The rules I'm allowed to use are Group 2 and Group 1 rules. I don't know about transposition, but I do know of a step called contra position. Also proofs are used later on, so it would be a good idea to understand the proofs also and how to get from point A to point B if you know what I mean.

Some practice problems would help me out, if you can come up with some, just to see if I understand it and get it down. Unfortunately Math is a big problem for me, so this might not come as easy to me as many people.

I'm open to any help I can get.

One of the big hurdles to overcome is decipher the different structures we utilize in propositional logic. Most of the rules are the same, only they go by different names and so on. Here is what I use:

Inference rules

Disjunctive Syllogism
Modus Ponens
Modus Tollens
Hypothetical Syllogism
Simplification
Conjunction
Addition
Constructive Dilemma

Nested Proofs

Indirect Proof
Conditional Proof

Replacement Rules

Commutation
Association
Double negation
demorgans rule
distribution
transposition
implication
exportation
tautology
equivalence

But tell me more about what you do not get. Is it how to set up the proof? How to format the argument for your proof? Or more specifically, what exactly do you think would help you out the best. You said you wanted a sample problem and a step by step guide on how to do it. At what point are you so I can help out?

The following is a problem I'm doing in the book to practice for the exam, the answer isn't in the book, that's why I'm trying it out, I was told to look over those two sections and do the problems in there.

These are all proof problems, I'll give all the ones that I want to look over, but I need to come up with a way to attack them and how to step by step solve them like steps shown below.

R & Q= Conj. 1,4
P = MP 3,5

2.

1. (P v Q) & R
   
2. (R & P) -> S
   
3. (Q & R) -> S /:. S
   

3.

1. P -> (Q->~R)
   
2. (~R -> S) v T
   
3. ~T & P /:. Q -> S
   

5.

1. (P -> Q) & R
   
2. ~S
   
3. S v (Q -> S) /:. P -> T
   

6.

1. P -> (Q & R)
   
2. R -> (Q -> S) /:. P -> S
   

8.

1. ~P v ~Q
   
2. (Q -> S) -> R /:. P -> R
   

9.

1. S
   
2. P -> (Q & R)
   
3. Q -> ~S /:. ~P
   

These are the problems I need help with and need to be able to understand how to solve these and also non proof problems. The exam is on Monday so I'm trying to study and get help badly.

~Max

Ok, lets start off with one that is a little easier in terms of our using the inference and replacement rules to find out what method best suits you.

Here is proof #9 done in 6 steps;


Now you issue is how to attack problems like these.

The first method you can use to attack a proof like this is to infer or replace all of the lines you are given to begin with. In the case of this problem, line #2 can be replaced via the exportation rule to make (R&Q)-->S. However, doing the problem this way is problematic because one you are done with that replacement, you are pretty much in the same boat because it does not give you any basic variables to break down the argument. When you want to attack a proof like this, it is always best to a) look for the most obvious inference rule, b)look for the most basic replacement rule. Keep an eye out for single variables, because those are perhaps the most helpful thing you can use in your proofs.

The second method involves working from the conclusion forwards. You basically take the conclusion, in this case P-->S, and basically deconstruct it buy inversing the line. So for example, the only way you could get P-->S is by either Transposition or Implication. Transposition would give you ~P-->~S and Implication would give you~PvS. This helps out very well in simpler proofs, but not so well in this one. This way is really difficult though, so use this as a last resort.

Third methodSTEP1. Since we want to use the conditional proof, we have to indent and Assume (AP) P, the antecedent of the conditional in our conclusion. This is useful to us because it gives us a single variable which we can now use to make easier inferences with. At this point keep in mind, now that you have the P, you need to derive at some point in the proof an S because only then can you derive a conditional proof. Look at the proof. Where is there an S? When you become more familiar with the proofs, you can deconstruct as you form the proof from two separate ends. But for now, just try to deconstruct everything and form from the pieces you have.

STEP2. We happen to have a use for out assumed premise. We can use modus ponens to derive Q&R. What we are essentially doing is trying to break down the proof into its constituent parts as much as possible. At this point, remember that you can break down a proof as much as you want and infer things that you may never use. Its wise to just break down everything to make sure you have a good inventory of inferences to use later on should you need it.

STEP3. As we said, we want to break down the problem into the simplest constituent parts. So lines 5 and 6 are simplifications of line 4 so that we have more single variables

STEP4. We see that one of the simplifications will help us derive Q-->S via modus ponens. At this point, notice how helpful it is now to just break down everything and then find out what stuff you can put together for your proof. It really helps out a lot.

STEP5. From all of the fragments you have so far you can now see that you can derive via modus ponens S from lines 5 and 7. You now have all you need to form the conditional proof.

STEP6. End the indentation and cite lines 3-8 where you started with P in line 3 and ended on line 8 with S, deriving via conditional proof P-->S.

So at this point, it may be helpful for you to tell me if any of these three methods are easy for you and if you prefer one to another. I can then elaborate some more on them and we can go through the other problems as well.

