Two Plus Two Poker Forums Logic! (Truth trees, Tautology, Contradictions.. :) )
 Register FAQ Search Today's Posts Mark Forums Read Video Directory TwoPlusTwo.com

 Notices

 Science, Math, and Philosophy Discussions regarding science, math, and/or philosophy.

 04-13-2008, 11:05 PM #1 Tumaterminator HOCKEY!   Join Date: Jul 2006 Posts: 26,445 Logic! (Truth trees, Tautology, Contradictions.. :) ) Okay, a truth tree tests for the consistency of an argument: If we want to test for a tautology (something that is true in every case) you: Take Argument (A) Negate it ~(A) Then run a truth tree, if it is closed completely, it is a tautology. A contradiction is FALSE in every case...How could we use truth trees to prove that something is a contradiction? My guess is that you first negate the argument at hand -- ~(A), run a truth tree, and if it is open at EVERY end, then it is a contradiction. I haven't given it too much thought, and I would like some help very soon if possible. Thank You.
 04-13-2008, 11:11 PM #2 Tumaterminator HOCKEY!   Join Date: Jul 2006 Posts: 26,445 Re: Logic! (Truth trees, Tautology, Contradictions.. :) ) I would like to update this: My new guess is that in order to test for a contradiction you: Take original argument, (A) , do not negate it, and run a truth tree. If it is completely closed at the bottom, it is a contradiction. Just need some confirmation on this.
04-14-2008, 11:31 AM   #3
46:1
old hand

Join Date: Feb 2008
Posts: 1,406
Re: Logic! (Truth trees, Tautology, Contradictions.. :) )

Answering for first-order logic, where you have proof by negation, formally this goes something like this:

Given any sentence P in First Order Logic (atomic or complexily composed) there is another sentence NOT P (or ~P). This sentence is true only and only if P is false.

Once u commit yourself to the truth of ~P this is tantamount to committing yourself to the falsity of P.

Why would you do this? Well sometimes the negation of statements is less complex, yet equivalent so you'd want to use a less complex statement. Also with negation elimination/introduction one can 'undress' the First Order sentence, to it's atomic parts.

'Undressing' the formulas goes a great way in providing a formal proof of the sentence.

For a great introduction into first order logic and a playfull approach to negation, try to get your hands on Tarski's World.

Edit:
Quote:
 My new guess is that in order to test for a contradiction you
A great way to test for contradictions in statements is to prove the statement holds a contradictio in terminis in its parts.
So if the sentence is like: -A && B --> (C || D) && E you try by using logical rules (such as modus ponens) to get something like (~A && A). If (~A && A) can be derived from the First order logic sentence you have proven the statement to hold contradiction.
Quote:
 test for a tautology
The tautology rule is an essential rule in first order logic. It simply says for every statement A you are allowed to posit A --> A (and A --> A --> A etc.)
So you are not testing for a tautology, you are even free to introduce them, so you can 'undress' the sentence further. A tautology does not change the truth value.

Also I don't remember using truth trees in first order logic, but for semantics and maybe lambda calculus. Using truth tables will make logical equivalence visable in a flash.

Last edited by 46:1; 04-14-2008 at 11:56 AM.

 04-14-2008, 02:25 PM #4 bigmonkey grinder     Join Date: May 2007 Posts: 649 Re: Logic! (Truth trees, Tautology, Contradictions.. :) ) A tautology is an argument that only consists of a conclusion and no premises, that is necessarily true in virtue of logical laws. An argument with premises and conclusion that is necessarily true is just a sound argument. You can test for a contradiction by making a truth table. It should tell you how to make these in most logic textbooks but I'll see if I can do it here anyway. To test a statement like (A & B) > ¬A, (where > is the material conditional), you do this: A--B--(A & B)-->--¬A T--T----T-----F----F T--F----F-----T----F F--T----F-----T----T F--F----F-----T----T You would fill in the > column last, which is the truth-conditions for (A & B) > ¬A. That sentence is always true except when both A and B are true. For a sentence to be a contradiction it needs to have an F in every row. Likewise to be a tautology it must have a T in every row. If you have 3 or more variables in your sentence, then you need a bigger truth table, with 8 rows in it (e.g. TTT, TTF, TFF etc.)
04-14-2008, 02:30 PM   #5
Justin A
Carpal \'Tunnel

