April
30, 2017 Sunday
Bedtime
Story
Basics of Propositional Calculus or Zeroth-order Logic
Propositional
calculus is also known as the sentential calculus and also as the zeroth-order
logic.
Notice
that the word ‘calculus’ and ‘logic’ are very often used interchangeably.
Propositional
calculus is developed with the help of two kinds of signs, one being variable
and the other being constant.
The
variable signs include letters like p, q, r… but they can have sentences
replace them.
These
variable signs are also known as “sentential variables”.
The
constant signs are either connectives or signs of punctuation.
They
are otherwise known as “sentential connectives”.
Examples
of sentential connectives are as follows.
‘ ∨
‘ ⊃ ’
stands for ‘if…then…’
‘.’
Stands for ‘and’
Punctuation
marks can be assigned to parenthesis brackets namely ‘ ( ‘ or ‘ ) ‘.
Following
this, the Formation Rules determine how these elementary signs can combine and
how sentences or formulas can be formed.
Let
me give few examples what kind of formation rules were set up for this formal
system.
It
isn’t that difficult as you would expect from mathematics.
If
a symbol ‘S’ is a formula, then it negation ~(S) is also a formula by default,
assuming the tilde sign stands for negation.
This
tilde sign or grapheme (smallest unit of a writing system of any given
language) in present modern day English stands for “approximately”, “about” or
“around”.
Further,
if S1 and S2 are formulas, then (S1) ∨
Same
thing holds true with sentential variables.
So
if ‘p’ is a formula, then its negation ~(p) is also a formula.
Similarly,
these formulas (p) ⊃
Now
let me show you what is not allowed.
‘(p)(~(q))’
cannot be a formula.
This
is so because though both ‘(p)’ and ‘~(q)’ are formulas by themselves, in the above
denied formula there is no sentential connective between them.
Similarly
a formula like ‘((p) ⊃
It
is simple and I want to think for yourself and tell me why.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night mon ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic engineer
and a former professor at BARC, does and teaches real mathematics and physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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