logic and decision making by rajnish kumar

7/28/2019 Logic and Decision Making by Rajnish Kumar

1/28

Logic and

Decision Making

Rajnish KumarProfessor IT

National Academy of Indian Railways


2/28

Decision Making

Full of confusion

Facts not available

Time is less

Resources limited

etc etc, hazaar bahaane


3/28

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/sound


4/28

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_system


5/28


6/28

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_consequent


7/28

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_consequent


8/28

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_questions


9/28

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?


10/28

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


11/28

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?


12/28

Answer

Mary!!

Of course


13/28

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?


14/28

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.


15/28

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.php


16/28

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."


17/28

?

Are there more words in the English language

that begin with the letter R or that have R as

their third letter?


18/28

?

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


19/28

?

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


20/28

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


21/28

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


22/28

Deductive Reasoning

Proposition

An assertion, which may be either true of false

Premise

Propositions about which arguments are made


23/28

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


24/28

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.


25/28

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


26/28

Some months have 31

days, some 30.

How many months have 28

days?

THINK!!!

5 seconds


27/28

THINK!!!

5 seconds

Divide 30 by half

andthen add 10

What do you get?


28/28

Logic did it ring in your mind

Think

Think

ThinkThank you

logic and decision making by rajnish kumar

Documents