generalised schemas can be treated as a single, new schema this new schema can then be used by other schemas (e.g. in a coordination process)
29. 29. Encapsulatio GeneralisatioExtraction Coordination n n “das geht ja immer” - “that works in all cases” realising that an operation is applicable to a whole class of objects or circumstances or realising that a number of operations is essentially the same assimilation context → generalising the applicability of a schema expectation context → generalising output to a class – e.g. a number, not a specific number instance operations → does the operation change through a generalisation? (in analogy to functions:) a mapping from an (intensionally defined!) class to another (intensionally defined) class → necessary for encapsulation
30. 30. experimental investigation Can these principles actually be observed? How do they work / intertwine in detail? Are there other mechanisms that play a role in abstraction?
31. 31. experimental investigation → Blackboard
32. 32. experimental investigationWhat can be observed in these interviews?
33. 33. experimental investigationWhat can be observed in these interviews? - genesis of schemas
34. 34. experimental investigationWhat can be observed in these interviews? - genesis of schemas - many people only use the base system without being able to explain it, therefore some insight in learning something “new” is possible
35. 35. experimental investigationWhat can be observed in these interviews? - genesis of schemas - many people only use the base system without being able to explain it, therefore some insight in learning something “new” is possible - through obfuscation of the numerical representation subjects have to discover that the constructed sequence is a numerical one at all (takes surprisingly long)
36. 36. experimental investigationPoints of interest:
37. 37. experimental investigationPoints of interest: - the problem with “0”: Subject 1: [3:35] “ A may be zero...” . . . [What is D°D?] [6:28] “We have to count on D times from D” counts with fingers: “A,B,C,D” “So D and then 4 more” (…) [6:53] “So, it has to be BD.”
38. 38. experimental investigationPoints of interest: - generating successors with a general production rule Subject 1: [26:00] [given sequence: A,C,BA,...?] “Seems to be every other number, so BC” “Then CA,CC,DA,DC,BAA,BAC,BBA,BBC...” [27:20] [given sequence: B,D,BB,...?] “BD,CB,CD,DB,DD,...” [Why?] “Its °C, thats leaving one out, that is easy.”
39. 39. experimental investigationPoints of interest: - generating successors with a general production rule Subject 2: [0:20] [given sequence: A,B,C,D,BA,BB...?] “BC,BD” [Then?] [1:10] “We left out A in the 2nd place, so we should skip C, so DA?” [And what do we do after DD?] “We could use E,F,G,H and do the same: E,F,G,H,FE,FF,FG,FH,HE,...”
40. 40. experimental investigationPoints of interest: - justification through analogy to base 10: Subject 1: [3:35] [What after DD?] “BAA.” [Why?] “DD is like 99, so we have to go on with 100, which is BAA.”
41. 41. experimental investigationPoints of interest: - transferring into base 10 before operating and then back again: Subject 1: [09:50] [CA°CC?] “EC.” [10:20] proposes to “decode” the numbers “CA is 3 times the 4 digits,so 9. “CC then is 9+2, so 11. 9+11 is 20, 18 is the nearest factor of 3 to 20, so we need the 6th letter of the alphabet... No, cant be.” (…) [12:40] “BAC!” “E would have been 4, but here BA is 4, just written as ten in the decimal system 10.”
42. 42. experimental investigationPoints of interest: - operating with numbers: Subject 1: [17:30] [What is C°C°C?] “C°C is … (counts with fingers) BB, no, … C is 2,and 2 more is BA, and BA°C is BC.”
43. 43. Wrap Up Encapsulatio GeneralisatioExtraction Coordination n n prioritised schemas in extraction parametrisation: coordinating schemas - one using the other/s as a regularity according to which it is applied coordination requires encapsulation (such that schemas can get used by another schema) encapsulation requires generalisation input / output is generalised to classes
44. 44. Wrap Up Encapsulatio GeneralisatioExtraction Coordination n n it does not suffice that an analogy is noticed transfer requires attention distinction btw. domains might eventually fall competence in a domain, besides understanding the basic principle (e.g. generating successor) also means possessing a bag of tricks: shortcuts, strategies, … it is reasonble to think that the “pure” principle is an abstraction of the formerly learned everyday tricks
45. 45. Psychologically Informed Aspects of a A General Mechanism of IntelligenceThats all, folks !