January 14, 2017 Saturday

Bedtime Story 

First-Order Logic

It is of utmost importance that we digress and look into this subject (of first-order and second-order) as it forms of the basis of logic and comes into play in fields as diverse as mathematics, computer science, linguistics and philosophy.

I need to remind you something that I wrote in my bed-time story some nights ago that logic arose in our human minds (and in all life forms in general) from the sheer complexity of biology.

But first things first.

First-order logic is also known as predicate logic.

Second-order logic is also known as propositional logic.

Now this gives us some hint as to what they imply.

It is hard for me to define first-order logic but there are two important aspects of it that can help in its understanding.

First-order logic uses quantifiers that allows the use of variables without resorting to propositions.

The first-order logic operates on predicates.

Now we have to define predicate.

In mathematical logic, a predicate is a Boolean-valued function of type:

P: X  {true, false}

This would be called predicate on X.

It means that the predicate P(X) will be true or false depending on the value of X.

So X is the quantifier.

Let me show you a quantifier with a mathematical example.

1 X 2 = 1 + 1

2 X 2 = 2 + 2

3 X 2 = 3 + 3

1000 X 2 = 1000 + 1000 and so on.

Then we can quantify natural number with the statement:

For each natural number n, n X 2 = n + n

We have created, in a manner of speaking, a Boolean-valued function that is predicated on n without resorting to any proposition for n.

In linguistics, the quantifiers include many, few, for some, lot, for everything etc.

A first-order logic statement will never say that “3 is a natural number”.

I hope with this you have got a simplistic idea of the concept of first-order logic.

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:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg