In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. It is denoted by the logical operator symbol ∃ (pronounced "there exists" or "for some"), which is called the existential quantifier. Existential quantification is distinct from ''universal'' quantification ("for all"), which asserts that the property or relation holds for ''any'' members of the domain.

Symbols are encoded and .

Basics

Consider a formula that states that some natural number multiplied by itself is 25. :

0·0 = 25, or 1·1 = 25, or 2·2 = 25, or 3·3 = 25, and so on.

This would seem to be a logical disjunction because of the repeated use of "or". However, the "and so on" makes this impossible to integrate and to interpret as a disjunction in formal logic. Instead, the statement could be rephrased more formally as :

For some natural number ''n'', ''n''·''n'' = 25.

This is a single statement using existential quantification.

This statement is more precise than the original one, as the phrase "and so on" does not necessarily include all natural numbers, and nothing more. Since the domain was not stated explicitly, the phrase could not be interpreted formally. In the quantified statement, on the other hand, the natural numbers are mentioned explicitly.

This particular example is true, because 5 is a natural number, and when we substitute 5 for ''n'', we produce "5·5 = 25", which is true. It does not matter that "''n''·''n'' = 25" is only true for a single natural number, 5; even the existence of a single solution is enough to prove the existential quantification true. In contrast, "For some even number ''n'', ''n''·''n'' = 25" is false, because there are no even solutions.

The ''domain of discourse'', which specifies which values the variable ''n'' is allowed to take, is therefore of critical importance in a statement's trueness or falseness. Logical conjunctions are used to restrict the domain of discourse to fulfill a given predicate. For example: :

For some positive odd number ''n'', ''n''·''n'' = 25"

is logically equivalent to :

For some natural number ''n'', ''n'' is odd and ''n''·''n'' = 25".

Here, "and" is the logical conjunction.

In symbolic logic, "∃" (a backwards letter "E" in a sans-serif font) is used to indicate existential quantification. Thus, if ''P''(''a'', ''b'', ''c'') is the predicate "''a''·''b'' = c" and $\backslash mathbb\{N\}$ is the set of natural numbers, then : $\backslash exists\{n\}\{\backslash in\}\backslash mathbb\{N\}\backslash ,\; P(n,n,25)$ is the (true) statement :

For some natural number ''n'', ''n''·''n'' = 25.

Similarly, if ''Q''(''n'') is the predicate "''n'' is even", then : $\backslash exists\{n\}\{\backslash in\}\backslash mathbb\{N\}\backslash ,\; \backslash big(Q(n)\backslash ;\backslash !\backslash ;\backslash !\; \{\backslash wedge\}\backslash ;\backslash !\backslash ;\backslash !\; P(n,n,25)\backslash big)$ is the (false) statement :

For some even number ''n'', ''n''·''n'' = 25.

In mathematics, the proof of a "some" statement may be achieved either by a constructive proof, which exhibits an object satisfying the "some" statement, or by a nonconstructive proof which shows that there must be such an object but without exhibiting one.

Properties

Negation

A quantified propositional function is a statement; thus, like statements, quantified functions can be negated. The $\backslash lnot\backslash$  symbol is used to denote negation.

For example, if P(''x'') is the propositional function "x is between 0 and 1", then, for a domain of discourse ''X'' of all natural numbers, the existential quantification "There exists a natural number ''x'' which is between 0 and 1" is symbolically stated: :$\backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)$

This can be demonstrated to be irrevocably false. Truthfully, it must be said, "It is not the case that there is a natural number ''x'' that is between 0 and 1", or, symbolically: :$\backslash lnot\backslash \; \backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)$.

If there is no element of the domain of discourse for which the statement is true, then it must be false for all of those elements. That is, the negation of :$\backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)$ is logically equivalent to "For any natural number ''x'', x is not between 0 and 1", or: :$\backslash forall\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; \backslash lnot\; P(x)$

Generally, then, the negation of a propositional function's existential quantification is a universal quantification of that propositional function's negation; symbolically, :$\backslash lnot\backslash \; \backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)\; \backslash equiv\backslash \; \backslash forall\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; \backslash lnot\; P(x)$

A common error is stating "all persons are not married" (i.e. "there exists no person who is married") when "not all persons are married" (i.e. "there exists a person who is not married") is intended: :$\backslash lnot\backslash \; \backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)\; \backslash equiv\backslash \; \backslash forall\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; \backslash lnot\; P(x)\; \backslash not\backslash equiv\backslash \; \backslash lnot\backslash \; \backslash forall\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)\; \backslash equiv\backslash \; \backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; \backslash lnot\; P(x)$

Negation is also expressible through a statement of "for no", as opposed to "for some": :$\backslash nexists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)\; \backslash equiv\; \backslash lnot\backslash \; \backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)$

Rules of Inference

A rule of inference is a rule justifying a logical step from hypothesis to conclusion. There are several rules of inference which utilize the existential quantifier.

