Varieties and variations.

During his sojourn with the Marsh Arabs of Iraq, Gavin Young noted that the local "sayyids"—"venerated men accepted [...] as descendants of the Prophet Muhammad and Ali ibn Abi Talib"—wore dark green keffiyeh ("cheffiyeh") in contrast to the black-and-white checkered examples typical of the area's inhabitants.  Many Palestinian keffiyehs are a mix of cotton and wool, which facilitates quick drying and, when desired, keeping the wearer's head warm. The keffiyeh is usually folded in half (into a triangle) and the fold worn across the forehead. Often, the keffiyeh is held in place by a circlet of rope called an "agal" (, ""). Some wearers wrap the keffiyeh into a turban, while others wear it loosely draped around the back and shoulders. A "taqiyah" is sometimes worn underneath the keffiyeh; in the past, it has also been wrapped around the rim of a fez. The keffiyeh is almost always of white cotton cloth, but many have a checkered pattern in red or black stitched into them. The plain white keffiyeh is most popular in the Arab states of the Persian Gulf—in Kuwait and Bahrain to the exclusion of almost any other style. The keffiyeh is worn by men of all ages, whether on the head or around the shoulders.  In Jordan, the red-and-white keffiyeh is strongly associated with the country and its heritage, because the red color was introduced by the Jordanian Bedouins under British rule, where it is known as the "shemagh mhadab". The Jordanian keffiyeh has decorative cotton or wool tassels on the sides; the bigger these tassels, the greater the garment's supposed value and the status of the person wearing it. It has long been worn by Bedouins and villagers and used as a symbol of honor and/or tribal identification. The tasseled red-and-white Jordanian "shemagh" is much thicker than the untasseled red-and-white shemagh seen in Persian Gulf countries.  In Egypt, the keffiyeh and the agal is worn by Bedouins specially in the Sinai Peninsula. It is also sometimes tied into a turban in varying styles.  In Yemen, the keffiyeh is used extensively in both red-white and black-white pattern. It spread during 1948 through Palestinian refugees.  In Malaysia, the keffiyeh has been worn by Muslim women as part of hijab fashion and during the Palestinian struggle against Israel. Many Malaysians wore it to show solidarity for Palestine.  Also in Indonesia the people used the keffiyeh to show their solidarity with the Palestinians.  In Turkey it was forbidden to wear a keffiyeh because it was seen as evidence of support of the PKK.  The keffiyeh, especially the all-white keffiyeh, is also known as the "ghutrah". This is particularly common in the Arabian Peninsula, where the optional skullcap is called a keffiyeh. The garment is also known in some areas as the "".  Roughly speaking:  Ordinary keffiyeh  A piece of white/orange/black cloth made from wool and cotton, worn primarily by Palestinians.  Shalls/Musar  A traditional scarf originated from Yemen, usually made of cotton or flax and decorated with many colors, but usually red and white; worn primarily by Yemen, & Oman.  Shemagh  A plain piece of cloth worn by the Arabian Gulf.  Dastmaal Yazdi  A traditional scarf in Iran, originally from the Yazd region of Iran.  Chafiyeh  A style of keffiyeh that originated in Iran, based on the Iranian Dastmaal Yazdi with influences from the Palestinian Keffiyeh. Often worn by Shi'a Muslims in Iran as well as Iraq and Lebanon to express support for Shi'a Political parties. The scarf gained popularity during the Iran-Iraq war as a sign of Shi'a resistance against Saddam. The Chafiyeh is also worn by Basij members of the Iranian Revolutionary Guard Corps, Hezbollah, as well as occasionally by members of Iraq's Popular Mobilization Forces, but also by ordinary Shia religious pilgrims not affiliated with any political group.  Ghutrah  A piece of white cloth made of cotton mild, worn in western Iraq and by the Arabs of the Arabian Gulf states.  Rezza  It is worn by inhabitants of North Africa.

Palestinian national symbol.

Traditionally worn by Palestinian farmers, the keffiyeh became worn by Palestinian men of any rank and became a symbol of Palestinian nationalism during the Arab Revolt of the 1930s. Its prominence increased during the 1960s with the beginning of the Palestinian resistance movement and its adoption by Palestinian leader Yasser Arafat.  The black-and-white fishnet pattern keffiyeh would later become Arafat's iconic symbol, and he would rarely be seen without it; only occasionally would he wear a military cap, or, in colder climates, a Russian-style "ushanka" hat. Arafat would wear his keffiyeh in a semi-traditional way, wrapped around his head via an "agal". He also wore a similarly patterned piece of cloth in the neckline of his military fatigues. Early on, he had made it his personal trademark to drape the scarf over his right shoulder only, arranging it in the rough shape of a triangle, to resemble the outlines of historic Palestine. This way of wearing the keffiyeh became a symbol of Arafat as a person and political leader, and it has not been imitated by other Palestinian leaders.  Another Palestinian figure associated with the keffiyeh is Leila Khaled, a female member of the armed wing of the Popular Front for the Liberation of Palestine. Several photographs of Khaled circulated in the Western newspapers after the hijacking of TWA Flight 840 and the Dawson's Field hijackings. These photos often included Khaled wearing a keffiyeh in the style of a Muslim woman's hijab, wrapped around the head and shoulders. This was unusual, as the keffiyeh is associated with Arab masculinity, and many believe this to be something of a fashion statement by Khaled, denoting her equality with men in the Palestinian armed struggle.  The colors of the stitching in a keffiyeh are also vaguely associated with Palestinians' political sympathies. Traditional black and white keffiyehs became associated with Fatah. Later, red and white keffiyehs were adopted by Palestinian Marxists, such as the PFLP.  The color symbolism of the scarves is by no means universally accepted by all Palestinians or Arabs. Its importance should not be overstated, as the scarves are used by Palestinians and Arabs of all political affiliations, as well as by those with no particular political sympathies.

Symbol of Palestinian solidarity.

The black and white chequered keffiyeh has become a symbol of Palestinian nationalism, dating back to the 1936–1939 Arab revolt in Palestine. Outside of the Middle East and North Africa, the keffiyeh first gained popularity among activists supporting the Palestinians in the conflict with Israel.  The wearing of the keffiyeh often comes with criticism from various political factions in the ongoing Israeli–Palestinian conflict. The slang "keffiyeh kinderlach" refers to young Jews, particularly college students, who sport a keffiyeh around the neck as a political/fashion statement. This term may have first appeared in print in an article by Bradley Burston in which he writes of "the suburban-exile kaffiyeh kinderlach of Berkeley, more Palestinian by far than the Palestinians" in their criticism of Israel. European activists have also worn the keffiyeh.  While Western protesters wear differing styles and shades of keffiyeh, the most prominent is the black-and-white keffiyeh. This is typically worn around the neck like a neckerchief, simply knotted in the front with the fabric allowed to drape over the back. Other popular styles include rectangular-shaped scarves with the basic black-and-white pattern in the body, with the ends knitted in the form of the Palestinian flag. Since the Al-Aqsa Intifada, these rectangular scarves have increasingly appeared with a combination of the Palestinian flag and Al-Aqsa Mosque printed on the ends of the fabric.

Production.

Today, this symbol of Palestinian identity is now largely imported from China. With the scarf's growing popularity in the 2000s, Chinese manufacturers entered the market, driving Palestinians out of the business. In 2008, Yasser Hirbawi, who for five decades had been the only Palestinian manufacturer of keffiyehs, is now struggling with sales. "Mother Jones" wrote, "Ironically, global support for Palestinian-statehood-as-fashion-accessory has put yet another nail in the coffin of the Occupied Territories' beleaguered economy."

Westerners in keffiyeh.

