Constructing, Selecting and Repairing Representations of Knowledge

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Constructing, Selecting and Repairing
Representations of Knowledge

• Alan Bundy
• University of Edinburgh

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Hypotheses

• The representation of a problem is often the key
  to its solution.
• Problem representations can be automatically both
  formed and repaired.

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Representation as the Key 1
Mutilated Checkerboard Can we tile board with
dominos?
Colouring of domino removes search from solution.
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Representation as the Key 2
Bouncing Ball Where does energy go at moment of
impact?
Essential to idealize ball as having extent.
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Representation as the Key 3
Idealisation of the bottle determines the answer.
Milko Problem Is the pressure the same before
and after the cream settles out?
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Representation as a Fluent

• World infinitely rich cannot model every aspect.
  
• Fixed representations cannot cope with changing
  world and new challenges.
• Representation needs to evolve under machine
  control.
• Need to change signatures not just beliefs.

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Formation of Representations 1

• Mecho Project solve mechanics problems stated in
  English.
• Real world objects idealized automatically.
• particles, inextensible strings, light pulleys.
• Idealization fossilized
• inferred from problem type.

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Formation of Representations 2

• Eco project assist users to construct ecological
  model.
• Heuristics for suggesting idealizations.
• Representation formation as interaction between
  human and machine.

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Formation of Representations 3

• Diamond Project constructs proofs without
  words.
• n2 idealized as both
• n rows of n dots
• n ell shapes
• Idealisations chosen via human interaction.

n2122n-1
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Repair of Representations 1

• Cynthia Project analogical editor for ML
  programs.
• Edit old ML program into new one.
• Powerful commands to change names, arguments,
  types, recursion, etc.
• Commands edit synthesis proof, from which program
  is rederived.
• Ensures well-formedness, coverage and termination
  of synthesised program.

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Repair of Representations 2

• HR Program creates new concepts and conjectures
  from examples.
• TM Program uses HR, Otter and Mace to repair
  faulty mathematical theories.
• TM methods based on Lakatos Proofs and
  Refutations.

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Repair of Representations 3

• ORS Program repairs faulty ontologies by
  analysing failed multi-agent plans.
• Changes include abstraction and refinement of
  signatures,
• e.g. adding arguments, changing predicates.
• Technology essential for Semantic Web

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Conclusion

• Formation of representation must be machine
  control.
• To deal with complex, changing world.
• Representational change triggered, for instance,
  by reasoning failures.
• Signature changes as well as belief revision.
• Major challenge for next half century.