Making and Breaking Arguments in Computer Science

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Making and Breaking Arguments in Computer Science

• CS710
• March 2007
• Suzanne Embury (IPG)

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Computer Science Research

• Question what is the end product of computer
  science research?

(One) Answer Arguments
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What is an Argument?
My algorithm needs fewer memory accesses than Xs
My algorithm is otherwise the same as Xs

• Conclusion
• Premise
• usually more than one
• Reasoning step
• generate intermediate conclusions

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What is an Argument?

• Conclusion
• Premise
• usually more than one
• Reasoning step
• generate intermediate conclusions

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Example Argument

• Norman Paton is running CS710
• Running CS710 lowers your blood sugar
• Therefore, Norman Paton has low blood sugar
• People with low blood sugar need to eat cream
  cakes
• Therefore, Norman Paton needs to eat cream cakes

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Some Common Mistakes

• Generating good code from compilers is an
  important problem nowadays. We analyse the
  parsed code to find the scope of reference for a
  variable that is, the smallest sub-program that
  accesses that variable. When sub-programs for
  different variables dont overlap, we can reuse
  the memory allocated, and speed up the compiled
  code.

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Whats the Difference?

• High level languages encourage users to declare
  as many variables as are necessary for clarity.
  But, a naïve compilation of programs written in
  this style can be inefficient, due to the
  repeated need to allocate and maintain memory for
  each variable. Since many variables are only
  accessed in a limited part of the program, we can
  save time by reusing allocated memory for new
  variables when we are sure that the old variable
  will not be accessed again by the program.

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Conclusions

• Focus on the problem as well as the solution
• Typical forms
• For problem P, S is a good solution
• For problem P, solution S is better than
  solution(s) T, U, V,
• For problem P, solution S is better than
  solution(s) T, U, V, , under conditions C

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Premises

• A claim that is self-evidently true
• An assumption from the context/conclusion
• A claim that is argued for (convincingly) by
  another authority
• Proof-by-citation beware!
• Something established earlier in your argument

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Reasoning Steps

• Many forms, from formal logic
• E.g. Modus Ponens
• P ? Q, P Q
• E.g. Hypothetical Syllogism
• P ? Q, Q ? R P ? R

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Example Argument

• Norman Paton is running CS710
• Running CS710 lowers your blood sugar
• People with low blood sugar need to eat cream
  cakes
• Therefore, Norman Paton needs to eat cream cakes

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Deductive vs Inductive Args

• Deductive arguments
• the conclusion necessarily follows from all
  (relevant) premises
• Validity and soundness of deductive args.
• Inductive arguments
• the conclusion probably follows from all premises
• Strength and cogency of inductive args.

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Examples (from Hurley)

• The meerkat is closely related to the suricat.
• The suricat thrives on beetle larvae.
• Therefore, we can expect that the meerkat thrives
  on beetle larvae.
• The meerkat is a member of the mongoose family.
• All members of the mongoose family are
  carnivores.
• Therefore, meerkats must also be carnivores.

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Yet More Examples

• 20 PhD students came to the research retreat.
• 18 were surveyed and said they had a good time.
• Therefore, all students who came to the research
  retreat had a good time.

• 20 PhD students came to the research retreat.
• 3 were surveyed and said they had a good time.
• Therefore, all students who came to the research
  retreat had a good time.

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Gathering Evidence

• In CS, we can use the full range of techniques
  for evaluating and proving conclusions

Formal Proof
Empirical Results
Inductive Arguments
Deductive Arguments
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Placing Arguments in the Public Domain

• Need to linearise your argument
• Create the paper structure around
  the argument structure
• E.g. For problem P, S is
  a better solution than T.

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Structure from Argument

• Describe problem P and motivate it as research
• Describe existing solution T. Identify areas of
  weakness and success criteria.
• Describe the new solution S.
• Evaluate solution relative to success criteria.
• Discuss strengths and weaknesses of S, and
  restate conclusion

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Motivate it as Research?

• When you place an argument in the public domain
  (e.g. publish a paper), you are obligated to
  include three additional arguments to motivate
  your work as research.

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Is it Research? (1)

• Would you class the following argument as
  research?
• The longer a pendulum is, the longer is takes to
  swing.
• Therefore, when the pendulum of a clock is
  lengthened, it slows down.

This is old news! Research must be NOVEL
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Is it Research (2)

• Would you class the following argument as
  research?
• A new business is set up to create a totally new
  kind of kitchen appliance. No one has ever sold
  this kind of product before.
• An invoicing system is needed for the business.

We know how to do this. Research must
be NON-TRIVIAL
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Is it Research? (3)

• Would you class the following argument as
  research?
• DIY stores in the US stock enough blue paint to
  cover a greater area than the surface of the
  moon.
• We can send astronauts and paint to the moon.
• Therefore, we can paint the moon blue.

This is pointless! Research must be OF VALUE
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Be Economical

• Every word of your paper/thesis/talk must support
  the argument.
• It should either
• Establish a premise
• Apply a reasoning step
• Explore alternatives
• Define a conclusion

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References

• A Concise Introduction to Logic
• Patrick J. Hurley
• Wadsworth Publishing Company
• Fifth edition, ISBN 0-534-21174-7, 1994
• A Rulebook for Arguments
• Anthony Weston
• Hackett Publishing Company
• Third edition, ISBN 0-87220-552-5, 2000