British Colonel T. E. Lawrence (better known as "Lawrence of Arabia") was probably the best-known Western wearer of the keffiyeh and agal during his involvement in the Arab Revolt in World War I. This image of Lawrence was later popularized by the film epic about him, "Lawrence of Arabia", in which he was played by Peter O'Toole.  The 1920s silent-film era of American cinema saw studios take to Orientalist themes of the exotic Middle East, possibly due to the view of Arabs as part of the Allies of World War I, and keffiyehs became a standard part of the theatrical wardrobe. These films and their male leads typically had Western actors in the role of an Arab, often wearing the keffiyeh with the agal (as with "The Sheik" and "The Son of the Sheik", starring actor Rudolph Valentino).  Erwin Rommel also commonly wore a keffiyeh during the Western Desert Campaign for practical reasons.

Fashion trend.

As with other articles of clothing worn in wartime, such as the T-shirt, fatigues and khaki pants, the keffiyeh has been seen as chic among non-Arabs in the West. Keffiyehs became popular in the United States in the late 1980s, at the start of the First Intifada, when bohemian girls and punks wore keffiyehs as scarves around their necks. In the early 2000s, keffiyehs were very popular among youths in Tokyo, who often wore them with camouflage clothing. The trend recurred in the mid-2000s in the United States, Europe, Canada and Australia, when the keffiyeh became popular as a fashion accessory, usually worn as a scarf around the neck in hipster circles. Stores such as Urban Outfitters and TopShop stocked the item (however, after some controversy over the retailer's decision to label the item "anti-war scarves" Urban Outfitters pulled it). In spring 2008, keffiyehs in colors like purple and mauve were given away in issues of fashion magazines in Spain and France. In UAE, males are inclining towards more western headgear while the women are developing preferences for dupatta—the traditional head cover of the Indian subcontinent. The appropriation of the keffiyeh as a fashion statement by non-Arab wearers separate from its political and historical meaning has been the subject of controversy in recent years. While it is worn often as a symbol of solidarity with the Palestinian struggle, the fashion industry has disregarded its significance by using its pattern and style in day-to-day clothing design. For example, in 2016 Topshop released a romper with the Keffiyeh print, calling it a "scarf playsuit". This led to accusations of cultural appropriation and Topshop eventually pulled the item from their website

The keffiyeh or kufiya ( ', meaning "from the city of Kufa" (); plural '), also known as a ghutrah (), shemagh ( '), (), mashadah (), chafiye, dastmal yazdi (, "destmal yezdî") or cemedanî (), is a traditional Arabian headdress, or what is sometimes called a habit, that originated in the Arabian Peninsula, and is now worn throughout the Middle-East region. It is fashioned from a square scarf, and is usually made of cotton. The keffiyeh is commonly found in arid regions, as it provides protection from sunburn, dust and sand. Toward the end of the 1980s, the keffiyeh became a fashion accessory in the United States and, during the early 2000s it became very popular among teenagers in Tokyo, Japan, where it is often worn with camouflage-style clothing.

Kefíja (: كوفية, "kūfiyyah", pl. كوفيات, "kūfiyyāt"), někdy též šemag či hovorově palestina, je tradiční arabská mužská pokrývka hlavy. Tvoří ji čtvercová tkanina, obvykle bavlněná, různým způsobem přehnutá a složená. Je typická pro oblasti se suchým a teplým podnebím, kde poskytuje ochranu proti přímému slunci a rovněž tak příležitostně ochranu úst a očí proti zvířenému prachu a písku. Může mít různý vzhled, mezi klasický patří kostkovaný vzor, zpravidla v kombinaci bílé a další (např. černé, červené, zelené) barvy.


Early life and education.

Qaboos was born in Salalah in Dhofar on 18 November 1940 as an only son of Sultan Said bin Taimur and Sultana Mazoon al-Mashani.  He received his primary and secondary education at Salalah, and was sent to a private educational establishment at Bury St Edmunds in England at age 16. At 20, he entered the Royal Military Academy Sandhurst. After graduating from Sandhurst in September 1962, he joined the British Army and was posted to the 1st Battalion The Cameronians (Scottish Rifles), serving with them in Germany for one year. He also held a staff appointment with the British Army.  After his military service, Qaboos studied local government subjects in England and then completed his education with a world tour chaperoned by Leslie Chauncy. Upon his return in 1966, he was placed under virtual house arrest in the Sultan's palace in Salalah by his father. Here he was kept isolated from government affairs, except for occasional briefings by his father's personal advisers. Qaboos studied Islam and the history of his country. His personal relationships were limited to a handpicked group of palace officials who were sons of his father's advisors and a few expatriate friends such as Tim Landon. Sultan Said said that he would not allow his son to be involved with the developing planning process, and Qaboos began to make known his desire for change—which was quietly supported by his expatriate visitors.

Political career.

Rise to power.

Qaboos acceded to the throne on 23 July 1970 following a successful coup against his father, with the aim of ending the country's isolation and using its oil revenue for modernization and development. He declared that the country would no longer be known as Muscat and Oman, but would change its name to "the Sultanate of Oman" in order to better reflect its political unity.  The coup was supported by the British, having been "planned in London by MI6 and by civil servants at the Ministry of Defence and the Foreign Office" and sanctioned by the Prime Minister, Harold Wilson.  The first pressing problem that Qaboos bin Said faced as Sultan was an armed communist insurgency from South Yemen, the Dhofar Rebellion (1962–1976). The sultanate eventually defeated the incursion with help from the Shah of Iran, Jordanian troops sent from his friend King Hussein of Jordan, British Special Forces and the Royal Air Force.

Reign as Sultan.

There were few rudiments of a modern state when Qaboos took power in the 1970 Omani coup d'état. Oman was a poorly developed country, severely lacking in infrastructure, healthcare, and education, with only six miles of paved roads and a population dependent on subsistence farming and fishing. Qaboos modernized the country using oil revenues. Schools and hospitals were built, and a modern infrastructure was laid down, with hundreds of kilometres of new roads paved, a telecommunications network established, projects for a port and airport that had begun prior to his reign were completed and a second port was built, and electrification was achieved. The government also began to search for new water resources and built a desalination plant, and the government encouraged the growth of the private enterprise, especially in development projects. Banks, hotels, insurance companies, and print media began to appear as the country developed economically. The Omani rial was established as the national currency, replacing the Indian rupee and Maria Theresa thaler. Later, additional ports were built, and universities were opened. In his first year in power, Qaboos also abolished slavery in Oman.  The political system which Qaboos established is that of an absolute monarchy. The Sultan's birthday, 18 November, is celebrated as Oman's national holiday. The first day of his reign, 23 July, is celebrated as Renaissance Day.  Oman has no system of checks and balances, and thus no separation of powers. All power is concentrated in the sultan, who is also chief of staff of the armed forces, Minister of Defence, Minister of Foreign Affairs and chairman of the Central Bank. All legislation since 1970 has been promulgated through royal decrees, including the 1996 Basic Law. The sultan appoints judges, and can grant pardons and commute sentences. The sultan's authority is inviolable and the sultan expects total subordination to his will.  Qaboos' closest advisors were reportedly security and intelligence professionals within the Palace Office, headed by General Sultan bin Mohammed al Numani.

2011 Omani protests.

The much-talked-about 2011 Omani protests were a series of protests in the Persian Gulf country of Oman that occurred as part of the revolutionary wave popularly known as the "Arab Spring".  The protesters demanded salary increases, lower living costs, the creation of more jobs and a reduction in corruption. Protests in Sohar, Oman's fifth-largest city, centered on the Globe Roundabout. The Sultan's responses included the dismissal of a third of the governing cabinet.  According to CBS News, 19 June 2011, Several protest leaders have been detained and released in rolling waves of arrests during the Arab Spring, and dissatisfaction with the state of affairs in the country is high. While disgruntlement amongst the populace is obvious, the extreme dearth of foreign press coverage and lack of general press freedom there leaves it unclear as to whether the protesters want the sultan to leave, or simply want their government to function better. Beyond the recent protests, there is concern about succession in the country, as there is no heir apparent or any clear legislation on who may be the next Sultan. He did give token concession to protesters yet detained social media activists. In August 2014, The Omani writer and human rights defender Mohammed Alfazari, the founder and editor-in-chief of the e-magazine Mowatin "Citizen", disappeared after going to the police station in the Al-Qurum district of Muscat, only to be pardoned some time later.