''Existential introduction'' concludes that, if the propositional function is known to be true for a particular element of the domain of discourse, then it must be true that there exists an element for which the proposition function is true. Symbolically,

:$P(a)\; \backslash to\backslash \; \backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)$

The reasoning behind existential elimination is as follows: If it is given that there exists an element for which the proposition function is true, and if a conclusion can be reached by giving that element an arbitrary name, that conclusion is necessarily true, as long as it does not contain the name. Symbolically, for an arbitrary ''c'' and for a proposition Q in which ''c'' does not appear:

:$\backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)\; \backslash to\backslash \; ((P(c)\; \backslash to\backslash \; Q)\; \backslash to\backslash \; Q)$

$P(c)\; \backslash to\backslash \; Q$ must be true for all values of ''c'' over the same domain ''X''; else, the logic does not follow: If ''c'' is not arbitrary, and is instead a specific element of the domain of discourse, then stating P(''c'') might unjustifiably give more information about that object.

Unlike the universal quantifier, the existential quantifier distributes over logical disjunctions:

$\backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)\; \backslash or\; Q(x)\; \backslash to\backslash \; (\backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; P(x)\; \backslash or\; \backslash exists\{x\}\{\backslash in\}\backslash mathbf\{X\}\backslash ,\; Q(x))$

The empty set

By convention, the formula $\backslash exists\; \{x\}\{\backslash in\}\backslash emptyset\; \backslash ,\; P(x)$ is always false, regardless of ''P''(''x''). This is because $\backslash emptyset$ denotes the empty set, and no ''x'' of any description – let alone an ''x'' fulfilling a given predicate ''P''(''x'') – exist in the empty set. See also vacuous truth.

Notes

See also

Uniqueness quantification

Quantifiers

First-order logic

References

Category:Logic Category:Quantification Category:Something

ca:Quantificador existencial cs:Existenční kvantifikátor da:Eksistenskvantor de:Existenzaussage et:Olemasolukvantor es:Cuantificador existencial eo:Ekzistokvantigilo fa:سور وجودی fr:Existence (mathématiques) it:Quantificatore esistenziale (simbolo) nl:Existentie ja:存在記号 pl:Kwantyfikator egzystencjalny pt:Quantificação existencial ru:Квантор существования sk:Existenčný kvantifikátor fi:Eksistenssikvanttori sv:Existenskvantifikator zh:存在量化

birthname	Liv Rundgren
birth date	July 01, 1977
birth place
occupation	Actress
yearsactive	1994–present
spouse	Royston Langdon (2003–2008; 1 child) }}

Liv Rundgren Tyler (born July 1, 1977) is an American actress and model. She is the daughter of Aerosmith's lead singer, Steven Tyler, and Bebe Buell, model and singer. Tyler began a career in modeling at the age of 14, but after less than a year she decided to focus on acting. She made her film debut in the 1994 film ''Silent Fall''. She then appeared in supporting roles in ''Empire Records'' (1995), ''Heavy'' (1996) and ''That Thing You Do!'' (1996). Tyler later achieved critical recognition in the leading role ''Stealing Beauty'' (1996). She followed this by starring in supporting roles including ''Inventing the Abbotts'' (1997) and ''Cookie's Fortune'' (1999).

Tyler achieved international recognition as a result of her portrayal of Elf maiden Arwen Undómiel in the ''Lord of the Rings'' film trilogy. She has appeared in an eclectic range of films, including the 2004 comedy ''Jersey Girl'', the indie film ''Lonesome Jim'' (2005), the drama ''Reign Over Me'' (2007) and big-budget studio films such as ''Armageddon'' (1998), ''The Strangers'' (2008) and ''The Incredible Hulk'' (2008).

