Logic Proof Help

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Reply Fri 6 Jun, 2008 02:01 pm
Originally posted by SteveP;

Hello everyone, this is my first post here. I'm glad to find some place where I can talk with people interested in Philosophy too. I'm mainly interested in Logic though.

I did have a question though, I'm taking basic philosophy right now and our professor gave us some questions to go over. I am completely stumped on four of them. He gave us a sheet with 18 rules for inference and replacement.

we are supposed to prove the arguments as valid. I'm hoping someone can help explain this to me.
And Logic pro's in the room? Don't laugh, they're hard for me. :p

Anyhow, here are the problems I have

1:
[A (B v C)] (D A)
~A
/∴ ~D


2:
A B
/∴ A ~(~B . ~C)

3:
~N S
S ~A
~A ~V
/∴ V (A . N)

4:
~W ~F
~F ~(E v A)
~E S
P A
/∴ ~W (S . ~P)


Thanks in advance for any help you can give me!
 
SteveP phil
 
Reply Fri 6 Jun, 2008 02:03 pm
@VideCorSpoon,
Ok, here's the image for the problem because the symbols above are messed up.

http://image.bayimg.com/najmhaabn.jpg
or the link to the image page if the first doesn't work bayimg - image: Picture 1.png - free uncensored image hosting
 
VideCorSpoon
 
Reply Fri 6 Jun, 2008 02:06 pm
@SteveP phil,
First question... Is the weather to your liking?

Second... Can you solve this with additional lines or are these lines the only lines you can use?

Thirdly, at what point in the class are you? Midterm?

Fourthly, what book are you using? Pray to Geebus if you are using the Bergmann et al edition of "The Logic Book."

Fifthly, What topic did you last cover?

Sixthly, Do you think ponies are pretty? You will be judged on your response quite thoroughly.
 
SteveP phil
 
Reply Fri 6 Jun, 2008 02:15 pm
@VideCorSpoon,
The weather is exemplary, thank you for asking.

I'm not sure exactly what you mean by solving with additional lines... but we can create lines using the rules of inference and replacement.

Actually this is near the end of the class. These are some example questions for the final on monday!!!!

"A concise introduction to Logic"

Chapter 7, Natural Deduction in propositional logic - or... these 18 rules we have.

I think Ponies are gangly and ugly. Shetland ponies are, however, still unattractive despite their lack of gangliness.
 
VideCorSpoon
 
Reply Fri 6 Jun, 2008 02:21 pm
@SteveP phil,
We are pleased by your response and shall make a sacrificial offering of a shetland pony to the Gods of Jelly to give you good luck for your exam on Monday. LOL!

Give me a little time and I'll solve them in the easiest way possible and post them and then we'll look over them if you have any other questions.
 
SteveP phil
 
Reply Fri 6 Jun, 2008 02:24 pm
@VideCorSpoon,
That sounds excellent. If you would include what lines you used on what rules (i.e. [1,3 MP] - lines one and three, rule modes ponens) that would really help me understand how you figured it out.
 
VideCorSpoon
 
Reply Fri 6 Jun, 2008 02:40 pm
@SteveP phil,
On problems 2, 3, and 4 the answers have a period in between the variables i.e. A --> ~ (~B . ~C)

Is this a conjunction symbol in your book?
 
VideCorSpoon
 
Reply Fri 6 Jun, 2008 03:53 pm
@VideCorSpoon,
http://i25.tinypic.com/xlcvph.jpg
The other problems will take a while... or not at all. Like I said, this guy is really something for a beginning propositional logic class.
 
SteveP phil
 
Reply Fri 6 Jun, 2008 04:44 pm
@VideCorSpoon,
Yeah, she said that Conditional Proofs are Ok. and also IP's

I'm gonna try and figure out what you did there. Very Happy
 
SteveP phil
 
Reply Fri 6 Jun, 2008 04:45 pm
@VideCorSpoon,
I assume that the --> you wrote is the horseshoe symbol I used?
 
SteveP phil
 
Reply Fri 6 Jun, 2008 04:51 pm
@SteveP phil,
yes, the . is an "and" symbol ( but, yet, although, however, still, etc.)
 
VideCorSpoon
 
Reply Fri 6 Jun, 2008 05:22 pm
@SteveP phil,
Yup, --> is the horse shoe.

The thing to remember with logical proofs is always look for the easiest solution, because its usually the right one. The trick I have found always works when you don't know what to do right off the bat is solve the problem in anyway and then from those trouble shooting solutions you may find a solution. It doesn't matter if you include them in your proof if you don't use them.

I usually pull out the conditional proof when I want to do half of the problem. Have you gone over conditional proofs or is that something she will allow you to do even though she hasn't covered it.

The other problems are proving to be a pain, but I'm still trying to solve them.
 
SteveP phil
 
Reply Fri 6 Jun, 2008 05:28 pm
@VideCorSpoon,
Yes, we have gone over conditional proofs. And I thank you very much for putting you time in and helping me figure out whats going on with these guys.
 
VideCorSpoon
 
Reply Fri 6 Jun, 2008 08:27 pm
@SteveP phil,
It's absolutely no problem.

Actually, I should be thanking you. It seems I got a little rusty with these complex proofs. This is a good brain scratch.

Those other three problems are pretty rough, but I'll try to get through them and post them for you.
 
Arjen
 
Reply Sat 7 Jun, 2008 01:39 am
@SteveP phil,
It is funny to see how many different notations can be used. I think
~ = negation
. = conjunction
horseshoe = implication


I have no clue what the slash and three dots mean though.

Anyone?

Smile
 
SteveP phil
 
Reply Sat 7 Jun, 2008 01:48 am
@Arjen,
yeah, ~ is negation . is a conjunction horseshoe is a "in then" statement.

the / triple dot is the conclusion.
 
VideCorSpoon
 
Reply Sat 7 Jun, 2008 09:09 am
@SteveP phil,
yup, also " " is used for conclusion, the turn style I believe.
 
SteveP phil
 
Reply Sat 7 Jun, 2008 11:42 pm
@VideCorSpoon,
Hello Mr. Spoon! Any progress on those toughies?

-Josh
 
VideCorSpoon
 
Reply Sun 8 Jun, 2008 06:29 am
@SteveP phil,
almost! #2 is turning out to be a real pain. But I'll be sure to post them in a few hours for you.
 
VideCorSpoon
 
Reply Sun 8 Jun, 2008 08:59 am
@VideCorSpoon,
http://i29.tinypic.com/33cy8as.jpg

I was able to solve #3... but 1 and 2 are another matter.

For number one, you have to eventually solve in your proof for D --> A in order to use Modus Tollens with line 2 (~A) to get ~D. That much is clear.But what is evading me is how to get A --> (B v C) and Modus Ponens to get D --> A. The only possible way I can think of solving this problem is with sub-structured nested proofs which I don't know if your allowed to use.

So the end of # 1 should look like this

#? - D --> A Modus Ponens ???
#? - ~D Modus Tollens 2, ???

For number two... that is a dill of a problem. Besides an indirect proof " A- AP" or conditional proof, the only two ways to kick off the proof are by transposition "~B v ~A" or implication "~A v B". The rest is nerve racking without complex nested proofs, and even then I'm not quite sure.

Sorry about that, I wish I could be more helpful. If you have any questions on the two I solved or want to try to troubleshoot the other two, let me know.
 
 

 
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