Predicate logic is different from propositional logic, in part because it has the concept of "quantifiers". A quantifier is used in conjunction with a variable (say "x") in order to talk about a general instance of x, and in doing so, this allows predicate logic to make statements about quantity.
The best-known quantifiers are the "existential quantifier", represented by ∃, and the "universal quantifier", represented by ∀. The existential quantifier is used to express statements of the form "there exists", and is true precisely when there is at least one mathematical object from the universe of discourse that matches the predicate or formula. On the other hand, the universal quantifier is used to express statements of the form "for all", and is true precisely when all possible mathematical objects of the universe of discourse match the specified predicate or formula.
In the notation of predicate logic, quantifiers directly precede (and thus introduce) variable names, which are then followed by other quantifiers or mathematical expressions, where the said variables are found. For example. one can use the expression formula_1 to mean "there is a person "x" such that for all persons "y", y likes x" ("someone is liked by everyone.").
formula_2
can be read as: "There is at least one cat which is black, and which likes (one or more) dogs."
formula_3
can be read as: "It is not true that every cat doesn't like any dog."
formula_4
can be read as: "There does not exist a cat which is also a dog."
Arapaho language
The Arapaho language (also Arapahoe) is a Plains Algonquian language (an areal rather than genetic grouping) spoken by elders in Wyoming. It is now spoken very little, and is in danger of becoming extinct.
Assamese language
Assamese ( translated as"Ôxômiya") () is the easternmost Indo-Aryan language, spoken most in the state of Assam in North-East India. It is also the main language of Assam. It is spoken in parts of Arunachal Pradesh and other northeast Indian states.
Avar language
The Avar language (self-designation "language of the mountains" or Авар мац "Avar language") belongs to the Avar-Andi-Tsez subgroup of the Alarodian Northeast-Caucasian (or Nakh-Dagestani) language family. It is spoken most in the eastern and southern parts of the Russian Caucasus republic of Dagestan, and the Balaken, Zakatala north-west area of Azerbaijan.
Azerbaijani language
The Azerbaijani language, also called Azeri, is a Turkic language that is spoken in Azerbaijan and northwestern Iran. Azerbaijani is the official language of the Republic of Azerbaijan.
Azerbaijani is also spoken in Dagestan (a republic of Russia), south-eastern and eastern Georgia, north eastern Turkey and in some parts of Ukraine and in northwestern Iran. In Dagesten, there are over 30 different languages, and Russian is used as a lingua franca.
Bashkir language
The Bashkir language (Native name: ) is a Turkic language. Speakers of the Bashkir language mostly live in the Russian republic of Bashkortostan. A large number of speakers also live in Tatarstan, Udmurtia, Perm Krai, Chelyabinsk, Orenburg, Sverdlovsk, and Kurgan Oblasts.
Like other languages of Russia, Bashkir uses an alphabet made up of Cyrillic letters. The Bashkir alphabet has 42 letters, made up of the 33 letters of the Russian alphabet and 9 more letters for special Bashkir sounds. These 9 letters and their sounds are:
Od language
Od (also called Oad, Odki) is a language spoken mostly about the Sindh and in a few in southern Punjab. It may also be spoken in Rajasthan, Republic of India.
Ilium/Olympos
Ilium/Olympos is a science fiction series that was written by Dan Simmons. The events in the books are set in motion by beings who have taken on the roles of the Greek gods. The first book in the series, "Illium" received the Locus Award for best book in 2004.
There are two books in the series:
Ilium (book)
Ilium is a science fiction book that was written by Dan Simmons. It is the first part of the "Ilium/Olympos" cycle, and is about the re-creation of the events in the "Iliad" on Mars.
In July 2004, "Ilium" got the Locus Award for best science fiction novel of 2003. It was later nominated for the 2004 Hugo Award for best book.
Olympos (book)
Olympos is a book that was written by Dan Simmons in 2005, and is the sequel to "Ilium" It is a science fiction book that ends the series Ilium/Olympos. It uses ideas from the "Iliad" and the "Odyssey".
Zulfiqar Ali Bhutto
Zulfiqar Ali Bhutto (, ; January 5, 1928 – April 4, 1979) was a Pakistani politician. He was the President of Pakistan from 1971 to 1973. He was Prime Minister of Pakistan from 1973 to 1977. He was the founder of the Pakistan Peoples Party (PPP), the largest and most influential political party in Pakistan.
He was educated at the University of California, Berkeley in the United States and Oxford University in the United Kingdom. Bhutto was executed by hanging in 1979 for ordering the murder of a political opponent. His execution was ordered by General Muhammad Zia-ul-Haq. Bhutto's supporters give him the honorific title Shaheed, the Urdu word for martyr. His name then becomes Shaheed-e-Azam Zulfiqar Ali Bhutto ("The Great Martyr") or sometimes Quaid-e-Awam (The Leader the Community).
He was married to Nusrat Bhutto (née Ispahnie) from 1951 until his death. Their elder daughter, Benazir Bhutto (1953-2007), was also Prime Minister of Pakistan, twice. The couple had three other children: son Murtaza Bhutto (1954-1996) daughter Sanam Bhutto (born 1957), and son Shahnawaz Bhutto (1958-1985).
Pothohar Plateau
The Pothohar Plateau (also spelled Pothwar, Potwar or Potohar) () is a plateau in Punjab, Pakistan. The area was the home of the Soan Culture (a stone age culture), and there are many fossils, tools, coins, and remains of ancient archaeological sites. The local people speak a dialect of Punjabi, called Pothohari or 'Potwari'.
Pahari languages
Pahari (or Pahaari) is a word for a number of dialects spoken across the Himalayan range, not limited to a single country. The word comes from 'pahar' meaning mountain. The word 'Pahaari' or 'Pahari' is an adjective in Hindi, Urdu, or Punjabi and it means 'of the mountain', so 'Pahari' means 'language of the mountain people'.
Pakistan, India and Nepal are all countries along which the Himalayas run, and in all three countries the word for mountain is Pahar this is due to the fact that Urdu, Nepali, Hindi and Punjabi are all related languages (they are all Indic languages of the Indo-European language family). The Pahari language is also part of this group. Travel in mountainous areas is difficult, so dialects close to each other can be very different.
Bose-Einstein statistics
In statistical mechanics, Bose-Einstein statistics means the statistics of a system where you can not tell the difference between any of the particles, and the particles are bosons. Bosons are fundamental particles like the photon.
The Bose-Einstein distribution tells you how many particles have a certain energy. The formula is
with formula_2 and where:
If formula_3, then the Maxwell–Boltzmann statistics is a good approximation.
Activision
Activision is an American video game company. It was the first third party in the industry's history. It was founded on October 1, 1979. On July 9, 2008, it merged with Vivendi to make a new company called Activision Blizzard. Activision is best known for "Tony Hawk's Pro Skater", "Call of Duty", and "Guitar Hero".
OXO
OXO is a tic-tac-toe video game, and one of the first video game ever made. It was made in 1952 for the EDSAC computer by Alexander S. Douglas for his Ph.D. thesis on human-computer interaction at the University of Cambridge.
Will Wright (game developer)