Since 2003, Tyler has served as a United Nations Children's Fund (UNICEF) Goodwill Ambassador for the United States, and as a spokesperson for Givenchy's line of perfume and cosmetics.

Early life

Tyler was born Liv Rundgren at Mount Sinai Hospital in New York. She is the first-born daughter of Bebe Buell, a model, singer, and former Playboy Playmate (Miss November 1974), and Steven Tyler, the lead singer of Aerosmith. Her mother named her after Norwegian actress Liv Ullmann, after seeing Ullmann on the cover of the March 5, 1977 issue of ''TV Guide''. She is of Italian, German, Polish, Russian and English ancestry on her father's side and also has three half-siblings: Mia Tyler (born 1978), Chelsea Anna Tallarico (born 1989), and Taj Monroe Tallarico (born 1992). Her maternal grandmother, Dorothea Johnson, founded the Protocol School of Washington.

At birth, Buell claimed that rock star Todd Rundgren was Tyler's biological father. At age nine, Tyler discovered that she was Steven Tyler's daughter after meeting him and noticing a resemblance she shared with his other daughter, Mia. When she asked her mother about the similarity, the secret was revealed. The truth about Tyler's paternity did not become public until five years later, in 1991, when she changed her name from Rundgren to Tyler, but kept the former as a middle name. Buell's alleged reason for the initial decision was that Steven was too heavily addicted to drugs at the time of her birth. Since learning the truth about her paternity, Liv and Steven have developed a close relationship. They have also worked together professionally, once when she appeared in Aerosmith's music video for "Crazy" in 1993 and again when Aerosmith performed many of the songs in the film ''Armageddon'' (1998), in which Liv Tyler starred.

Tyler attended the Congressional Schools of Virginia, Breakwater School and Waynflete School in Portland, Maine, before returning to New York City with her mother at the age of 12. She went to York Preparatory in New York City for junior high and high school, after her mother researched the school to accommodate Tyler's ADHD. She graduated in 1995, and left to continue her acting career. When asked about the way she spent her early life, Tyler said: "For me, I didn’t get much of a childhood in my teen years because I’ve been working since I was 14. But that also kept me out of trouble. When everybody was doing acid and partying like crazy, I was at work on a movie in Tuscany ... having my own fun, of course, but it was a different kind of thing. I have no regrets. I love the way my life has gone."

Career

Early work

At the age of 14, Tyler received her first modeling job with assistance of Paulina Porizkova who took photos of her that ended up in ''Interview'' magazine. She later starred in television commercials. However, she became bored with her modeling career less than a year after it started, and decided to go into acting. She never took acting lessons. Tyler first became known to television audiences when she starred alongside Alicia Silverstone in the music video for Aerosmith's 1993 song "Crazy".

Tyler made her feature film debut in ''Silent Fall'' in 1994, where she played the older sister of an autistic boy. In 1995, she starred in the comedy drama ''Empire Records''. Tyler has described ''Empire Records'' as "one of the best experiences" she has ever had. Soon after, she landed a supporting role in James Mangold's 1996 drama ''Heavy'' as Callie, a naive young waitress. The film received favorable reviews; critic Janet Maslin noted: "Ms. Tyler ... gives a charmingly ingenuous performance, betraying no self-consciousness about her lush good looks."

Popular success

Tyler had her breakthrough role in ''Stealing Beauty'' (1996), in which she played Lucy Harmon, an innocent, romantic teenager who travels to Italy intent on losing her virginity. The film received generally mixed reviews, but Tyler's performance was favored by the critics; ''Variety'' wrote: "Tyler is the perfect accomplice. At times sweetly awkward, at others composed and serene, the actress appears to respond effortlessly and intuitively to the camera, creating a rich sense of what Lucy is about that often is not explicit in the dialogue." ''Empire'' noted, "Liv Tyler (here radiantly resembling a ganglier young Ava Gardner) with a rare opportunity to enamour, a break she capitalises on with composure." The film was directed by Bernardo Bertolucci, who chose Tyler for the role after meeting with a number of young girls in Los Angeles, including Tyler's music video co-star Alicia Silverstone. Bertolucci claimed "there was something missing in all of them". He later admitted that what he saw in Tyler was a ''gravitas'' he described as "a New York aura". During promotion of the film, Tyler admitted she wanted to separate herself from the character during production; "I tried my damnedest not to think of my own situation. But at one point, after a take, I just started to cry and cry. I remembered when I found out about my dad and how we just stared at each other from head to toe taking in every nook and cranny."

