Problem Solving Method in Turings Model of Intelligence

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Problem Solving Method in Turings Model of
Intelligence

• Francisco Hernández Quiroz
• fhq_at_fciencias.unam.mx
• Raymundo Morado
• morado_at_servidor.unam.mx

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ABSTRACT

• Turing machines model of intelligence can be
  motivated by some mathematical and philosophical
  assumptions
• Mechanical intelligence can be seen as the
  application of some method
• TMs embody a method for information processing
  through syntactical transformation
• The method is mechanical, finite, with
  identifiable results, disregarding time and
  space
• What might happen if the assumptions were to be
  rejected or weakened?

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General Assumptions about Method

• Intelligence As Method-Related
• Information Processing, and solving as syntactic
  transformation
• Solving As Rule Following
• Solving As Acting
• Invariance of the Problem
• Relative irrelevance of the Past

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Intelligence As Method-Related

• Intelligence is an ability to solve a problem
  methodically
• That is equivalent to the ability to apply an
  algorithm
• An underlying thesis is that intelligence is
  effective calculability

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Solving as Syntactic Transformation

• In Turing's model to solve a problem is akin to
  processing information
• Solving problems is to modify a representation
  until it becomes the solution
• But acting on reality cannot be identified with
  acting on one of its representations

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Solving As Rule Following

• The TM model uses rules for the representation of
  the internal dynamics of the agent
• There are ways of solving problems that are not
  rule-basedvisual pattern matchingstimulus/reac
  tion in living organismsconnectionist methods

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Solving As Acting

• Solving a problem is not only a sequence of
  steps, but also each step is an action
• This includes actively waiting for something to
  happen
• But there are problems that get solved in due
  time
• All the agent has to do is not to interfere

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Invariance of the Problem

• The conditions of the problem do not change in
  time
• The input for the Turing machine is fixed
• A difficulty is that for some problems there
  seems to be no finite way of specifying the
  complete conditions
• This is the famous Frame Problem
• But even if there is a finite way of specifying a
  problem, the specification might not be suitable
  for a TM

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Relative irrelevance of the Past

• It is not necessary to examine the whole history
  of a calculation
• The description of the situation might include a
  record of the past
• This akin to Laplacian causality
• But there are features of the worlds past that
  dont appear in a description of the present

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Specific Assumptions about Method

• The Method as a Mechanism
• TMs as Model of Mechanical Problem Solving
• Finiteness of the Method
• Identifiable Results
• Infinite Resources
• Spatial Complexity

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The Method as a Mechanism

• TMs model implies that a method in mechanical
• But not everybody agrees on this issue
• This has to do with the debate about the semantic
  capabilities of TMs

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TMs as Model of Mechanical Problem Solving

• TMs model assumes that every problem solvable
  via a mechanical procedure may be solved by TMs
• This is called the Church-Turing thesis
• Most expert would accept this thesis, but the
  debate is not over yet

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Finiteness of the Method

• A method is a finitely specifiable recipe
• But agents capable of storing and handling an
  infinite set of instructions can be conceived, at
  least in principle
• The specification of methods for such agents does
  not need to be finite

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Identifiable Results

• Intelligence is to be judged by its visible
  results
• However, it is not a minor question whether all
  intelligent behavior is visible or whether the
  result must be identifiable as such

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Infinite Resources

• There is no need to consider how many steps are
  taken or how many cells are used to solve the
  problem
• Considerations of efficiency and resource
  limitations are to be modeled afterwards
• How realistic is this assumption?

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Spatial Complexity

• A TMs tape should be infinite
• This point of view disregarded spatial complexity
  issues unknown in Turing's time

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CONCLUSIONS

• We presented some philosophical and mathematical
  assumptions in Turings model of intelligence
• A proper appreciation of them is necessary for
  understanding the model and its limitations
• This understanding is also crucial to correctly
  assess the advantages of alternative models

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REFERENCES

• E. Börger, E. Grädel, Y. Gurevich, The Classical
  Decision Problem (Springer, Universitext, 2001)
• P.M. Churchland, Learning and Conceptual Change
  The View from the Neurons
• Davis, M., The Myth of Hypercomputation
• D. Hilbert, W. Ackermann, Principles of
  Mathematical Logic (Chelsea Publishing Company,
  1950)
• J. McCarthy, P. Hayes, 1969. Some philosophical
  problems from the standpoint of artificial
  intelligence

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• J. Mycka, J.F. Costa, Real recursive functions
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• H.T. Siegelmann, Neural Networks and Analog
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  (Birkhäuser, Progress in Theoretical Computer
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• A.M Turing, On Computable Numbers, with an
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• A.M. Turing, Computing Machinery and
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