Foreign policy.

Under Qaboos, Oman fostered closer ties with Iran than other Arab states of the Persian Gulf, and was careful to appear neutral and maintain a balance between the West and Iran. As a result, Oman often acted as an intermediary between the United States and Iran. Qaboos helped mediate secret US-Iran talks in 2013 that led two years later to the international nuclear pact, from which the United States withdrew in 2018.  In 2011, Qaboos facilitated the release of American hikers who were held by Iran, paying $1 million for their freedom.  Oman did not join the Saudi Arabian-led intervention in Yemen against the Houthis in 2015, and did not take sides in a Persian Gulf dispute that saw Saudi Arabia and its allies impose an embargo on Qatar in 2016.  In October 2018, Qaboos invited Prime Minister of Israel Benjamin Netanyahu to visit Oman, a country that does not have official diplomatic ties with Israel. Netanyahu was the first Israeli prime minister to visit Oman since Shimon Peres in 1996.

Philanthropy.

Qaboos financed the construction or maintenance of a number of mosques, notably the Sultan Qaboos Grand Mosque, as well as the holy places of other religions.  Through a donation to UNESCO in the early 1990s, he funded the Sultan Qaboos Prize for Environmental Preservation, to afford recognition to outstanding contributions in the management or preservation of the environment. The prize has been awarded every two years since 1991.

Personal life.

Sultan Qaboos was a Muslim of the Ibadi denomination, which has traditionally ruled Oman. Although Oman is predominantly Muslim, Qaboos granted freedom of religion in the country and financed the construction of four Catholic and Protestant churches in the country as well as several Hindu temples.  Qaboos bin Said was an avid fan and promoter of classical music. His 120-member orchestra has a high reputation in the Middle East. The orchestra consists entirely of young Omanis who, since 1986, audition as children and grow up as members of the symphonic ensemble. They play locally and traveled abroad with the sultan. Argentine composer Lalo Schifrin was commissioned to compose a work entitled "Symphonic Impressions of Oman". The Sultan was particularly enthusiastic about the pipe organ. The Royal Opera House Muscat features the second largest mobile pipe organ in the world, which has three specially made organ stops, named the "Royal Solo" in his honour. He was also a patron of local folk musician Salim Rashid Suri, making him a cultural consultant, in which role Suri wrote songs praising the Sultan and his family.  On 22 March 1976, Qaboos bin Said married his first cousin, Kamila "née" Sayyida Nawwal bint Tariq Al Said (born 1951), daughter of Sayyid Tariq bin Taimur Al Said and his second wife, Sayyida Shawana bint Nasir Al Said. The marriage ended in divorce in 1979. She remarried in 2005. The marriage produced no heirs, and Qaboos bin Said wrote secret documents naming the successor to his realm.  In September 1995, Qaboos was involved in a car accident in Salalah just outside his palace, which claimed the life of one of his most prominent and influential ministers, Qais Bin Abdul Munim Al Zawawi.  In his obituary, "The Times" described rumours throughout his life of "liaisons with elegant young European men".

Illness and death.

From 2014, Qaboos suffered from colon cancer, for which he received treatment. On 14 December 2019, he was reported to be terminal with a short time to live after his stay for medical treatment in UZ Leuven in Belgium and returned home because he wanted to die in his own country. He died on 10 January 2020 at the age of 79. The following day, the government declared three days of national mourning and said the country's flag would be flown at half-staff for a period of 40 days.

Succession.

Unlike the heads of other Arab states of the Persian Gulf, Qaboos did not publicly name an heir. Article 6 of the constitution says the royal family should choose a new sultan within three days of the position falling vacant. If the royal family council fails to agree, a letter containing a name penned by Sultan Qaboos should be opened in the presence of a defence council of military and security officials, supreme court chiefs, and heads of the two quasi-parliamentary advisory assemblies. Analysts saw the rules as an elaborate means of Sultan Qaboos securing his choice for successor without causing controversy by making it public during his lifetime, since it was considered unlikely that the royal family would be able to agree on a successor on its own.  Qaboos had no children nor siblings; there are other male members of the Omani royal family including paternal uncles and their families. Using same-generation primogeniture, the successor to Qaboos would appear to be the children of his late uncle, Sayyid Tariq bin Taimur Al Said, Oman's first prime minister before the sultan took over the position himself (and his former father-in-law). Oman watchers believed the top contenders to succeed Qaboos were three of Tariq's sons: Assad bin Tariq Al Said, Deputy Prime Minister for International Relations and Cooperation and the Sultan's special representative; Shihab bin Tariq, a retired Royal Navy of Oman commander; and Haitham bin Tariq Al Said, the Minister of Heritage and National Culture.  On 11 January 2020, Oman state TV said authorities had opened the letter by Sultan Qaboos bin Said naming his successor, announcing shortly that Haitham bin Tariq is the country's ruling sultan. Haitham bin Tariq has children, two sons and two daughters.

Military ranks.

Qaboos held the following ranks:

Foreign honours.

"° means Royal Ark"

Qaboos bin Said (, ; 18 November 1940 – 10 January 2020) was the Sultan of Oman from 23 July 1970 until his death. A fifteenth-generation descendant of the founder of the House of Al Said, he was the longest-serving leader in the Middle East and Arab world at the time of his death.

Kábús ibn Sa'íd ibn Tajmúr al-Sa'íd, arabsky: (* 18. listopadu 1940 Salála, † 10. ledna 2020 Maskat) byl od roku 1970 až do své smrti sultánem a zároveň předsedou vlády Ománu. Narodil se jako jediný syn sultána Saída bin Tajmúra. Nástupcem se stal 11. ledna jeho bratranec, dosavadní ministr kultury Hajsám bin Tárik Saíd.


Development of modal logic.

In addition to his non-modal syllogistic, Aristotle also developed a modal syllogistic in Book I of his "Prior Analytics" (chs 8–22), which Theophrastus attempted to improve. There are also passages in Aristotle's work, such as the famous sea-battle argument in "De Interpretatione" §9, that are now seen as anticipations of the connection of modal logic with potentiality and time. In the Hellenistic period, the logicians Diodorus Cronus, Philo the Dialectician and the Stoic Chrysippus each developed a modal system that accounted for the interdefinability of possibility and necessity, accepted axiom T (see below), and combined elements of modal logic and temporal logic in attempts to solve the notorious Master Argument. The earliest formal system of modal logic was developed by Avicenna, who ultimately developed a theory of "temporally modal" syllogistic. Modal logic as a self-aware subject owes much to the writings of the Scholastics, in particular William of Ockham and John Duns Scotus, who reasoned informally in a modal manner, mainly to analyze statements about essence and accident.  C. I. Lewis founded modern modal logic in his 1910 Harvard thesis and in a series of scholarly articles beginning in 1912. This work culminated in his 1932 book "Symbolic Logic" (with C. H. Langford), which introduced the five systems "S1" through "S5".  Ruth C. Barcan (later Ruth Barcan Marcus) developed the first axiomatic systems of quantified modal logic — first and second order extensions of Lewis' "S2", "S4", and "S5".  The contemporary era in modal semantics began in 1959, when Saul Kripke (then only a 19-year-old Harvard University undergraduate) introduced the now-standard Kripke semantics for modal logics. These are commonly referred to as "possible worlds" semantics. Kripke and A. N. Prior had previously corresponded at some length. Kripke semantics is basically simple, but proofs are eased using semantic-tableaux or analytic tableaux, as explained by E. W. Beth.  A. N. Prior created modern temporal logic, closely related to modal logic, in 1957 by adding modal operators [F] and [P] meaning "eventually" and "previously". Vaughan Pratt introduced dynamic logic in 1976. In 1977, Amir Pnueli proposed using temporal logic to formalise the behaviour of continually operating concurrent programs. Flavors of temporal logic include propositional dynamic logic (PDL), propositional linear temporal logic (PLTL), linear temporal logic (LTL), computation tree logic (CTL), Hennessy–Milner logic, and "T".  The mathematical structure of modal logic, namely Boolean algebras augmented with unary operations (often called modal algebras), began to emerge with J. C. C. McKinsey's 1941 proof that "S2" and "S4" are decidable, and reached full flower in the work of Alfred Tarski and his student Bjarni Jónsson (Jónsson and Tarski 1951–52). This work revealed that "S4" and "S5" are models of interior algebra, a proper extension of Boolean algebra originally designed to capture the properties of the interior and closure operators of topology. Texts on modal logic typically do little more than mention its connections with the study of Boolean algebras and topology. For a thorough survey of the history of formal modal logic and of the associated mathematics, see Robert Goldblatt (2006).

