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7/28/2019 Logic and Decision Making by Rajnish Kumar
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Logic and
Decision Making
Rajnish KumarProfessor IT
National Academy of Indian Railways
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Decision Making
Full of confusion
Facts not available
Time is less
Resources limited
etc etc, hazaar bahaane
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Use Logic
What is logic? the science that investigates the principles
governing correct or reliable inference.
the system or principles of reasoning applicable toany branch of knowledge or study.
reason or sound judgment, as in utterances or
actions: There wasn't much logic in her move. convincing forcefulness; inexorable truth or
persuasiveness: the irresistible logic of the facts.
http://dictionary.reference.com/browse/soundhttp://dictionary.reference.com/browse/sound7/28/2019 Logic and Decision Making by Rajnish Kumar
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Properties of a Logical System
Among the important properties that logical systems can have:
Consistency, which means that no theorem of the system
contradicts another.
Validity, which means that the system's rules of proof willnever allow a false inference from true premises.
Completeness, of a logical system, which means that if a
formula is true, it can be proven (if it is true, it is a theorem of
the system).
Soundness, this is the converse of completeness. A distinct,
peripheral use of soundness refers to arguments, which
means that the premises of a valid argument are true in the
actual world.
http://en.wikipedia.org/wiki/Logical_systemhttp://en.wikipedia.org/wiki/Consistency_proofhttp://en.wikipedia.org/wiki/Validityhttp://en.wikipedia.org/wiki/Completenesshttp://en.wikipedia.org/wiki/Soundnesshttp://en.wikipedia.org/wiki/Soundnesshttp://en.wikipedia.org/wiki/Completenesshttp://en.wikipedia.org/wiki/Validityhttp://en.wikipedia.org/wiki/Consistency_proofhttp://en.wikipedia.org/wiki/Logical_system7/28/2019 Logic and Decision Making by Rajnish Kumar
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Common Fallacies
Affirming the consequent and Denying the antecedent:draws a conclusion from premises that do not support that conclusion by
confusing necessary and sufficient conditions. Affirming the consequent Example:
Argument: If people have the flu, they cough. Torres is coughing.Therefore, Torres has the flu.
Problem: Other things, such as asthma, can cause someone to cough. Theargument treats having the flu as a necessary condition of coughing; in fact,having the flu is a sufficient condition of coughing, but it is not necessary tohave the flu for one to cough.
Argument: If it rains, the ground gets wet. The ground is wet, therefore itrained.
Problem: There are other ways by which the ground could get wet (e.g.someone spilled water).
http://en.wikipedia.org/wiki/Affirming_the_consequenthttp://en.wikipedia.org/wiki/Denying_the_antecedenthttp://en.wikipedia.org/wiki/Affirming_the_consequenthttp://en.wikipedia.org/wiki/Necessary_conditionhttp://en.wikipedia.org/wiki/Sufficient_conditionhttp://en.wikipedia.org/wiki/Sufficient_conditionhttp://en.wikipedia.org/wiki/Necessary_conditionhttp://en.wikipedia.org/wiki/Sufficient_conditionhttp://en.wikipedia.org/wiki/Sufficient_conditionhttp://en.wikipedia.org/wiki/Necessary_conditionhttp://en.wikipedia.org/wiki/Affirming_the_consequenthttp://en.wikipedia.org/wiki/Denying_the_antecedenthttp://en.wikipedia.org/wiki/Affirming_the_consequent7/28/2019 Logic and Decision Making by Rajnish Kumar
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Common Fallacies
Affirming the consequent and Denying the antecedent:
Denying the antecedent Example
Argument: If it is raining outside, it must becloudy. It is not raining outside. Therefore, it isnot cloudy.
Problem: Rain is a sufficient condition ofcloudiness, but cloudy conditions do notnecessarily imply rain.
http://en.wikipedia.org/wiki/Affirming_the_consequenthttp://en.wikipedia.org/wiki/Denying_the_antecedenthttp://en.wikipedia.org/wiki/Denying_the_antecedenthttp://en.wikipedia.org/wiki/Sufficient_conditionhttp://en.wikipedia.org/wiki/Sufficient_conditionhttp://en.wikipedia.org/wiki/Denying_the_antecedenthttp://en.wikipedia.org/wiki/Denying_the_antecedenthttp://en.wikipedia.org/wiki/Affirming_the_consequent7/28/2019 Logic and Decision Making by Rajnish Kumar
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Common Fallacies
Fallacy of many questions
groups more than one question in the form of asingle question.
Example
Argument: Have you stopped beating your
wife? Problem: Either a yes or no answer is an
admission of guilt to beating your wife.
http://en.wikipedia.org/wiki/Fallacy_of_many_questionshttp://en.wikipedia.org/wiki/Fallacy_of_many_questions7/28/2019 Logic and Decision Making by Rajnish Kumar
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Let us do some RIDDLES
BRIDGE and TORCH Problem
Four people come to a river in the night. There is anarrow bridge, but it can only hold two people at a time.
They have one torch and, because it's night, the torch hasto be used when crossing the bridge.
Person A can cross the bridge in one minute, B in two minutes,
C in five minutes, and
D in eight minutes.