Join Date: May 2004
Location: Dallas
Posts: 9,010
Re: Logic! (Truth trees, Tautology, Contradictions.. :) )

Quote:
 Originally Posted by bigmonkey A tautology is an argument that only consists of a conclusion and no premises, that is necessarily true in virtue of logical laws. An argument with premises and conclusion that is necessarily true is just a sound argument. You can test for a contradiction by making a truth table. It should tell you how to make these in most logic textbooks but I'll see if I can do it here anyway. To test a statement like (A & B) > ¬A, (where > is the material conditional), you do this: A--B--(A & B)-->--¬A T--T----T-----F----F T--F----F-----T----F F--T----F-----T----T F--F----F-----T----T You would fill in the > column last, which is the truth-conditions for (A & B) > ¬A. That sentence is always true except when both A and B are true. For a sentence to be a contradiction it needs to have an F in every row. Likewise to be a tautology it must have a T in every row. If you have 3 or more variables in your sentence, then you need a bigger truth table, with 8 rows in it (e.g. TTT, TTF, TFF etc.)
What is the symbol in front of the last A?

 04-14-2008, 02:33 PM #6 46:1 old hand   Join Date: Feb 2008 Posts: 1,406 Re: Logic! (Truth trees, Tautology, Contradictions.. :) ) ¬ = negation. also written as ~ or NOT.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Two Plus Two     Two Plus Two Magazine Forum     The Best of Two Plus Two     The Two Plus Two Bonus Program     Two Plus Two Pokercast     Two Plus Two Videos     Marketplace         General Marketplace         Staking - Offering Stakes         Staking - Seeking Stakes         Staking - Selling Shares - Online         Staking - Selling Shares - Live         Staking Rails         Transaction Feedback & Disputes     Commercial Marketplace     Staking - Offering Stakes     About the Forums Fantasy Sports     Fantasy Sports         Sporting Events General Poker Discussion     Beginners Questions     Live Casino Poker         Poker Venues         Regional Communities     Poker Goals & Challenges     Books and Publications     Poker Theory     Poker Tells/Behavior, hosted by: Zachary Elwood     News, Views, and Gossip     Twitch - Watch and Discuss Live Online Poker     Televised Poker     Home Poker     Poker Legislation & PPA Discussion hosted by Rich Muny     That's What She Said!     Poker Beats, Brags, and Variance Coaching/Training     Coaching Advice     Cash Game Poker Coach Listings     Tournament/SNG Poker Coach Listings International Forums     Deutsch         BBV [German]     Français     Two Plus Two en Espańol No Limit Hold'em     Medium-High Stakes PL/NL     Micro-Small Stakes PL/NL     Medium-High Stakes Full Ring     Micro-Small Stakes Full Ring     Heads Up NL     Live Low-stakes NL Limit Texas Hold'em     Mid-High Stakes Limit     Micro-Small Stakes Limit Tournament Poker     STT Strategy     Heads Up SNG and Spin and Gos     Mid-High Stakes MTT     Small Stakes MTT     MTT Community     MTTc - Live         WPT.com Other Poker     High Stakes PL Omaha     Small Stakes PL Omaha     Omaha/8     Stud     Draw and Other Poker General Gambling     Backgammon Forum hosted by Bill Robertie.     Probability     Psychology     Sports Betting     Other Gambling Games Internet Poker     Internet Poker         Winning Poker Network         nj.partypoker.com         Global Poker     Commercial Software     Software         Commercial Software         Free Software     nj.partypoker.com         WPT.com 2+2 Communities     Other Other Topics         OOTV         Game of Thrones     The Lounge: Discussion+Review     EDF     Las Vegas Lifestyle     BBV4Life         omg omg omg     House of Blogs Sports and Games     Sporting Events         Single-Team Season Threads         Fantasy Sports     Wrestling     Golf     Pool, Snooker, and Billiards     Chess and Other Board Games     Video Games         League of Legends         Hearthstone     Puzzles and Other Games Other Topics     Politics         Economics     Business, Finance, and Investing     Travel     Science, Math, and Philosophy     History     Religion, God, and Theology     Health and Fitness     Student Life     The Studio     Laughs or Links!     Computer Technical Help     Programming

All times are GMT -4. The time now is 10:46 AM.

 Contact Us - Two Plus Two Publishing LLC - Privacy Statement - Top