I'm still confused on how to go from point A to point B and so forth, I need to find an easy way to understand how to deduce the proofs and how to solve them. I'm feeling like I should give up and just focus on the stuff I know, but I want to do well on this exam.

Any help is appreciated

One of the best things I can tell you to do is to memorize all of the inference and replacement rules back and forth... even if you are not required to do so. In that way, you will be able to instantly register what works, what doesn't work, what translates and what doesn't. Beyond that, one of the three methods I pointed out would be best. You had mentioned that you had favored the third method best. What exactly would you like to know more about beyond what I had outlined?

Folks, modal logic is above my pay grade like all math beyond simple arithmetic. I find that theists pobably don't do any better with it than with regular language. Check out Howard Jordan Sobel's great book " Logic and Theism,' which has much modal logic.

Leibniz did very well with logic... very very well, and he was a theist. Same could be said for most all other rationalist and a majority of empiricist philosophers. However, I would point out that this is only propositional logic, not modal logic in terms of the formal system. There is some point where propositional logic relies on necessary and sufficient truths, but modal logic relies heavy on syllogistic modal principles which snowball truth values.

Dr Paul Draper agrees with me that by talking above our pay grades, philosophers using modal logic and abstruseness cannot convey to the public why we accept what we accept. If they learn something from each other and then translate that into our common languages, then fine.
Now, some find my style baroque but nevertheless understandable and nice whilst others cannot stomach it!
Thanks for the thanks, friends.
Leibniz made two blunders: [1] the big one is that of asking why is their Existence rather than non-existence as how could that be, and why would one find non-existence possible as nothingness since Pythagoras is meaningless and
[2] he errs with the principle of sufficient reason as it is nothing more that obscurantism added to real causes and answers.
Logic is the bane of theists. See the presumption of naturalism and arguments for God for evidence of that.
" Life is its own validation and reward and ultimate meaning.'
'Religion is mythinformation."

I suppose you meant to write necessary and sufficient conditions, not truths. I never heard of sufficient truths.

The modal logic that I know relies on possible world diagrams. See Norman Swartz and Raymond Bradley, Possible Worlds, 1979.

What is snowball truth values?

What good is all that when we others cannot fathom it so that it cannot influence our thinking? Why not just use standard language to advance arguments?
" Logic and Theism," would be an even better book if it were all in standard language rather than that incomprehensible stuff!

It isn't incomprehensible once you learn it. No more than math is once you learn it. Why do y9u think that unless everyone understands something without learning it, it is incomprehensible. Is Japanese incomprehensible?

---------- Post added 11-09-2009 at 02:17 AM ----------



Transposition is another name for contra-position. This resource may be useful to you.

LOL! So it is! I suppose congratulations are in order for for finding an incorrect part of a half year old proof. You never know what you will uncover when you have enough time on your hands... I wish I did. I suppose I should give all of these proofs and tutorials a serious walk through. Good work Emil! The forum is lucky to have such an apt and studious member frequenting the logic section.

conversation is but there is a word within logic called converse. Yet that has does not allow you to move from P→Q to Q→P. The converse, in this instance, is just redirecting the order of the letters. From the converse of P→Q is Q→P which logically identical to P→Q's inverse, ~P→~Q

You are quite right about that, it is better late than never. The best thing that can help out our fellow members is accuracy and reliability, especially on threads that do not generate as much traffic as they once did. As to the what the typo-ed inference is called, I don't have the slightest idea. Never seen it before. However, human ingenuity knows no bounds, so I will venture to conjure one up. Replacement rule... I dub thee "ignoring the obvious," or Obviare Veritas. Only by ignoring the obvious can we infer opposite truth values at our beckon whim within a closed system.

1. P->R
2. R->Q
3. P->Q, HS.
4. ~PvQ, Imp.






1. ~P v S
2. ~T -> ~S
3. P->S, Imp 1.
4. S->T, trans, 2.
5. P->T, HS, 3,4.





1. F -> R
2. L -> S
3. ~C
4. (R & S) -> C
5. ~(R&S), MT 3,4.
6.~Rv~S, DeM 5.
7.R->~S, Imp, 6.
8. F->~S, HS, 7,1.
9. S->~F, Trans, 8.
10. L->~F, HS, 9,2.
11. ~Lv~F, Imp, 10.


I'll get the rest later.

---------- Post added 11-09-2009 at 11:42 PM ----------

1. (P v Q) & R
   
2. (R & P) -> S
   
3. (Q & R) -> S
   
4. R->(P->S), Exp,2.
   
5. R, Simp, 1.
   
6. P->S, MP, 4,5.
   
7. (R&Q)->S, Com, 3.
   
8. R->(Q->S), Exp, 7.
   
9. Q->S, MP, 5,8.
   
10. (Q->S) & (P->S), Conj, 6,9.
    
11. PvQ, Simp, 1.
    
12. QvP, Comm, 11.
    
13. SvS, CD, 12, 10.
    
14. S, Taut, 12.
    

Screw this...im bored.