When two people cross the bridge together, they mustmove at the slower person's pace. The question is, canthey all get across the bridge in 15 minutes or less?
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SolutionA can cross the bridge in one minute,
B in two minutes,
C in five minutes, andD in eight minutes.
Elapsed Time Starting Side Action Ending Side
0 minutes A B C D
2 minutes C D
A and B cross
forward, taking 2minutes
A B
3 minutes A C DA returns, taking 1
minuteB
11 minutes A
C and D cross
forward, taking 8minutes B C D
13 minutes A BB returns, taking 2
minutesC D
15 minutes
A and B cross
forward, taking 2
minutes
A B C D
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MUMs baby
Mary's mum has four children.
The first child is called April.
The second May.
The third June.
What is the name of the fourth child?
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Answer
Mary!!
Of course
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Two Strings
You have two strings whose only known
property is that when you light one end of
either string it takes exactly one hour to burn.
The rate at which the strings will burn iscompletely random and each string is
different.
How do you measure 45 minutes?
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Answer
Light both the ends of the first string and oneend of the second string.
30 minutes will have passed when the first stringis fully burned, which means 30 minutes have
burned off the second string.
Light the end of the second string and when it isfully burned, 45 minutes will have passed.
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Some good links to induce logical
thinkinghttp://easycalculation.com/puzzles/logical/logical1.php
http://www.folj.com/puzzles/easy.htm
http://www.logicalpuzzle.com/eng/examples_e.html
http://puzzle.dse.nl/logical/index_us.html
http://logic.philosophy.ox.ac.uk/
http://www.harryhiker.com/fe/fe-0--00.htm
http://easycalculation.com/puzzles/logical/logical1.phphttp://www.folj.com/puzzles/easy.htmhttp://www.logicalpuzzle.com/eng/examples_e.htmlhttp://puzzle.dse.nl/logical/index_us.htmlhttp://logic.philosophy.ox.ac.uk/http://www.harryhiker.com/fe/fe-0--00.htmhttp://www.harryhiker.com/fe/fe-0--00.htmhttp://www.harryhiker.com/fe/fe-0--00.htmhttp://www.harryhiker.com/fe/fe-0--00.htmhttp://www.harryhiker.com/fe/fe-0--00.htmhttp://www.harryhiker.com/fe/fe-0--00.htmhttp://logic.philosophy.ox.ac.uk/http://puzzle.dse.nl/logical/index_us.htmlhttp://www.logicalpuzzle.com/eng/examples_e.htmlhttp://www.folj.com/puzzles/easy.htmhttp://easycalculation.com/puzzles/logical/logical1.php7/28/2019 Logic and Decision Making by Rajnish Kumar
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Dilemmas in decision making
Any solution only two methods
HEURISTICS- refers to experience-based techniques forproblem solving, learning, and discovery. Where anexhaustive search is impractical, heuristic methods areused to speed up the process of finding a satisfactorysolution.
Examples of this method include using a rule of thumb, aneducated guess, an intuitive judgment, or common sense.
ALGORITHMS- "a set of rules that precisely defines asequence of operations."
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?
Are there more words in the English language
that begin with the letter R or that have R as
their third letter?
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?
Calculate in your head the answer to the
following problem:
8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
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?
Calculate in your head the answer to the
following problem:
1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
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Judgment and Decision Making
Heuristics and Biases
Availability R letter problem We make judgments on the basis of how easily we can call
to mind what we perceive as relevant instances of a
phenomenon (e.g. words beginning with letter R) Anchoring-and-adjustment heuristic calculation
question People provide a higher estimate for the first sequence
than for the second because their computation for the
anchor the first few digits multiplied by each other renders a
higher estimate from which they make an adjustment toreach a final estimate
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Judgment and Decision Making
Heuristics and Biases
Overconfidence
And individuals overvaluation of her or his own
skills, knowledge, or judgments
People tend to overestimate the accuracy of their
judgments
Example: When people were 100% confident in their answers,
they were right only 80% of the time
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Deductive Reasoning
Proposition
An assertion, which may be either true of false
Premise
Propositions about which arguments are made
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Deductive Reasoning
Conditional Reasoning
The reasoner must draw a conclusion based on an if-
then proposition
Deductive validity Does not equate with truth
You can reach deductively valid conclusions that are
completely untrue with respect to the world
People are more likely mistakenly to accept an illogical
argument as logical if the conclusion is factually true
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Deductive Reasoning
Example
1. If Larry is sick, then he will be absent from school.
2. If Larry is absent, then he will miss his classwork.
3. If Larry is sick, then he will miss his classwork.
Is the final statement always true?
We also conclude that this could be a false statement.
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So, being logical
Logic to be used logically or it could end in a
fallacy.
Logic helps in removing biases, prejudices.
Reduces time taken for decision. I f given
enough time many decisions could be better.
But in real world, no TIMEone example
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Some months have 31
days, some 30.
How many months have 28
days?
THINK!!!
5 seconds
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THINK!!!
5 seconds
Divide 30 by half
andthen add 10
What do you get?
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Logic did it ring in your mind
Think
Think
ThinkThank you