Derivations
in [Logic]
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From: Jim Spriggs on 13 Jun 2005 18:11 1st Semester Logic Student wrote: > > ... this is a philosophy class; which I know > you hate. Really?
From: William Elliot on 13 Jun 2005 18:14 On Mon, 13 Jun 2005, 1st Semester Logic Student wrote: > 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 > This web site if of no use as it uses too many special characters that show up as weird graphics which render the text unreadable.
From: Ken Quirici on 13 Jun 2005 19:52 1st Semester Logic Student wrote: > 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? Do you know what 'SD' stands for? That might be a start. Thanks. Ken > 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: H. J. Sander Bruggink on 14 Jun 2005 06:04 1st Semester Logic Student wrote: > > http://www.unc.edu/~theis/logic/SDrules.html These rules look like a Fitch-style natural deduction system for propositional logic. But what does SD stand for? It's not a standard name for any logic I know of. groente -- Sander
From: H. J. Sander Bruggink on 14 Jun 2005 06:06
1st Semester Logic Student wrote: > Any answers, advice, help, suggestions? Some hints (or at least very good heuristics): * if you need to prove something of the form A v B, then usually you need negation elimination somewhere in your derivation; * otherwise, the overall structure of many derivations is: first eliminate the operators of the premise(s) (elimination rules), then introduce the operators of the conclusion(s) (introduction rules). * there are many exceptions to these "rules"! groente -- Sander |