Semantics.

Model theory.

The semantics for modal logic are usually given as follows: First we define a "frame", which consists of a non-empty set, "G", whose members are generally called possible worlds, and a binary relation, "R", that holds (or not) between the possible worlds of "G". This binary relation is called the "accessibility relation". For example, "w R u" means that the world "u" is accessible from world "w". That is to say, the state of affairs known as "u" is a live possibility for "w". This gives a pair, formula_6. Some formulations of modal logic also include a constant term in "G", conventionally called "the actual world", which is often symbolized as formula_7.  Next, the "frame" is extended to a "model" by specifying the truth-values of all propositions at each of the worlds in "G". We do so by defining a relation "v" between possible worlds and positive literals. If there is a world "w" such that formula_8, then "P" is true at "w". A model is thus an ordered triple, formula_9.  Then we recursively define the truth of a formula at a world in a model:  According to these semantics, a truth is "necessary" with respect to a possible world "w" if it is true at every world that is accessible to "w", and "possible" if it is true at some world that is accessible to "w". Possibility thereby depends upon the accessibility relation "R", which allows us to express the relative nature of possibility. For example, we might say that given our laws of physics it is not possible for humans to travel faster than the speed of light, but that given other circumstances it could have been possible to do so. Using the accessibility relation we can translate this scenario as follows: At all of the worlds accessible to our own world, it is not the case that humans can travel faster than the speed of light, but at one of these accessible worlds there is "another" world accessible from "those" worlds but not accessible from our own at which humans can travel faster than the speed of light.  It should also be noted that the definition of □ makes vacuously true certain sentences, since when it speaks of "every world that is accessible to "w"" it takes for granted the usual mathematical interpretation of the word "every" (see vacuous truth). Hence, if a world "w" doesn't have any accessible worlds, any sentence beginning with □ is true.  The different systems of modal logic are distinguished by the properties of their corresponding accessibility relations. There are several systems that have been espoused (often called "frame conditions"). An accessibility relation is:  The logics that stem from these frame conditions are:  The Euclidean property along with reflexivity yields symmetry and transitivity. (The Euclidean property can be obtained, as well, from symmetry and transitivity.) Hence if the accessibility relation "R" is reflexive and Euclidean, "R" is provably symmetric and transitive as well. Hence for models of S5, "R" is an equivalence relation, because "R" is reflexive, symmetric and transitive.  We can prove that these frames produce the same set of valid sentences as do the frames where all worlds can see all other worlds of "W" ("i.e.", where "R" is a "total" relation). This gives the corresponding "modal graph" which is total complete ("i.e.", no more edges (relations) can be added). For example, in any modal logic based on frame conditions:  If we consider frames based on the total relation we can just say that We can drop the accessibility clause from the latter stipulation because in such total frames it is trivially true of all "w" and "u" that "w R u". But note that this does not have to be the case in all S5 frames, which can still consist of multiple parts that are fully connected among themselves but still disconnected from each other.  All of these logical systems can also be defined axiomatically, as is shown in the next section. For example, in S5, the axioms formula_27, formula_28 and formula_29 (corresponding to "symmetry", "transitivity" and "reflexivity", respectively) hold, whereas at least one of these axioms does not hold in each of the other, weaker logics.

Axiomatic systems.

The first formalizations of modal logic were axiomatic. Numerous variations with very different properties have been proposed since C. I. Lewis began working in the area in 1910. Hughes and Cresswell (1996), for example, describe 42 normal and 25 non-normal modal logics. Zeman (1973) describes some systems Hughes and Cresswell omit.  Modern treatments of modal logic begin by augmenting the propositional calculus with two unary operations, one denoting "necessity" and the other "possibility". The notation of C. I. Lewis, much employed since, denotes "necessarily "p"" by a prefixed "box" (□"p") whose scope is established by parentheses. Likewise, a prefixed "diamond" (◇"p") denotes "possibly "p"". Regardless of notation, each of these operators is definable in terms of the other in classical modal logic: Hence □ and ◇ form a dual pair of operators.  In many modal logics, the necessity and possibility operators satisfy the following analogues of de Morgan's laws from Boolean algebra:  Precisely what axioms and rules must be added to the propositional calculus to create a usable system of modal logic is a matter of philosophical opinion, often driven by the theorems one wishes to prove; or, in computer science, it is a matter of what sort of computational or deductive system one wishes to model. Many modal logics, known collectively as normal modal logics, include the following rule and axiom:  The weakest normal modal logic, named "K" in honor of Saul Kripke, is simply the propositional calculus augmented by □, the rule N, and the axiom K. "K" is weak in that it fails to determine whether a proposition can be necessary but only contingently necessary. That is, it is not a theorem of "K" that if □"p" is true then □□"p" is true, i.e., that necessary truths are "necessarily necessary". If such perplexities are deemed forced and artificial, this defect of "K" is not a great one. In any case, different answers to such questions yield different systems of modal logic.  Adding axioms to "K" gives rise to other well-known modal systems. One cannot prove in "K" that if ""p" is necessary" then "p" is true. The axiom T remedies this defect: T holds in most but not all modal logics. Zeman (1973) describes a few exceptions, such as "S1".  Other well-known elementary axioms are:  These yield the systems (axioms in bold, systems in italics): "K" through "S5" form a nested hierarchy of systems, making up the core of normal modal logic. But specific rules or sets of rules may be appropriate for specific systems. For example, in deontic logic, formula_32 (If it ought to be that "p", then it is permitted that "p") seems appropriate, but we should probably not include that formula_31. In fact, to do so is to commit the naturalistic fallacy (i.e. to state that what is natural is also good, by saying that if "p" is the case, "p" ought to be permitted).  The commonly employed system "S5" simply makes all modal truths necessary. For example, if "p" is possible, then it is "necessary" that "p" is possible. Also, if "p" is necessary, then it is necessary that "p" is necessary. Other systems of modal logic have been formulated, in part because "S5" does not describe every kind of modality of interest.

Structural proof theory.

Sequent calculi and systems of natural deduction have been developed for several modal logics, but it has proven hard to combine generality with other features expected of good structural proof theories, such as purity (the proof theory does not introduce extra-logical notions such as labels) and analyticity (the logical rules support a clean notion of analytic proof). More complex calculi have been applied to modal logic to achieve generality.

Decision methods.

