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⊗2QUESTIONS⊗*


Why math as a domain for investigating theory formation?
What are some potential concrete applications of this?
How will the success of the system be measured?
What experiments can be done on AM?
What is our model of math research? 
What given knowledge will AM initially start with?
How will this knowledge be represented?
What is the control mechanism; what does AM "do"?
What are some examples of individual knowledge modules?
What are some examples of communities of modules 
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   	    interacting, developing new modules?
What is the timetable for AM?    Its current state?

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⊗2WHY MATH RESEARCH⊗*


1) No uncertainties in the data
2) Reliance upon experts   ≡  introspection
3) Hard science is easier than soft science
4) No single task
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⊗2POTENTIAL APPLICATIONS⊗*


1) Representation: used in other knowledge-based systems
2) Specific criteria: valid for other sciences
3) Repertoire of initial knowledge: foundation for humans
4) Behavior vs size: evolution of thy formation task
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⊗2MEASURING SUCCESS⊗*


1) Achievements
2) Chain of reasoning
3) User-System interactions
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⊗2EXPERIMENTS WITH AM⊗*


1) Remove individual concept modules
2) Alter weights of various criteria
3) Development in new mathematical fields
4) Development in new non-mathematical fields
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⊗2MATH RESEARCH MODEL⊗*


1) Observe → Notice regularity → Formalize → Finalize → Develop
2) Searching controlled by evaluation criteria
3) Importance of non-formal judgmental knowledge
4) Independence of domain and of level
5) Multiple represenations
6) Need for intuition about nearby fields
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⊗2A few of AM's criteria⊗*


A RELATION R⊂AxB IS INTERESTING IF:

1) The image of each aεA satisfies some B-interesting property
2) For all x,yεA, R(x) and R(y) are related by some B-int. reln.
3) A and B are in some interesting relation; especially: A=B


A STRUCTURE S IS INTERESTING IF:

1) Each element of S satisfies some ele-interesting property
2) We know that some member of S will be very interesting.
3) S satisfies some interesting property for that type of struc.


Some Interesting Properties of SETs and BAGs:
				Singleton, Disjoint, Equal



Letting PS indicate all sets whose elements are themselves bags,
we find three interesting relations on SETSxPS:

R1: the image of each sεS is a singleton set 
R2: the image of each pair of s,tεS are disjoint sets
R3: the image of each pair s,tεS are equal sets in PS
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