She later appeared in ''That Thing You Do!'' (1996), a movie about a fictional one-hit wonder rock band called The Oneders, following their whirlwind rise to the top of the pop charts, and just as quickly, their plunge back to obscurity. The film was written and directed by Tom Hanks. It grossed over $25 million worldwide, and was met with favorable reviews. The following year, she appeared in ''Inventing the Abbotts'' in 1997, in which she played the daughter of Will Patton and Barbara Williams' characters. The movie is based on a short story by Sue Miller. ''Entertainment Weekly'' declared Tyler's performance as "lovely and pliant". That same year, Tyler was chosen by ''People'' magazine as one of the 50 Most Beautiful People.

Tyler next appeared in ''Armageddon'' (1998), where she played the daughter of Bruce Willis' character and love interest of Ben Affleck's character. The film generated mixed reviews, but was a box office success earning $553 million worldwide. The movie included the songs "I Don't Want to Miss a Thing" and "What Kind of Love Are You On" by Aerosmith. In a 2001 interview with ''The Guardian'', she admitted that she turned down the role in ''Armageddon''; "I really didn't want to do it at first and I turned it down a couple of times, but the biggest reason I changed my mind was because I was scared of it. I wanted to try it for that very reason. I mean, I'm not really in this to do amazing things in my career - I just want it to be special when I make a movie."

She was then cast in the drama ''Onegin'' (1999), a film based on the 19th century Russian novel of the same name by Alexander Pushkin, in which she portrayed Tatyana Larina and co-starred with Ralph Fiennes. Tyler was required to master an English accent, though Stephen Holden of the ''New York Times'' felt that her approximation of an English accent was "inert". The film was critically and financially unsuccessful. That same year, she appeared in the historical comedy film ''Plunkett & Macleane''.

She later appeared in two films directed by Robert Altman, ''Cookie's Fortune'' (1999) and ''Dr. T & the Women'' (2000). In ''Cookie's Fortune'', she was part of an ensemble cast that included Glenn Close, Julianne Moore, Chris O'Donnell, and Patricia Neal. Her performance well received among critics; Salon.com wrote: "This is the first time in which Tyler's acting is a match for her beauty (she's always been a bit forlorn). Altman helps her find some snap, but a relaxed, silly snap, as in the cartoon sound she makes when she takes a midday swig of bourbon. The lazy geniality of the movie is summed up by the way Emma [Tyler's character] saunters off to take a swim with her cowboy hat and pint of Wild Turkey." ''Entertainment Weekly'' also noted that Tyler is "sweetly gruff as the tomboy troublemaker". In the romantic comedy, ''Dr. T & the Women'', she played Marilyn, a gynecological patient of Richard Gere's character, who is the lesbian lover of his daughter, played by Kate Hudson.

In 2001, Tyler played the object of infatuation for three men (Matt Dillon, John Goodman and Paul Reiser) in the black comedy ''One Night at McCool's''. In discussion of the role, she said: "This was definitely the first part where I had to be so physically aware and have people so aware of me physically. Maybe it's not hard for anybody else, but it is a bit for me. I mean I love my body and I feel very comfortable in my skin, but this was tough." Peter Travers of ''Rolling Stone'' wrote: "Tyler, a true beauty, gives the role a valiant try, but her range is too limited to play this amalgam of female perfection."

Recent work

In 2001, she starred in the feature film ''The Lord of the Rings: The Fellowship of the Ring'', directed by Peter Jackson. She played the Elf maiden Arwen Undómiel. The film is based on the first volume of J. R. R. Tolkien's ''The Lord of the Rings''. The filmmakers approached Tyler after seeing her performance in ''Plunkett & Macleane''. She learned to speak the fictitious Elvish language that was created by Tolkien. Mick LaSalle of the ''San Francisco Chronicle'' noted that Tyler's performance was "lovely and earnest".

A year later, Tyler again starred as Arwen in ''The Lord of the Rings: The Two Towers'', the second installment of the series. The film received favorable reviews. Tyler spent months before filming learning swordfighting, to be used during the concluding battle scenes in ''The Two Towers'', though her scenes from the battle were removed after the script was changed. The film was an enormous box office success, earning over $926 million worldwide, out grossing its predecessor, which earned over $871 million. In 2003, Tyler featured in the third and last installment of the series, ''The Lord of the Rings: The Return of the King''.