Analytic tableaux provide the most popular decision method for modal logics.

Alethic logic.

Modalities of necessity and possibility are called "alethic" modalities. They are also sometimes called "special" modalities, from the Latin "species". Modal logic was first developed to deal with these concepts, and only afterward was extended to others. For this reason, or perhaps for their familiarity and simplicity, necessity and possibility are often casually treated as "the" subject matter of modal logic. Moreover, it is easier to make sense of relativizing necessity, e.g. to legal, physical, nomological, epistemic, and so on, than it is to make sense of relativizing other notions.  In classical modal logic, a proposition is said to be  In classical modal logic, therefore, the notion of either possibility or necessity may be taken to be basic, where these other notions are defined in terms of it in the manner of De Morgan duality. Intuitionistic modal logic treats possibility and necessity as not perfectly symmetric.  For example, suppose that while walking to the convenience store we pass Friedrich's house, and observe that the lights are off. On the way back, we observe that they have been turned on. (Of course, this analogy does not apply alethic modality in a "truly" rigorous fashion; for it to do so, it would have to axiomatically make such statements as "human beings cannot rise from the dead", "Socrates was a human being and not an immortal vampire", and "we did not take hallucinogenic drugs which caused us to falsely believe the lights were on", "ad infinitum". Absolute certainty of truth or falsehood exists only in the sense of logically constructed abstract concepts such as "it is impossible to draw a triangle with four sides" and "all bachelors are unmarried".)  For those with difficulty with the concept of something being possible but not true, the meaning of these terms may be made more comprehensible by thinking of multiple "possible worlds" (in the sense of Leibniz) or "alternate universes"; something "necessary" is true in all possible worlds, something "possible" is true in at least one possible world. These "possible world semantics" are formalized with Kripke semantics.

Physical possibility.

Something is physically, or nomically, possible if it is permitted by the laws of physics. For example, current theory is thought to allow for there to be an atom with an atomic number of 126, even if there are no such atoms in existence. In contrast, while it is logically possible to accelerate beyond the speed of light, modern science stipulates that it is not physically possible for material particles or information.

Metaphysical possibility.

Philosophers debate if objects have properties independent of those dictated by scientific laws. For example, it might be metaphysically necessary, as some who advocate physicalism have thought, that all thinking beings have bodies and can experience the passage of time. Saul Kripke has argued that every person necessarily has the parents they do have: anyone with different parents would not be the same person.  Metaphysical possibility has been thought to be more restricting than bare logical possibility (i.e., fewer things are metaphysically possible than are logically possible). However, its exact relation (if any) to logical possibility or to physical possibility is a matter of dispute. Philosophers also disagree over whether metaphysical truths are necessary merely "by definition", or whether they reflect some underlying deep facts about the world, or something else entirely.

Epistemic logic.

Epistemic modalities (from the Greek "episteme", knowledge), deal with the "certainty" of sentences. The □ operator is translated as "x knows that...", and the ◇ operator is translated as "For all x knows, it may be true that..." In ordinary speech both metaphysical and epistemic modalities are often expressed in similar words; the following contrasts may help:  A person, Jones, might reasonably say "both": (1) "No, it is "not" possible that Bigfoot exists; I am quite certain of that"; "and", (2) "Sure, it's "possible" that Bigfoots could exist". What Jones means by (1) is that, given all the available information, there is no question remaining as to whether Bigfoot exists. This is an epistemic claim. By (2) he makes the "metaphysical" claim that it is "possible for" Bigfoot to exist, "even though he does not": there is no physical or biological reason that large, featherless, bipedal creatures with thick hair could not exist in the forests of North America (regardless of whether or not they do). Similarly, "it is possible for the person reading this sentence to be fourteen feet tall and named Chad" is "metaphysically" true (such a person would not somehow be prevented from doing so on account of their height and name), but not "alethically" true unless you match that description, and not "epistemically" true if it's known that fourteen-foot-tall human beings have never existed.  From the other direction, Jones might say, (3) "It is "possible" that Goldbach's conjecture is true; but also "possible" that it is false", and "also" (4) "if it "is" true, then it is necessarily true, and not possibly false". Here Jones means that it is "epistemically possible" that it is true or false, for all he knows (Goldbach's conjecture has not been proven either true or false), but if there "is" a proof (heretofore undiscovered), then it would show that it is not "logically" possible for Goldbach's conjecture to be false—there could be no set of numbers that violated it. Logical possibility is a form of "alethic" possibility; (4) makes a claim about whether it is possible (i.e., logically speaking) that a mathematical truth to have been false, but (3) only makes a claim about whether it is possible, for all Jones knows, (i.e., speaking of certitude) that the mathematical claim is specifically either true or false, and so again Jones does not contradict himself. It is worthwhile to observe that Jones is not necessarily correct: It is possible (epistemically) that Goldbach's conjecture is both true and unprovable.  Epistemic possibilities also bear on the actual world in a way that metaphysical possibilities do not. Metaphysical possibilities bear on ways the world "might have been," but epistemic possibilities bear on the way the world "may be" (for all we know). Suppose, for example, that I want to know whether or not to take an umbrella before I leave. If you tell me "it is "possible that" it is raining outside" – in the sense of epistemic possibility – then that would weigh on whether or not I take the umbrella. But if you just tell me that "it is "possible for" it to rain outside" – in the sense of "metaphysical possibility" – then I am no better off for this bit of modal enlightenment.  Some features of epistemic modal logic are in debate. For example, if "x" knows that "p", does "x" know that it knows that "p"? That is to say, should □"P" → □□"P" be an axiom in these systems? While the answer to this question is unclear, there is at least one axiom that is generally included in epistemic modal logic, because it is minimally true of all normal modal logics (see the section on axiomatic systems):  It has been questioned whether the epistemic and alethic modalities should be considered distinct from each other. The criticism states that there is no real difference between "the truth in the world" (alethic) and "the truth in an individual's mind" (epistemic). An investigation has not found a single language in which alethic and epistemic modalities are formally distinguished, as by the means of a grammatical mood.

Temporal logic.

Temporal logic is an approach to the semantics of expressions with tense, that is, expressions with qualifications of when. Some expressions, such as '2 + 2 = 4', are true at all times, while tensed expressions such as 'John is happy' are only true sometimes.  In temporal logic, tense constructions are treated in terms of modalities, where a standard method for formalizing talk of time is to use "two" pairs of operators, one for the past and one for the future (P will just mean 'it is presently the case that P'). For example:  There are then at least three modal logics that we can develop. For example, we can stipulate that,  Or we can trade these operators to deal only with the future (or past). For example,  or,  The operators F and G may seem initially foreign, but they create normal modal systems. Note that FP" is the same as ¬G¬"P". We can combine the above operators to form complex statements. For example, PP" → □P"P" says (effectively), "Everything that is past and true is necessary".  It seems reasonable to say that possibly it will rain tomorrow, and possibly it won't; on the other hand, since we can't change the past, if it is true that it rained yesterday, it probably isn't true that it may not have rained yesterday. It seems the past is "fixed", or necessary, in a way the future is not. This is sometimes referred to as accidental necessity. But if the past is "fixed", and everything that is in the future will eventually be in the past, then it seems plausible to say that future events are necessary too.  Similarly, the problem of future contingents considers the semantics of assertions about the future: is either of the propositions 'There will be a sea battle tomorrow', or 'There will not be a sea battle tomorrow' now true? Considering this thesis led Aristotle to reject the principle of bivalence for assertions concerning the future.  Additional binary operators are also relevant to temporal logics, "q.v." Linear Temporal Logic.  Versions of temporal logic can be used in computer science to model computer operations and prove theorems about them. In one version, ◇"P" means "at a future time in the computation it is possible that the computer state will be such that P is true"; □"P" means "at all future times in the computation P will be true". In another version, ◇"P" means "at the immediate next state of the computation, "P" might be true"; □"P" means "at the immediate next state of the computation, P will be true". These differ in the choice of Accessibility relation. (P always means "P is true at the current computer state".) These two examples involve nondeterministic or not-fully-understood computations; there are many other modal logics specialized to different types of program analysis. Each one naturally leads to slightly different axioms.

