The Logical Way to Natural Intelligence

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• The Logical Way to Natural Intelligence
• Bob Kowalski
• Imperial College London
• reporting work by
• Luis Pereira
• Steffen Hoelldobler
• Fariba Sadri
• Marek Sergot
• Keith Stenning
• Michiel van Lambalgen
• myself and others

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This talk
Computational logic
Computer language Legal language Natural
language Neural networks
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• Outline of this talk
• People are not logical.
• The Wason selection task
• The Byrne suppression problem
• Logic in the observation-thought-action cycle.
• The London Underground Emergency Notice
• People need to be logical.
• The British Nationality Act
• Wason and Byrne reconsidered.

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• Some distinctions
• Logic as a descriptive versus
• logic as a normative model of thought.
• Logic as subconcious, automatic thought
  versus logic as conscious, effortful thought.
• My thesis is that computational logic is a good
  descriptive model for subconscious thinking and
  a good normative model for conscious thinking and
  communication.

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• Outline of this talk
• People are not logical.
• The Wason selection task
• The Byrne suppression problem
• Logic in the observation-thought-action cycle.
• The London Underground Emergency Notice
• People need to be logical.
• The British Nationality Act
• Wason and Byrne reconsidered.

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• Wason selection task
• Four cards, letters on one side, numbers on the
  other.
• Determine whether the following rule holds
• If there is a vowel on one side,
• then there is an even number on the other side.
• Only 5-10 of all people select the right cards.

A
F
2
7
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• Wason selection task
• Determine whether the following rule holds
• If a person is drinking beer in a bar,
• then the person should be over eighteen.
• Most people get the right answer.
• Conclusion?
• People dont use logic, but have evolved a
  cheater detection scheme
• If you receive a benefit,
• then you must meet its requirement.

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The Byrne suppression problem
If she has an essay to write, she will study late
in the library. She has an essay to write. 95
of all subjects conclude She will study late in
the library.
Add If the library is open she will study late
in the library. Only 60 of all subjects
conclude She will study late in the library.
Conclusion? People are not logical.
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• Outline of this talk
• People are not logical.
• The Wason selection task
• The Byrne suppression problem
• Logic in the observation-thought-action cycle.
• The London Underground Emergency Notice
• People need to be logical.
• The British Nationality Act
• Wason and Byrne reconsidered.

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Logic needs to be put in its place as one way
of thinking in the observation-thought-action
cycle of an intelligent agent
An agent
think
observation
action
motor processing
Perceptual processing
The world
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Dealing with Emergencies on the London
underground
An agent
Maintenance goal
If there is an emergency then get help There is
an emergency
Achievement goal
Forward reasoning
get help
alert the driver
There is a fire
Backward reasoning
press the alarm signal button
observe
act
The world
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A logical/linguistic representation
Goal If there is an emergency then I get
help. Beliefs A person gets help if (and only
if) the person alerts the driver. A person
alerts the driver if (and only if) the person
presses the alarm signal button. There is an
emergency if (and only if) there is a fire or
one person attacks another or someone
becomes seriously ill or there is an
accident. There is a fire if (and only if)
there are flames or there is smoke.
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• Outline of this talk
• People are not logical.
• The Wason selection task
• The Byrne suppression problem
• Logic in the observation-thought-action cycle.
• The London Underground Emergency Notice
• People need to be logical.
• The British Nationality Act
• Wason and Byrne reconsidered.

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(No Transcript)
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Subsection 1.-(1) 1.-(1) A person born in the
United Kingdom after commencement shall be a
British citizen if at the time of the birth his
father or mother is (a) a British citizen
or (b) settled in the United Kingdom.
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The logic of subsection 1.-(1) A person shall be
a British citizen by 1.-(1) if the person was
born in the United Kingdom and the person was
born after commencement and a parent of the
person was a British citizen at the time of the
persons birth or a parent of the person was
settled in the United Kingdom at the time of the
persons birth.
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Subsection 1.-(2) (2) A new-born infant who,
after commencement, is found abandoned in the
United Kingdom shall, unless the contrary is
shown, be deemed for the purposes of subsection
(1) (a) to have been born in the United
Kingdom after commencement and (b) to have
been born to a parent who at the time of the
birth was a British citizen or settled in the
United Kingdom.
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The logic of subsection 1.-(2) The conditions of
1.-(1) hold for a person if the person was
found new-born abandoned in the United
Kingdom after commencement and it can not be
shown that it is not the case that the
conditions of 1.-(1) hold for the person.
Or more precisely (2) A person who is found
abandoned in the United Kingdom after
commencement shall be deemed to satisfy the
conditions of subsection (1), unless the contrary
is shown.
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• Outline of this talk
• People are not logical.
• The Wason selection task
• The Byrne suppression problem
• Logic in the observation-thought-action cycle.
• The London Underground Emergency Notice
• People need to be logical.
• The British Nationality Act
• Wason and Byrne reconsidered.

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Computational Logic explains performance on the
Wason selection task

• If there is a vowel on one side,
• then there is an even number on the other side.
• Interpretation as a logic program inhibits the
  contrapositive
• If it is not the case that there is a vowel on
  one side,
• then it is not the case that there is an even
  number on the other side.
• Interpretation of if as if-and-only-if justifies
  the converse
• If there is an even number on one side,
• then there is a vowel on the other side.

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• If a person is drinking beer in a bar,
• then the person should be over eighteen.
• Here the implication has an obvious use in an
  agents observation-thought-action cycle.
• It is natural to interpret the implication as a
  goal. Goals do not typically have if-and-only-if
  form and do not inhibit the contrapositive
• If a person is not over eighteen,
• then the person should not be drinking beer in a
  bar.

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Computational Logic explains performance on the
Byrne suppression problem
If she has an essay to write, she will study late
in the library. If the library is open, she
will study late in the library. can be
reinterpreted logically as a default rule and an
exception
If she has an essay to write and it can not be
shown that it is not the case that she will study
late in the library, then she will study late in
the library. Only if the library is open, will
she study late in the library i.e. She will not
study late in the library if the library is not
open.
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Conclusions
The Language of Thought versus Natural Language.
Computational logic is a candidate for the
language of thought. Natural language is an
imperfect expression of the language of thought.
(Even seemingly logical use of natural language
needs to be interpreted into its intended logical
form.) Logic for dealing with the concrete real
world versus logic for dealing with abstract
imaginary worlds. The primary purpose of
thinking is to help with reacting to observations
and with generating appropriate actions. Natural
language puzzles in seemingly logical form do not
necessarily bear upon the question of whether
people use logic to deal with their own
experiences.
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Logic programs can be implemented by neural
networks (Hoeldobler et al)
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Logic needs to be put in its place
To stay alive, observe the world, think, decid
e what actions to perform, act, continue to
stay alive. Logic is one way of
thinking. Logic used this way is applied
directly to situations that arise in every day
life.
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A simpler formulation in the style of subsection
1.-(2) (2) A person who is found abandoned in the
United Kingdom shall, unless the contrary is
shown, be deemed to satisfy the conditions of
subsection (1).
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This talk
Computer language Legal language Natural
language Neural networks
Computational logic as a wide spectrum language
of thought and communication.