Lecture - 9 First Order Logic

Lecture Series on Artificial Intelligence by Prof. P. Dasgupta, Department of Computer Science & Engineering, I.I.T,kharagpur. For More details on NPTEL visit http://nptel.iitm.ac.in

Category:

Education

Tags:

• First
• Order
• Logic

[bandinopla]

hemmm.... i'm from argentine, i speak spanish and i learned english watching movies and i can undestand pretty well what Prof. Dasgupta is saying... so mabe is you ?

[warhols25]

Illuminating ! YouTube is the future of the world !

[hac1m]

his handwriting is sooooooo good

[potatoqueue]

I don't really think Russell's paradox is actually a paradox because of the fact that there's no constraint that says only a barber can shave someone.

[blablabla1000able]

this is AWESOME, thank you

[eatme690808]

@asharma78901 Thanks for the clear explanation! For anyone else confused, another way to look at is that for ANY score in Bio, you can always find someone with a higher score in History.

[AJSwisgirl]

@michaelkarpeles He is answering your confusion in second bit in the example. There exists student x and doesn't take history x or bilogy x that is as you mentioned s1 doesn't take neither of them. You confused me too

:-)) Your explanation hard to understand.

[AJSwisgirl]

@michaelkarpeles I think you're  confused, what Prof. wrote is correct. "All student x implies takes history x and biology x ,, negating all sentence will read Not all student..........,.,.,., what ur trying to say is beyond me.

he's not talking 2 students in here or saying s1 or s2 ? there are no information that s1 takes no classes. And sentence doesn't start with there exist... and connective is ^ (and) not V (or).

[subhanice]

ya thanks to the prof so nice of u people to uplaod it i was struggling with it since morning and now i know fol :)

[michaelkarpeles]

@asharma78901

This is actually incorrect. The first order logic sentence may seem to read like the English sentence, but they are not equivalent. Please refer to my other post which illustrates a case wherein this logical solution does not hold for a legal knowledge base.

Best wishes

- Mek

[michaelkarpeles]

@michaelkarpeles

Case: Assume KB of students s1 takes no classes and s2 takes both biology and history. Thus s1 results in FALSE for Student(x) => Takes(History, x) ^ Takes(Biology,x) and becomes TRUE once the Universal quantifier is negated. However, s2 results in Student(x) => Takes(History, x) ^ Takes(Biology,x) evaluating to TRUE, thus becoming FALSE after negation. This sentence thus results in FALSE when it is obviously TRUE that in our KB, not all students take both History & Biology.

[michaelkarpeles]

I apologize, but there is indeed an error in the example. Please see my follow up post as a case is provided.

For the English sentence: "Not all students take both History & Biology",

The FOL solution sentence: ~[Vx Student(x) => Takes(History, x) ^ Takes(Biology,x)] is incorrect.

The correct solution (which is not logically equivalent) is:

Ex Student(x) => ~Taking(Biology, x) v ~Taking(History, x)

Explanation: 2 students in KB. 1 takes 0 classes. 1 takes both bio and history. Conflict.