I started learning python as a
programing language over a year now and started working on NLP and A.I.
programming about 2 months ago, but I never thought I would find concepts of
computer programing and AI in my Philosophy course, yet here we are, studying
Modus Ponens and Modus Tollens. One of the areas of Philosophy's logic's course
is studying how logical statements and syllogisms are formed, and surprisingly
enough the same concepts go into making A.I. and NLP-based computer
programs.
Like when can we call an A.I.
intelligent? When it, with some of the already available data, can infer or
deduce new data. That exactly is what we study in logic's course.
Anyways now, back to the topic.
Modus Ponens
Modus Ponens refers to categorical syllogisms which are in the form:
1) p ⊃ q (read as if p then
q)
2) p (given that p is true)
3) ∴ q (we conclude that
therefore q must be true)
An example would be -
"If it rains today then the
playground will be wet."
Now breaking the compound statement
into simple statements and marking them with variables we get:
Let "It rains today" be 'p'.
Let "The field is/will be
wet" be 'q'.
Now let the new true information (p) be
:
"It rained today"
Now from these two pieces of
information given, the A.I. through Modus Ponens should be able to extract the
conclusion (q) that:
"Therefore the playground must be
wet"
Concluding syllogisms like this is
called Modus Ponens.
Modus Tollens
Modus Tollens refers to categorical syllogisms which are in the form:
1) p ⊃ q (read as if p then
q)
2) ~q (given that
negation/ opposite of q is true)
3) ∴ ~p (we conclude
that therefore negation/opposite of p is true)
Taking the same example we can say
-
"If it rains today then the
playground will be wet."
Now breaking the compound statement
into simple statements and marking them with variables we get:
Let "It rains today" be 'p'.
Let "The field is/will be
wet" be 'q'.
Now let the new true information that
negation of q is true (~q) be :
"The playground is not wet"
Now from these two pieces of
information given, the A.I. through Modus Tollens should be able to extract the
conclusion (~p) that:
"Therefore it must not have rained
today"
Concluding syllogisms like this is
called Modus Tollens.
Use in real life A.I.s
Modus Pollens and Modus Tollens are just two of the four rules of
inference that are used for making logical operators. Real-life example of A.I.
using this will be logic structures used in Alexa. Alexa is coded with -
"If it is raining then umbrellas are used (p)". Following this
statement given and using the structure of Modus Ponens, the next time a user
asks - "What will be tomorrow's weather?", Alexa fetches the weather
data and suppose that it obtains data that 'it will rain tomorrow (q)', then by
Modus Ponens it can reply back to the user - "The weather prediction says
it will rain tomorrow, so carry an umbrella outside."
Additional Facts
We discussed three
words today - 'Modus', 'Ponens', 'Tollens'. The easy way
to remember and separate Modus Ponens from Modus Tollens will be by knowing
their root words and what they mean.
'Modus' is a
Latin word that has its origin as a Proto-Indo-European root. In Latin, modus
means 'the way in which something is done'. Remember the term 'Modus Operandi'?
A common term used with serial killers to describe their 'way of operation'
i.e. the specific way that they kill.
'Ponens' too
is a Latin word that means 'by putting or stacking'. Therefore Modus Ponens
literally means 'method in which things are put together' just like putting
together the fact that if p is given true then q must be true too.
'Tollens' too
is a Latin word that means 'by taking away'. Therefore Modus Tollens literally
means 'method in which things are taken away' just like taking away the truth
function of q resulting in 'not q' being true which gives the conclusion that
'not p' must be true.
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