Derivations
in [Logic]
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From: 1st Semester Logic Student on 12 Jun 2005 18:05 Hey all, We have recently moved on to the wonderful world of "derivations." :P I have found that there is more than one way to derive a sentence in SL from the premis. How would you guys go about showing that the following derviation claims hold in SD? Obviously we need to construct a derivation. How can I type my derivations on the message board? The following are the ones I'm working on now. Any advice on the best ways of deriving the following would be helpful as well as any tactics that may be the best. I have read of a way to work backwards, but I stink at that so far, so I'm just working from the premis down to what it is I'm trying to derive. a) {A v B, ~B} single-turnstile A b) {[A horseshoe (~B horseshoe C)], A & ~B} single-turnstile C v E c) {(~A v ~B) horseshoe C, D & ~C} single-turnstile A d) {A horseshoe ~~B, C horseshoe ~B} single-tunrstile ~(A & C) Now, in the above I wrote out some of the symbols (horseshoe and single-turnstile) so that everyone would be able to read it. Please forgive my "noobieness." Obviously everything before the single-turnstile are the main assumptions and after the turnstile is the conclusion which is what I'm trying to derive. I have some others that I'm trying to show are a theorem in SD. I am doing this by deriving them from an empty set. This part confuses me more than the above. Some of these problems are the following: e) A horseshoe (B horseshoe A) f) ~A horseshoe ((B & A) horseshoe C) g) (A v B) horseshoe (B v A) h) A tripplebar ~~A Any answers, advice, help, suggestions? I have some truth tables to work on as well, but they seem very straight forward and I don't think I need any help with those. I may type up the questions and what I got as answers just to let you guys check my work. Thanks! Logic Noob
From: Jim Spriggs on 12 Jun 2005 19:57 1st Semester Logic Student wrote: > .... How would you guys go about showing that the following > derviation claims hold in SD? ... > > a) {A v B, ~B} single-turnstile A > b) {[A horseshoe (~B horseshoe C)], A & ~B} single-turnstile C v E > c) {(~A v ~B) horseshoe C, D & ~C} single-turnstile A > d) {A horseshoe ~~B, C horseshoe ~B} single-tunrstile ~(A & C) What is SD? How you deduce things depends on the deductive system you're using. What are your rules? What are your axioms? Do you have any derived rules yet? I'd write |- for single turnstile -> for horseshoe.
From: William Elliot on 13 Jun 2005 03:34 On Sun, 12 Jun 2005, Jim Spriggs wrote: > 1st Semester Logic Student wrote: > > > .... How would you guys go about showing that the following > > derviation claims hold in SD? ... > > > > a) {A v B, ~B} single-turnstile A > > b) {[A horseshoe (~B horseshoe C)], A & ~B} single-turnstile C v E > > c) {(~A v ~B) horseshoe C, D & ~C} single-turnstile A > > d) {A horseshoe ~~B, C horseshoe ~B} single-tunrstile ~(A & C) > > What is SD? How you deduce things depends on the deductive system > you're using. What are your rules? What are your axioms? Do you have > any derived rules yet? > > I'd write |- for single turnstile > -> for horseshoe. > A v B, ~B |- A is also common usage for a). As we don't know what SL and SD are, I'll to it my way. ~B B -> ~B B -> B B -> ~B&B ~B&B -> A B -> A A -> A B -> A AvB -> A AvB AvB -> A A
From: 1st Semester Logic Student on 13 Jun 2005 16:44 Hey guys! Here is a link to the rules of SD. I'm supprised you guys haven't heard of it. It seems to be in every logic book I've seen although I know you guys are more math based and this is a philosophy class; which I know you hate. All the rules we use are found at this website. Although it is not from my university, they are using the same rules we (our book) uses. http://www.unc.edu/~theis/logic/SDrules.html Thanks!
From: Jim Spriggs on 13 Jun 2005 17:22
1st Semester Logic Student wrote: > > Hey guys! > > Here is a link to the rules of SD. I'm supprised you guys haven't heard > of it. It seems to be in every logic book I've seen Without looking too closely either at the web page or at the book, they seem to be the rules in one book out of however many I've got. Since they appear in not only all of the books you've got, but all you've seen, you win. What prize would you like? > although I know you > guys are more math based and this is a philosophy class This is irrelevant. We just cannot know what rules, etc, you may use. Ok, there's a circumstance in which someone here might know: if they are attending your course and recognize the questions. |