Deontic logic.

Likewise talk of morality, or of obligation and norms generally, seems to have a modal structure. The difference between "You must do this" and "You may do this" looks a lot like the difference between "This is necessary" and "This is possible". Such logics are called "deontic", from the Greek for "duty".  Deontic logics commonly lack the axiom T semantically corresponding to the reflexivity of the accessibility relation in Kripke semantics: in symbols, formula_43. Interpreting □ as "it is obligatory that", T informally says that every obligation is true. For example, if it is obligatory not to kill others (i.e. killing is morally forbidden), then T implies that people actually do not kill others. The consequent is obviously false.  Instead, using Kripke semantics, we say that though our own world does not realize all obligations, the worlds accessible to it do (i.e., T holds at these worlds). These worlds are called idealized worlds. "P" is obligatory with respect to our own world if at all idealized worlds accessible to our world, "P" holds. Though this was one of the first interpretations of the formal semantics, it has recently come under criticism.  One other principle that is often (at least traditionally) accepted as a deontic principle is "D", formula_44, which corresponds to the seriality (or extendability or unboundedness) of the accessibility relation. It is an embodiment of the Kantian idea that "ought implies can". (Clearly the "can" can be interpreted in various senses, e.g. in a moral or alethic sense.)

Intuitive problems with deontic logic.

When we try to formalize ethics with standard modal logic, we run into some problems. Suppose that we have a proposition "K": you have stolen some money, and another, "Q": you have stolen a small amount of money. Now suppose we want to express the thought that "if you have stolen some money, it ought to be a small amount of money". There are two likely candidates,  But (1) and "K" together entail □"Q", which says that it ought to be the case that you have stolen a small amount of money. This surely isn't right, because you ought not to have stolen anything at all. And (2) doesn't work either: If the right representation of "if you have stolen some money it ought to be a small amount" is (2), then the right representation of (3) "if you have stolen some money then it ought to be a large amount" is formula_47. Now suppose (as seems reasonable) that you ought not to steal anything, or formula_48. But then we can deduce formula_47 via formula_50 and formula_51 (the contrapositive of formula_52); so sentence (3) follows from our hypothesis (of course the same logic shows sentence (2)). But that can't be right, and is not right when we use natural language. Telling someone they should not steal certainly does not imply that they should steal large amounts of money if they do engage in theft.

Doxastic logic.

"Doxastic logic" concerns the logic of belief (of some set of agents). The term doxastic is derived from the ancient Greek "doxa" which means "belief". Typically, a doxastic logic uses □, often written "B", to mean "It is believed that", or when relativized to a particular agent s, "It is believed by s that".

Other modal logics.

Significantly, modal logics can be developed to accommodate most of these idioms; it is the fact of their common logical structure (the use of "intensional" sentential operators) that make them all varieties of the same thing.

The ontology of possibility.

In the most common interpretation of modal logic, one considers "logically possible worlds". If a statement is true in all possible worlds, then it is a necessary truth. If a statement happens to be true in our world, but is not true in all possible worlds, then it is a contingent truth. A statement that is true in some possible world (not necessarily our own) is called a possible truth.  Under this "possible worlds idiom," to maintain that Bigfoot's existence is possible but not actual, one says, "There is some possible world in which Bigfoot exists; but in the actual world, Bigfoot does not exist". However, it is unclear what this claim commits us to. Are we really alleging the existence of possible worlds, every bit as real as our actual world, just not actual? Saul Kripke believes that 'possible world' is something of a misnomer – that the term 'possible world' is just a useful way of visualizing the concept of possibility. For him, the sentences "you could have rolled a 4 instead of a 6" and "there is a possible world where you rolled a 4, but you rolled a 6 in the actual world" are not significantly different statements, and neither commit us to the existence of a possible world. David Lewis, on the other hand, made himself notorious by biting the bullet, asserting that all merely possible worlds are as real as our own, and that what distinguishes our world as "actual" is simply that it is indeed our world – "this" world. That position is a major tenet of "modal realism". Some philosophers decline to endorse any version of modal realism, considering it ontologically extravagant, and prefer to seek various ways to paraphrase away these ontological commitments. Robert Adams holds that 'possible worlds' are better thought of as 'world-stories', or consistent sets of propositions. Thus, it is possible that you rolled a 4 if such a state of affairs can be described coherently.  Computer scientists will generally pick a highly specific interpretation of the modal operators specialized to the particular sort of computation being analysed. In place of "all worlds", you may have "all possible next states of the computer", or "all possible future states of the computer".

Further applications.

Modal logics have begun to be used in areas of the humanities such as literature, poetry, art and history.

Controversies.

Nicholas Rescher has argued that Bertrand Russell rejected modal logic, and that this rejection led to the theory of modal logic languishing for decades. However, Jan Dejnozka has argued against this view, stating that a modal system which Dejnozka calls "MDL" is described in Russell's works, although Russell did believe the concept of modality to "come from confusing propositions with propositional functions," as he wrote in "The Analysis of Matter".  Arthur Norman Prior warned Ruth Barcan Marcus to prepare well in the debates concerning quantified modal logic with Willard Van Orman Quine, due to the biases against modal logic.

Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality. A modal—a word that expresses a modality—qualifies a statement. For example, the statement "John is happy" might be qualified by saying that John is "usually" happy, in which case the term "usually" is functioning as a modal. The traditional alethic modalities, or modalities of truth, include possibility ("Possibly, "p"", "It is possible that "p""), necessity ("Necessarily, "p"", "It is necessary that "p""), and impossibility ("Impossibly, "p"", "It is impossible that "p""). Other modalities that have been formalized in modal logic include temporal modalities, or modalities of time (notably, "It was the case that "p"", "It has always been that "p"", "It will be that "p"", "It will always be that "p""), deontic modalities (notably, "It is obligatory that "p"", and "It is permissible that "p""), epistemic modalities, or modalities of knowledge ("It is known that "p"") and doxastic modalities, or modalities of belief ("It is believed that "p"").

Modální logika je oblast logiky zkoumající logické operace, tzv. modality (modální operátory jsou například „je možné, je nutné, je nemožné“).


Theories of rational thinking.

Max Weber.

The German scholar Max Weber proposed an interpretation of social action that distinguished between four different idealized types of rationality.  The first, which he called "Zweckrational" or purposive/instrumental rationality, is related to the expectations about the behavior of other human beings or objects in the environment. These expectations serve as means for a particular actor to attain ends, ends which Weber noted were "rationally pursued and calculated." The second type, Weber called "Wertrational" or value/belief-oriented. Here the action is undertaken for what one might call reasons intrinsic to the actor: some ethical, aesthetic, religious or other motives, independent of whether it will lead to success. The third type was affectual, determined by an actor's specific affect, feeling, or emotion—to which Weber himself said that this was a kind of rationality that was on the borderline of what he considered "meaningfully oriented." The fourth was traditional or conventional, determined by ingrained habituation. Weber emphasized that it was very unusual to find only one of these orientations: combinations were the norm. His usage also makes clear that he considered the first two as more significant than the others, and it is arguable that the third and fourth are subtypes of the first two.  The advantage in Weber's interpretation of rationality is that it avoids a value-laden assessment, say, that certain kinds of beliefs are irrational. Instead, Weber suggests that ground or motive can be given—for religious or affect reasons, for example—that may meet the criterion of explanation or justification even if it is not an explanation that fits the "Zweckrational" orientation of means and ends. The opposite is therefore also true: some means-ends explanations will not satisfy those whose grounds for action are "Wertrational".  Weber's constructions of rationality have been critiqued both from a Habermasian (1984) perspective (as devoid of social context and under-theorised in terms of social power) and also from a feminist perspective (Eagleton, 2003) whereby Weber's rationality constructs are viewed as imbued with masculine values and oriented toward the maintenance of male power. An alternative position on rationality (which includes both bounded rationality, as well as the affective and value-based arguments of Weber) can be found in the critique of Etzioni (1988), who reframes thought on decision-making to argue for a reversal of the position put forward by Weber. Etzioni illustrates how purposive/instrumental reasoning is subordinated by normative considerations (ideas on how people 'ought' to behave) and affective considerations (as a support system for the development of human relationships).

