- published: 14 Dec 2013
- views: 7015
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. As such, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Together with model theory, axiomatic set theory, and recursion theory, proof theory is one of the so-called four pillars of the foundations of mathematics.
Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also focuses on applications in computer science, linguistics, and philosophy.
Although the formalisation of logic was much advanced by the work of such figures as Gottlob Frege, Giuseppe Peano, Bertrand Russell, and Richard Dedekind, the story of modern proof theory is often seen as being established by David Hilbert, who initiated what is called Hilbert's program in the foundations of mathematics. The central idea of this program was that if we could give finitary proofs of consistency for all the sophisticated formal theories needed by mathematicians, then we could ground these theories by means of a metamathematical argument, which shows that all of their purely universal assertions (more technically their provable sentences) are finitarily true; once so grounded we do not care about the non-finitary meaning of their existential theorems, regarding these as pseudo-meaningful stipulations of the existence of ideal entities.
The September 11 attacks (also referred to as September 11, September 11th, or 9/11) were a series of four coordinated terrorist attacks by the Islamic terrorist group al-Qaeda on the United States on the morning of Tuesday, September 11, 2001. The attacks consisted of suicide attacks used to target symbolic U.S. landmarks.
Four passenger airliners—which all departed from airports on the U.S. East Coast bound for California—were hijacked by 19 al-Qaeda terrorists to be flown into buildings. Two of the planes, American Airlines Flight 11 and United Airlines Flight 175, were crashed into the North and South towers, respectively, of the World Trade Center complex in New York City. Within an hour and 42 minutes, both 110-story towers collapsed, with debris and the resulting fires causing partial or complete collapse of all other buildings in the World Trade Center complex, including the 47-story 7 World Trade Center tower, as well as significant damage to ten other large surrounding structures. A third plane, American Airlines Flight 77, was crashed into the Pentagon (the headquarters of the United States Department of Defense) in Arlington County, Virginia, leading to a partial collapse in the Pentagon's western side. The fourth plane, United Airlines Flight 93, initially was steered toward Washington, D.C., but crashed into a field near Shanksville, Pennsylvania, after its passengers tried to overcome the hijackers. In total, the attacks claimed the lives of 2,996 people (including the 19 hijackers) and caused at least $10 billion in property and infrastructure damage and $3 trillion in total costs. It was the deadliest incident for firefighters and law enforcement officers in the history of the United States, with 343 and 72 killed respectively.
A wedding anniversary is the anniversary of the date a wedding took place. Traditional names exist for some of them: for instance, 50 years of marriage is called a "golden wedding anniversary" or simply a "golden anniversary" or "golden." 25 years is silver or silver anniversary And 75 years is Diamond or Diamond anniversary.
The historic origins of wedding anniversaries date back to the Holy Roman Empire, when husbands crowned their wives with a silver wreath on their twenty-fifth anniversary, and a gold wreath on the fiftieth. Later, principally in the twentieth century, commercialism led to the addition of more anniversaries being represented by a named gift.
In the Commonwealth realms, one can receive a message from the monarch for 60th, 65th, and 70th wedding anniversaries, and any wedding anniversary after that. This is done by applying to Buckingham Palace in the United Kingdom, or to the Governor-General's office in the other Commonwealth realms.
2013 (MMXIII) was a common year starting on Tuesday (dominical letter F) of the Gregorian calendar, the 2013th year of the Common Era (CE) and Anno Domini (AD) designations, the 13th year of the 3rd millennium, the 13th year of the 21st century, and the 4th year of the 2010s decade.
2013 was designated as:
September 11 is the 254th day of the year (255th in leap years) in the Gregorian calendar. There are 111 days remaining until the end of the year.
It is usually the first day of the year in the Coptic calendar and Ethiopian calendar (in the period AD 1900 to AD 2099).
Frank Pfenning - Proof Theory Foundations, Lecture 1, Oregon Programming Languages Summer School 2012, University of Oregon For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
Frank Pfenning - Proof Theory Foundations, Lecture 2, Oregon Programming Languages Summer School 2012, University of Oregon For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
View full lesson here: http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical-theory Euclid of Alexandria revolutionized the way that mathematics is written, presented or thought about, and introduced the concept of mathematical proofs. Discover what it takes to move from a loose theory or idea to a universally convincing proof. Lesson by Scott Kennedy, animation by Karrot Animation.
