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Anyone W/ Formal Logic Experience?


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#1 Heretic Monkey

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Posted 19 September 2006 - 08:47 PM

I have to do some exercises for homework for my LOG 335 class at NCSU, and there's one i just can't prove. I was wondering if anyone here has any training using Sentential Calculus or experience with derivations of SC sentences. Anyway, here's the example:

1. D <-> B
2. ~B -> C

Conclusion: ~D -> B

Granted, these aren't the technical symbols for the language of logic, but i didn't feel like dragging out the character map. Any help w/ this proof would be appreciated!

EDIT: As far as i can tell, there's not interpretation that would form a counter-example (make the conclusion true while the premises are false)

Edited by Heretic Monkey, 19 September 2006 - 09:28 PM.


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#2 cowsgonemadd3

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Posted 19 September 2006 - 09:36 PM

What type of math is this?

#3 Animal

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Posted 19 September 2006 - 09:47 PM

CGM,

I was wondering if anyone here has any training using Sentential Calculus


HM,

Sorry, But that sort of stuff just gives me major brain cramps. :thumbsup:

Edit: To add the HM reply

Edited by Animal, 19 September 2006 - 09:54 PM.

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#4 Heretic Monkey

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Posted 20 September 2006 - 08:44 AM

I take back what i said in the first post. I think there IS a counter-example. If I(D) = False and I(B)= False, that makes the conclusion FALSE. It also makes Pr1 TRUE, and with the interpretation of I( C)=True, it makes both the premises true while the conclusion is false. Hopefully that's a suitable response.

BTW: Animal, what happened to your "Be (***) Safe"? Those always make me laugh.....

Edited by Heretic Monkey, 20 September 2006 - 10:28 AM.


#5 cowsgonemadd3

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Posted 20 September 2006 - 09:26 AM

Very sorry I missed it...bonk lol

I havent taken calculus yet so I wont be any help.

#6 jgweed

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Posted 20 September 2006 - 10:02 AM

It would certainly help if you used common logic notation. Or put the syllogism into words (if/then, iff, implies) that can I can retranslate into logical notation, and provide some help.
Cheers,
John
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#7 Heretic Monkey

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Posted 20 September 2006 - 10:26 AM

K, i'll try that:

{Pr1} ... 1 ... D iff B ... P
{Pr2} ... 2 ... If NOT B, then C ... P

And i'm trying to get to If NOT D, then B.

The instructions say to provide a legal proof OR a counter-example. As far as i can tell, i couldn't find ANY suitable proof that guarantees that the conclusion follows from the premises. This is the notation we've been working w/ in my LOG335 class. I'm also taking MA225, which involves pure math proofs. However, they use a double-barred arrow for "IF THEN" and "IFF", like => and <=>.

Let me see if i can get the character map to work:

{Pr1} ... 1 ... D ↔ B... P
{Pr2} ... 2 ... ČB → C ... P
EDIT: Character map fails... there are blanks where the bars should be.... oh well

Hope that's somewhat clearer John...

Edited by Heretic Monkey, 20 September 2006 - 10:28 AM.





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