Psychology.

In the psychology of reasoning, psychologists and cognitive scientists have defended different positions on human rationality. One prominent view, due to Philip Johnson-Laird and Ruth M. J. Byrne among others is that humans are rational in principle but they err in practice, that is, humans have the competence to be rational but their performance is limited by various factors. However, it has been argued that many standard tests of reasoning, such as those on the conjunction fallacy, on the Wason selection task, or the base rate fallacy suffer from methodological and conceptual problems. This has led to disputes in psychology over whether researchers should (only) use standard rules of logic, probability theory and statistics, or rational choice theory as norms of good reasoning. Opponents of this view, such as Gerd Gigerenzer, favor a conception of bounded rationality, especially for tasks under high uncertainty.

Richard Brandt.

Richard Brandt proposed a "reforming definition" of rationality, arguing someone is rational if their notions survive a form of cognitive-psychotherapy.

Quality.

Abulof argues that rationality has become an "essentially contested concept," as its "proper use... inevitably involves endless disputes." He identifies "four fronts" for the disputes about the meaning of rationality:  It is believed by some philosophers (notably A. C. Grayling) that a good rationale must be independent of emotions, personal feelings or any kind of instincts. Any process of evaluation or analysis, that may be called rational, is expected to be highly objective, logical and "mechanical". If these minimum requirements are not satisfied i.e. if a person has been, even slightly, influenced by personal emotions, feelings, instincts, or culturally specific moral codes and norms, then the analysis may be termed irrational, due to the injection of subjective bias.  Modern cognitive science and neuroscience show that studying the role of emotion in mental function (including topics ranging from flashes of scientific insight to making future plans), that no human has ever satisfied this criterion, except perhaps a person with no affective feelings, for example, an individual with a massively damaged amygdala or severe psychopathy. Thus, such an idealized form of rationality is best exemplified by computers, and not people. However, scholars may productively appeal to the idealization as a point of reference.

Theoretical and practical.

Kant had distinguished theoretical from practical reason. Rationality theorist Jesús Mosterín makes a parallel distinction between theoretical and practical rationality, although, according to him, reason and rationality are not the same: reason would be a psychological faculty, whereas rationality is an optimizing strategy. Humans are not rational by definition, but they can think and behave rationally or not, depending on whether they apply, explicitly or implicitly, the strategy of theoretical and practical rationality to the thoughts they accept and to the actions they perform.  The distinction is also described as that between epistemic rationality, the attempt to form beliefs in an unbiased manner, and instrumental rationality.  Theoretical rationality has a formal component that reduces to logical consistency and a material component that reduces to empirical support, relying on our inborn mechanisms of signal detection and interpretation. Mosterín distinguishes between involuntary and implicit belief, on the one hand, and voluntary and explicit acceptance, on the other. Theoretical rationality can more properly be said to regulate our acceptances than our beliefs. Practical rationality is the strategy for living one's best possible life, achieving your most important goals and your own preferences in as far as possible.

Examples in different fields.

Logic.

As the study of arguments that are correct in virtue of their form, logic is of fundamental importance in the study of rationality. The study of rationality in logic is more concerned with epistemic rationality, that is, attaining beliefs in a rational manner, than instrumental rationality.

Economics.

Rationality plays a key role in economics and there are several strands to this. Firstly, there is the concept of instrumentality—basically the idea that people and organisations are instrumentally rational—that is, adopt the best actions to achieve their goals. Secondly, there is an axiomatic concept that rationality is a matter of being logically consistent within your preferences and beliefs. Thirdly, people have focused on the accuracy of beliefs and full use of information—in this view, a person who is not rational has beliefs that don't fully use the information they have.  Debates within economic sociology also arise as to whether or not people or organizations are "really" rational, as well as whether it makes sense to model them as such in formal models. Some have argued that a kind of bounded rationality makes more sense for such models.  Others think that any kind of rationality along the lines of rational choice theory is a useless concept for understanding human behavior; the term "homo economicus" (economic man: the imaginary man being assumed in economic models who is logically consistent but amoral) was coined largely in honor of this view. Behavioral economics aims to account for economic actors as they actually are, allowing for psychological biases, rather than assuming idealized instrumental rationality.

Artificial intelligence.

Within artificial intelligence, a "rational agent" is typically one that maximizes its expected utility, given its current knowledge. Utility is the usefulness of the consequences of its actions. The utility function is arbitrarily defined by the designer, but should be a function of "performance", which is the directly measurable consequences, such as winning or losing money. In order to make a safe agent that plays defensively, a nonlinear function of performance is often desired, so that the reward for winning is lower than the punishment for losing. An agent might be rational within its own problem area, but finding the rational decision for arbitrarily complex problems is not practically possible. The rationality of human thought is a key problem in the psychology of reasoning.

International relations.

There is an ongoing debate over the merits of using “rationality” in the study of international relations (IR). Some scholars hold it indispensable. Others are more critical. Still, the pervasive and persistent usage of "rationality" in political science and IR is beyond dispute. "Rationality" remains ubiquitous in this field. Abulof finds that Some 40% of all scholarly references to "foreign policy" allude to "rationality"—and this ratio goes up to more than half of pertinent academic publications in the 2000s. He further argues that when it comes to concrete security and foreign policies, IR employment of rationality borders on "malpractice": rationality-based descriptions are largely either false or unfalsifiable; many observers fail to explicate the meaning of "rationality" they employ; and the concept is frequently used politically to distinguish between "us and them."

Rationality is the quality or state of being rational – that is, being based on or agreeable to reason. Rationality implies the conformity of one's beliefs with one's reasons to believe, and of one's actions with one's reasons for action. "Rationality" has different specialized meanings in philosophy, economics, sociology, psychology, evolutionary biology, game theory and political science.

Racionalita (z lat. "ratio", rozum a "rationalis", rozumný) znamená rozumnost či rozumovost, schopnost myslet, rozhodovat se a jednat na základě rozvahy, případně rozumných účelů a cílů, které lze obhájit důvody. Jako racionální se často hodnotí určité rozhodování a jednání právě vzhledem k nějakému cíli („cílová“ nebo „účelová racionalita“, instrumentální racionalita, ekonomická racionalita).


Early years.

János Bródy was born on 5 April 1946 in Budapest as the child of András Bródy, Széchenyi Award-winning economist, and Márta Vajna, a teacher.  After his graduation from the Puskás Tivadar Telecommunication Technical School, in 1964 he joined the beat band Illés after the advice of Zsuzsa Koncz. The band, which previously gained its Budapest-wide fame from small club concerts playing Italian and English hits (like ones from The Hurricanes, The Shadows and The Beatles) recorded its first albums "Long Tall Sally" and "Little Richard/Chapel". The band was more and more often accompanied by the young Levente Szörényi, with whom Bródy began their acclaimed musical partnership. After many of the members finished university, the band went through multiple changes, but was getting more and more fame. In 1969 Bródy graduated as an electrical engineer at the Budapest University of Technology.

