Representations and Reasoning
Mateja Jamnik
University of Cambridge
http://www.cl.cam.ac.uk/~mj201
History
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Polya - How to solve it: importance of problem
representation
Simon – The Sciences of the Artificial: solving
a problem means representing it so that the
solution becomes trivial
Amarel 1968: first in automation of
representation design
Van Baalen 1989: success in automated
representation design method for predicate
calculus representations
AR- difficult since usually only one representation
available to the system
Diagrammatic Represenations
Alternative to symbolic representation
n2 = 1 + 3 + 5 + … + (2n+1)
a2 + b2 = c2
Transformation of Representations
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Different reps within
diagrammatic
reasoning
Transformations not
always possible
If the right choice is
made, the solution
becomes trivial
Examples of Right Choice of Rep
n2 = 1 + 3 + 5 + … + (2n+1)
(2n + 1)2= 1 + 4(2) + 4(2.2) + … + 4(2.n)
n
= 1 + 4.
n
n
i 1
i 1
 (2i  1) =  n
 2i
i 1
(2n)2 = 8Tri(n - 1) + 4n
Some Reps are Ambiguous
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Is this a square?
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Is it even/odd?
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What happens when
we manipulate
diagram?
How do we
disambiguate
abstractions?