Following the success of ''The Lord of the Rings'', she appeared opposite her ''Armageddon'' co-star Ben Affleck in writer-director Kevin Smith's romantic comedy ''Jersey Girl'' (2004), playing a woman who re-opens a widowed father's heart to love, played by Affleck. In an interview with MTV News, Tyler confessed that she felt "scared and vulnerable" while filming ''Jersey Girl'', adding "I was so used to those other elements of the character [Arwen]. On ''The Lord of the Rings'', a lot of things were done in post-production, whereas this was really just about me and Ben sitting there, just shooting off dialogue." However, she reiterated that doing ''Jersey Girl'' was what she wanted to do.

In 2005, she appeared in Steve Buscemi's independent drama ''Lonesome Jim'', where she was cast alongside Casey Affleck, as a single mother and nurse who reconnects with an old fling who has returned to their small town of Indiana after a failed run as a novelist in New York. The film was screened at a special presentation at the 2005 Sundance Film Festival where it was nominated for the Grand Jury Prize. Tyler's next appearance in film was in a supporting role as an insightful therapist who tries to help a once-successful dentist (Adam Sandler) cope with the loss of his family during the events of the September 11th attacks in ''Reign Over Me'' (2007).

In 2008, she starred in the horror-thriller ''The Strangers'' with Scott Speedman, a film about a young couple who are terrorized one night by three masked assailants in their remote country house. Although the film garnered a mixed reception among critics, it was a box office success. In an interview with ''Entertainment Weekly'', she noted that ''The Strangers'' was the most challenging role of her career. "It was as far as I could push myself in every way: physically, emotionally, mentally."

She appeared in ''The Incredible Hulk'' (2008), in which she played Dr. Betty Ross, the love interest of the title character, played by Edward Norton. Tyler was attracted to the love story in the script, and was a fan of the television show. She said filming the part was "very physical, which was fun", and compared her performance to "a deer caught in the headlights". ''The Incredible Hulk'' was a box office success, earning over $262 million worldwide. ''The Washington Post'', in review of the film, wrote: "Tyler gives Betty an appropriately angelic nimbus of ethereal gentleness as the one Beauty who can tame the Beast ... during their most pivotal encounters."

Tyler is appearing in two films released in 2011: ''Super'' and ''The Ledge''. In April 2011, publishing house Rodale announced that Tyler and her grandmother Dorothea Johnson, a noted etiquette expert, have written a book called "Modern Manners." Rodale plans to release the book in May 2012.

Personal life

In 1998, Tyler began dating British musician Royston Langdon of the band Spacehog. She and Langdon became engaged in February 2001, and married in Barbados on March 25, 2003. On December 14, 2004, she gave birth to a son, Milo William Langdon. On May 8, 2008, the couple confirmed through representatives that they would be separating but remain friends. In an interview with the Australian ''Daily Telegraph'', Tyler revealed that her separation from Langdon led her to move to Los Angeles, explaining that it was hard to be in the New York home they shared. In June 2010, Tyler stated she was "far too sensitive" for casual dates, adding "I fall in love once in a blue moon."

Tyler is an active supporter of the charitable United Nations Children's Fund (UNICEF). She was appointed as a Goodwill Ambassador for the United States in 2003. In November 2004, she hosted the lighting of the UNICEF Snowflake in New York City. Tyler also served as spokesperson for the 2004 Givenchy Mother's Day promotion, in support of UNICEF's Maternal & Neonatal Tetanus (MNT) campaign.

Since 2004, she has donated to the Women's Cancer Research Fund to support innovative research, education, and outreach directed at the development of more effective approaches to the early diagnosis, treatment and prevention of all women's cancers. In October 2007, Tyler, along with her mother, Bebe Buell and her grandmother, Dorothea Johnson, helped launch the Emergen-C Pink energy drink, in which the event was in honor of Breast Cancer Awareness month.

She is good friends with designer Stella McCartney, model Helena Christensen and actresses Kate Hudson and Gwyneth Paltrow. Tyler was formerly a vegan, but has since begun to eat meat. In 2003, she became the spokesperson for Givenchy perfume and cosmetics; in 2005 the brand named a rose after her, which was used in one of its fragrances. In 2009, Tyler signed on for two more years as Givenchy spokesperson.

