Logic analysis technique
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| Logic analysis |
We frequently use the term ‘logic’. People who use logic to back up their comments, decisions or actions are considered as logical. Sometimes this term is interchangeably used with the term ‘rational’. People who do not behave or act according to commonly accepted norms are termed as irrational. Human beings do not always follow stringent logic.
Nevertheless ‘logic’ is a well-defined
technical term; there is nothing vague in ‘logic’. In logic domain, there is
truth or falsity of propositions, nothing in between. It is kind of black and
white Boolean world. One says, the statement or the proposition – “Rainee is a good
girl” can either be true or false. Thus this statement or proposition is a
valid proposition in logic. “Rainee is a somewhat good girl” in contrast is not a
valid proposition because somewhat introduces uncertainty and it is difficult
to determine whether the statement is purely true or surely false.
Though real life cannot really
be represented or explained using logic, still logic analysis as a technique in
real life problem solving undoubtedly is valuable.
Let us look at this concept
domain more closely by solving a problem from Martin Gardner’s South Sea
adventure stories.
Problem 1: Which path would you take? (version 1)
A logician while visiting the
South Seas is at a fork. He needed to know which of the two roads in front of
him leads to the village. Perchance he has two willing natives available near
at hand. But one of them is from a tribe of invariable truth-tellers, and the
other from a tribe of invariable liars. He knows this predicament but does not
know which one is the liar or the truth-teller. The natives though know each
other well. The logician
can ask only one question to any one of the natives. Can he know the
right path to the village?
To remind you, Logic Analysis
is a discipline where there are statements or propositions which can only be
true or false (yes or no) and logicians are experts in dealing with problems in
this domain. As you are not a logician, logic domain is new to you. The process
of solving logic problems is new to you. But even though you are not a
logician, at least you are a problem solver who is supposed to proceed solving
any problem systematically.
So you need to proceed using
deductive reasoning systematically, not in any random or chaotic manner. Here
you must stop and try to solve the problem yourself. You should try at least
for 15 minutes for solving the problem. To give you an opportunity of solving
the problem yourself, we would delay explaining the solution only a little
bit.
Our break is over. Here goes our
reasoning.
The logician can ask the all
important single question to only one of the natives without knowing whether
the native is the liar or the truth teller. Depending on the answer he will
know which the right path is. If the answer is different from the two natives he
can never be certain. So a necessary
condition for the question to surely lead you to the right path, the answer must
be same whether the native to whom the question is asked is the liar or the truth
teller. How to form such a question?
Consider that a habitual truth
teller can be symbolized as a logic transformation box that outputs the same
logic variable state it takes as inputs. The following figure depicts the
situation,
Similarly,
the logic transformation box for the habitual liar will be to reverse the state
of input. In other words, if the input is YES, it will output with answer NO
and vice versa. The following figure depicts the situation,
So you understand
that a single question will surely produce two values as answer from the two natives.
This cannot be the solution then. It implies surely that a single simple question
will not be the answer-you need then to ask not a simple question but a compound question
comprising of two simple questions. You arrive at this conclusion by your deductive
reasoning mechanism.
Knowing that reversing twice
restores the original state, we may think of asking the habitual liar two
questions in conjunction, “Will
you answer YES if I ask you whether the path on the right is the path to the
village?” The second part of the compound question goes as the first
input to the logic transformation box of the habitual liar reversing the state
of the input. In terms of our problem it means, if in reality the path on the
right were the path to the village, the TRUE answer to this part of the
question would be YES, but as the liar must reverse the state, he must answer
with NO. This is hypothetical, but still the habitual liar has no other option
than to imagine that his answer to the second part of the question would be a
NO. This NO then goes as input to the logic transformation box of the liar for
answering the first part of the question and completing his whole task. Being a logic state reversing mechanism, the
liar would have to reverse this NO to YES and actually arriving at the TRUE
answer to the original core statement. The truth teller poses no problem as he
does not do any transformation in each of the two transformation stages. An
input of YES passes straight through as YES in the output. Note that, the
question could have been “path on the left” instead of “path on the right” and
also “NO” instead of “YES”. Try
these out. The figure below depicts the transformation sequence for the
habitual liar.
Even though you are not a logician, you proceeded by adopting a systematic approach
and finally arrived at the solution.
We will learn to solve a more complicated logic problem next session.
Read my other blogs on Innovative idea generation and its basic principles and Get smart, get innovative usingTRIZ
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