Logic for CS by Dr. S. Arun Kumar, Department of Computer Science and Engineering, IIT Delhi. For more details on NPTEL visit http://nptel.iitm.ac.in
9/11 No Planes Used to Hit WTC - Witnesses Proof Theory - (The Pyrotechnic was caused from the Gas Leak the Naudet Brothers and head fireman on 9/11 were looking for. The Natural Gas was used to fill several upper floors of the WTC). The recent news of New York Buildings on Fire from a "Gas Explosion" is used to cover up this idea. The Pyrotechnic was "set off" with a Hologram or Projected Kinetic Device or Both. - Your Psychological Operation (Ace Baker) - Fake Alien Invasion 1938. http://www.youtube.com/watch?v=Gl8p16YE2YY 9/11 9/11 2013 9/11 anniversary 9/11 anniversary 2013 9/11 anniversary ceremony 9/11 10th anniversary ceremony 9/11 events 9/11 events 2013 9/11 events anniversary 2013 9/11 memorial 9/11 memorial museum 9/11 memorial 2013 9/11 memorial service 2013 9/11 address 2013 ...
NASA and world Freemasonry have pulled off the greatest hoax, propagated the most phenomenal lie, and perpetuated the most complete indoctrination in history. The biggest Lie ever told to mankind is that Earth is a globe. Here's another proof, based on scientific, historical and physical facts to explain the phenomenon. After this video you may change your way of thinking and use brain and sight. Thanks for watching.
Ever wonder how Einstein proved E=mc²? This is how. Pi day (3.14) is Albert Einstein's Birthday! To celebrate, we'll explain 4 of his most groundbreaking papers from 1905, when he was just 26 years old. minutephysics is now on Google+ - http://bit.ly/qzEwc6 And facebook - http://facebook.com/minutephysics And twitter - @minutephysics Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! Music by Nathaniel Schroeder NEW ALBUM!! -- http://juliansaporiti.bandcamp.com/album/lusitania youtube: http://bit.ly/pakJLE Thanks to Nima Doroud and Alex Yale for contributions and to Perimeter Institute for support. Created by Henry Reich
Like pizza and turtles? Subscribe, Dude! ►► http://bit.ly/1dI8VBH Luke, DON'T Destroy the Death Star! ►► http://bit.ly/1PWjnRn Ant Man: Deadliest Superhero! ►► http://bit.ly/1RPEsD7 Wait, you're telling me these guys are teenagers who randomly got doused with some sewer juice and turned into turtles? Who fight crime? Using ninja tactics? While eating pizza? And living underground? HAH, that's CRAZY! ...NO, my friends, NO IT ISN'T. Like the theme song? Thanks to CARF! https://www.youtube.com/user/carfmobile SOCIAL MEDIA: Twitter: @MatPatGT Facebook: facebook.com/GameTheorists Instagram: instagram.com/matpatgt MORE FILM THEORY! Breaking Bad Ending's Hidden Truth ► http://bit.ly/1PAXFqr Is LUKE SKYWALKER Really Evil?!? ► http://bit.ly/22l8VMy The TRUTH about Jon Snow ► http://bit.ly/1dH...
Hello Neighbor has plenty of evidence as to who the neighbor is and what he's doing in his basement. My theory covers all material distributed by the developer thus far, as well as busts some popular myths around the game and explores what we can expect in future updates. This game is going to be quite a story. Basement Trailer ► https://www.youtube.com/watch?v=O41H9yESyHA Producer Update ► https://www.youtube.com/watch?v=6XUXvth1Pbs Check out my gameplay of Hello Neighbor! ► https://www.youtube.com/playlist?list=PL5SfwcMShbfUSQXXtZDOzma5ebcHPqViX Subscribe for more Hello Neighbor ► https://www.youtube.com/CaptainSauce?sub_confirmation=1 Patreon ► https://www.patreon.com/captainsauce Twitter ► https://twitter.com/TheCaptainSauce Facebook ► https://www.facebook.com/CaptainSauce?ref=aymt_h...
gr8
National Geographic - Parallel Universe Parallel Universe Theory And Proof Documentary
Frank Pfenning - Proof Theory Foundations, Lecture 1, Oregon Programming Languages Summer School 2012, University of Oregon For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
Frank Pfenning - Proof Theory Foundations, Lecture 2, Oregon Programming Languages Summer School 2012, University of Oregon For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
Frank Pfenning - Proof Theory Foundations, Lecture 3, Oregon Programming Languages Summer School 2012, University of Oregon For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
Frank Pfenning - Proof Theory Foundations, Lecture 4, Oregon Programming Languages Summer School 2012, University of Oregon For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
NEW WORLD ORDER IS NOT A CONSPIRACY THEORY PROOF 2016. -- JOIN US -- Subscribe ● https://www.youtube.com/anonymousupdates?sub_confirmation=1 Anonymous Google+ ● https://google.com/+AnonymousUpdates Anonymous Twitter ● http://twitter.com/UpdateAnon