Filmography

!Year	!Film	!Role	!Notes
1994 in film	1994	''Silent Fall''	Sylvie Warden
rowspan="2"		Callie
''Empire Records''	Corey Mason
rowspan="2"	''Stealing Beauty''	Lucy Harmon	Nominated – Young Star Award for Best Performance by a Young Actress in a Drama Film
''That Thing You Do!''	Faye Dolan
rowspan="2"	''Inventing the Abbotts''	Pamela Abbott
	Girl in Bus Station	Cameo appearance
		Grace Stamper	Nominated – MTV Movie Award for Best Female PerformanceNominated – MTV Movie Award for Best On-Screen Duo Shared with Ben AffleckNominated – Blockbuster Entertainment Award for Favorite Actress -Science Fiction
rowspan="3"	''Plunkett & Macleane''	Lady Rebecca Gibson
''Cookie's Fortune''	Emma Duvall
	Tatyana Larina	Russian Guild of Film Critics Award for Best Foreign Actress
	''Dr. T & the Women''	Marilyn
rowspan="2"	''One Night at McCool's''	Jewel
''The Lord of the Rings: The Fellowship of the Ring''
	''The Lord of the Rings: The Two Towers''	Arwen Undómiel	Online Film Critics Society Award for Best EnsemblePhoenix Film Critics Society Award for Best Cast Nominated – Screen Actors Guild Award for Outstanding Performance by a Cast
	''The Lord of the Rings: The Return of the King''	Arwen Undómiel	Screen Actors Guild Award for Outstanding Performance by a CastBroadcast Film Critics Association Award for Best CastNational Board of Review Award for Best Cast Nominated – Phoenix Film Critics Society Award for Best Ensemble
		Maya
	''Lonesome Jim''	Anika
	''Reign Over Me''	Dr. Angela Oakhurst
rowspan="3"	''The Strangers''	Kristen McKay	Scream Awards for Best Horror Actress Nominated – Teen Choice Award for Choice Movie Actress: Horror/Thriller
	Betty Ross
	Clare Cooper
rowspan="2"		Sarah
	Shana

References

Further reading

Corliss, Richard. "One life to Liv -- But can she act?." ''Time''. June 17, 1996. Accessed January 8, 2009.

Fischer, Paul. "The Liv Factor." Girl.com. 2001. Accessed January 8, 2009.

Mottram, James. "BBC Movies - Liv Tyler interview." BBC Films. December 5, 2001. Accessed January 6, 2009.

Mzimba, Lizo. "Liv Tyler on Two Towers: full interview." BBC News. December 10, 2002. Accessed January 7, 2009.

Head, Steve. "IGN: An Interview with Liv Tyler". IGN Movies. December 16, 2002. Accessed January 12, 2009.

Otto, Jeff. "IGN: An Interview with Orlando Bloom and Liv Tyler." IGN Movies. December 17, 2003. Accessed January 8, 2009.

Fischer, Paul. "Exclusive Liv Tyler Interview." Girl.com. 2003. Accessed January 8, 2009.

Cole, Bethan. "Cover story: Liv a little." ''The Times''. February 29, 2004. Accessed January 13, 2009.

Head, Steve. "IGN: An Interview with Liv Tyler - Bringing it on home for Jersey Girl." IGN Movies. April 2, 2004. Accessed January 19, 2009.

Collura, Scott. "IGN: Liv Tyler Talks The Hobbit." IGN Movies. May 20, 2008. Accessed January 13, 2009.

Barnard, Linda. "It's a scream." ''Toronto Star''. May 31, 2008. Accessed January 9, 2009.

Palmer, Alun. "Interview: Liv Tyler on her son, work and marriage break up." ''Daily Mirror''. June 12, 2008. Accessed January 7, 2009.

Thompson, B. "Interview: Liv Tyler." ''Montreal Gazette''. June 12, 2008. Accessed January 7, 2009.

External links

Category:Actors from New York City Category:American female models Category:American film actors Category:Outstanding Performance by a Cast in a Motion Picture Screen Actors Guild Award winners Category:People from Portland, Maine Category:UNICEF people Category:1977 births Category:Living people Category:American people of Italian descent Category:American people of Polish descent Category:American people of Russian descent Category:People of Calabrian descent

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