Question: What sport does John McCarthy and UFC 2 have in common?

Context paragraphs:
McCarthy Formalism: In computer science and recursion theory the McCarthy Formalism (1963) of computer scientist John McCarthy clarifies the notion of recursive functions by use of the IF-THEN-ELSE construction common to computer science, together with four of the operators of primitive recursive functions: zero, successor, equality of numbers and composition.  The conditional operator replaces both primitive recursion and the mu-operator.

John McCarthy (referee): John Michael McCarthy (born October 12, 1962) is an American mixed martial arts referee, perhaps best known for his officiating of numerous bouts promoted by the Ultimate Fighting Championship (UFC) dating back to UFC 2.  Known to fans as "Big" John McCarthy, he took a brief sabbatical from officiating toward the end of 2007 to pursue a career in television commentary for The Fight Network and also provided commentary for Affliction, before returning to his role as a referee in 2008.  McCarthy is also a former Los Angeles Police Officer, and a Tactical Self-Defense Instructor at the Los Angeles Police Academy, as well as the founder of C.O.M.M.A.N.D: a training and certification school for MMA referees and judges.  He has also officiated bouts in Bellator, and is a qualified boxing referee.  In February 2015, Big John & Bellator commentator Sean Wheelock launched their new weekly podcast, Let's Get It On with Big John McCarthy & Sean Wheelock.

Circumscription (logic): Circumscription is a non-monotonic logic created by John McCarthy to formalize the common sense assumption that things are as expected unless otherwise specified.  Circumscription was later used by McCarthy in an attempt to solve the frame problem.  To implement circumscription in his initial formulation, McCarthy augmented first-order logic to allow the minimization of the extension of some predicates, where the extension of a predicate is the set of tuples of values the predicate is true on.  This minimization is similar to the closed world assumption that what is not known to be true is false.

John P. McCarthy: John P. McCarthy (March 17, 1884 – September 4, 1962), also known as J.P. McCarthy or simply as John McCarthy, was an American director and screenwriter of the 1920s through 1945.  He began in the film industry in front of the camera, as an actor in silent films and film shorts during the 1910s, before moving behind the camera in 1920.  He would usually direct his own screenplays.  Although he directed the occasional drama or comedy, his specialty was the Western, which make up most of his filmography.

UFC 2: The Ultimate Fighting Championship Part II (later renamed UFC 2: No Way Out) was a mixed martial arts (MMA) event held by the Ultimate Fighting Championship (UFC) on March 11, 1994, at Mammoth Gardens in Denver, Colorado.  The event was seen live on pay-per-view in the United States, and was later released on home video.

UFC: Throwdown: UFC: Throwdown, known in Japan as UFC: Tapout 2 on the PlayStation 2 and UFC 2 Tapout Final Spec.  on the GameCube, is a video game of the fighting game genre released in 2002 by Genki / Capcom Production Studio 3.  The game is based on the Ultimate Fighting Championship.

1994 in UFC: The year 1994 is the 2nd year in the history of the Ultimate Fighting Championship (UFC), a mixed martial arts promotion based in the United States.  In 1994 the UFC held 3 events beginning with, "UFC 2".

William McCarthy, Baron McCarthy: William Edward John McCarthy, Baron McCarthy (30 July 1925 – 18 November 2012) was a British Labour politician.  McCarthy was a fellow of Nuffield College and Templeton College, Oxford and a specialist in industrial relations.  He was created a life peer in 1976.  From 1979 to 1997 he was Opposition Spokesperson for Employment.  McCarthy was described as "one of Britain’s most influential academics in the field of industrial relations, a painstaking arbiter in the most testing of disputes. . "

Advice taker: The advice taker was a hypothetical computer program, proposed by John McCarthy in his 1958 paper "Programs with Common Sense".  It was probably the first proposal to use logic to represent information in a computer and not just as the subject matter of another program.  It may also have been the first paper to propose common sense reasoning ability as the key to artificial intelligence.  In his paper, McCarthy advocated:

Blind Flight: Blind Flight is a 2003 British film directed by John Furse, starring Ian Hart and Linus Roache.  It is based on the true-life story of the kidnapping and imprisonment of the Irish academic Brian Keenan and the English journalist John McCarthy, two of the hostages in the Lebanon hostage crisis.  The film is based on Keenan's memoir, "An Evil Cradling" and "Some Other Rainbow" by John McCarthy who was a screenplay consultant.  The film received widespread critical acclaim, being nominated for six awards, and winning a BAFTA.

Supporting paragraphs: John McCarthy (referee) UFC 2
Answer: mixed martial arts