Music career.

Illés and Fonográf.

By 1967 Illés band was not only playing western music, but they played original compositions and the lyrics was Hungarian. Bródy wrote coded lyrics that – embedding the possibility of multiple interpretations – criticised the communist regime, turning their increasingly crowded events to implicit protests. Szörényi was also experimenting with fusing folk music into rock. By 1972, Illés was increasingly under the pressure due to both passive state harassment, and the huge fan base, which demanded a more popular style compared to their original artistic goals.  In 10 June 1973 at a massive beat event in Diósgyőr, Bródy turned to fans and said ""We also wish to thank for the work of the police forces. Yes, I'm serious, as there was many of you who already came here yesterday from Miskolc, many of you who couldn't sleep anywhere, wanted to spend the night out in Avas. For them, the police provided shelter, even if not as comfortable as the bed at home, and let them out today morning, asking them if they slept well, and wishing them fun for tonight."" Bródy was sentenced to a one-month residual ban and 5000Ft fine. In his absence, the band started to fall apart, with members sacrificing more and more time to own projects. On 2 November 1973 the band officially split, with founder Lajos Illés re-founding it with new members. After seven years, in 1981 the band gave a final concert with the original members, and while their disagreements remained, group work manifested in talks, documentaries, and concerts in 1990, 1996, 2001 and – marked by the death of drummer Zoltán Pásztory – a last two in 2005.  The same year, in 1973, the Szörényi brothers and Bródy started a new band, Fonográf, with László Tolcsvay, Mihály Móricz and Oszkár Németh. Fonográf played a fusion of progressive rock and folk including country music. Between 1974 and 1984 the band released eleven full albums. Bródy and Szörényi founding Fonográf. Fonográf was also a virtually a workshop with numerous collaborators, notably Zsuzsa Koncz and Judit Halász, while the members also developed their own projects with the group's backing. Their lyrics still featured anti-regime ideas, often coming under heavy censorship. In 1973, discs of Koncz's album "Jelbeszéd", written by Bródy was withdrawn from stores and shredded.

Plays.

The 80s marked successful theatrical compositions for the Bródy-Szörényi duo, like Kőműves Kelemen in 1982, cult rock opera István, a király in 1983, or Fehér Anna in 1988. As member projects took increasingly different paths, Fonográf dissolved after three large concerts in 1984.  Bródy's relationship with Szörényi soured after the first democratic elections in 1990 when they began to support rival political parties, restricting their joint artistic work to the few last concerts of Illés and Fonográf. However they continue to appear together.

Solo career.

Bródy's own performing career began with concerts in the Court Theatre (Várszínház) and the University Stage of ELTE. His first album, "Hungarian Blues", released in 1980, contained songs that were dominant throughout his later career: mellow, critical, ironical ballads about general life in the 80s, and after 1990, the disappointment in the newly democratized country. Besides giving a few larger solo concerts (notably in 1994), Bródy favors smaller, intimate club and chamber events. He also continued his work on theatrical plays, like "A Kiátkozott" (1997) and "Volt egyszer egy csapat" (2005).

János Kristóf Bródy (Hungarian: Bródy János, born 5 April 1946) is a Hungarian pop singer-songwriter, guitarist, composer and scriptwriter. Successful both with the bands Illés and Fonográf and in his solo career, writing lyrics for singers like Zsuzsa Koncz or for rock operas like István, a király, he was a major figure of the Hungarian music scene in the 60s–90s.

János Bródy (v maďarštině Bródy János [bródy jánoš], * 5. dubna 1946 v Budapešti, Maďarsko) je maďarský zpěvák, kytarista, skladatel a textař. Patří k výrazným postavám maďarské rockové kultury.


Description.

"S. stercoraria" is sexually dimorphic, with an average lifespan of one to two months. The adult males are bright golden-yellow with orange-yellow fur on the front legs. Females are a little duller in color, with pronounced green-brown tinges, and no brightly colored fur on the front legs. The adults range from 5 to 11 mm in length, and the males are generally larger than the females. The physical features of separate "S. stercoraria" populations can vary greatly, due in part to the range of locations in which the species is found. Generally, they are located in cooler temperate regions, including North America, Asia, and Europe. They may also favor higher higher altitudes, such as the Pyrenees and Swiss Alps.

Feeding.

The adults mainly prey on smaller insects — mostly other Diptera. They can also consume nectar and dung as additional sources of energy. In a laboratory setting, adult "S. stercoraria" can live solely on "Drosophila" and water. Females spend most of their time foraging in vegetation and only visit dung pats to mate and oviposit on the dung surface. Both males and females are attracted to dung by scent, and approach dung pats against the wind. Males spend most of their time on the dung, waiting for females and feeding on other insects that visit the dung, such as blow flies. In the absence of other prey, the yellow dung fly may turn to cannibalism. The larvae are coprophagous, relying on dung for nutrition.

Reproduction.

"S. stercoraria" breeds on the dung of many large mammals, but generally prefers fresh cattle dung. The operational sex ratio on these pats is very male-biased and competition is high. Females are small and have limited precopulatory choice. Copulation lasts 20–50 minutes, after which the male attempts to guard the female from other males. Both males and females often mate with multiple partners. Reproductive success depends on a variety of factors, including sperm competition, nutrition, and environmental temperature.

Anatomy.

Females have paired accessory glands, which supply lubricants to the reproductive system and secrete protein-rich egg shells. Sperm is received in a large structure called the bursa copulatrix, and is stored in a structure called the spermatheca. "Scathophaga" species have three spermathecae, (one pair and one singlet), each with its own narrow duct that connects it to the bursa. Sperm can be stored in the spermathecae for days, weeks, or even years, and sperm from several males can be stored simultaneously. Males have two projections, the paralobes, which are used to hold onto a female during copulation. Between the paralobes is the intromittent organ, the aedeagus, which transfers sperm into the female's bursa copulatrix.

Behavior.

During copulation, sperm is not directly deposited into sperm-storing organs. Ejaculation occurs in the bursa copulatrix, and then females actively move sperm into the spermathecae using their muscular spermathecal invagination to pump sperm into transit. This gives females a level of control over which and how much sperm enters her system, an example of cryptic female choice. Although current results are inconclusive regarding whether or not females are cryptically selecting for a better phenotypic match, a female may benefit from having variable sperm fertilizing her offspring. Such adaptations are advantageous because females benefit from being able to control which sperm are successful in fertilizing eggs. The females may not be aware of which sperm are better suited for her offspring, but simply that being able to control the proportion of sperm from multiple mates can maximize the possibility of an optimal phenotypic match. It is to her advantage to have multiple males’ sperm reach her eggs, rather than just one. After copulation, females prefer to lay their eggs on the small hills of the dung surface, avoiding depressions and pointed areas. This survival strategy aims to prevent desiccation and drowning so the eggs are placed where they have the greatest chance of surviving.

Sexual conflict.

Many studies have studied the many manifestations of sexual conflict, including postmating sexual selection, in the yellow dung fly. Sperm competition occurs when a female mates with multiple males. Each male's sperm is then in direct competition to fertilize the eggs. Sperm mix quickly once they reach the female's stores. The goal of males is to displace the sperm of other males as much as possible. Larger males tend to have longer copulation times and greater rates of sperm displacement. The fertilization success of males that were secondary mates increased as their body size relative to the first male increased.  Traits such as body size, testis size, and sperm length are variable, as well as heritable in "S. stercoraria" males. Larger sperm may be advantageous if they have greater propulsion along the female's spermathecal duct, resulting in higher fertilization success rates. When competition among males is high and females are mating with multiple males, those with the largest testes also have the most success in terms of proportion of sperm that fertilize a female's eggs. The resulting male offspring would then have a similar advantage. A positive correlation was found between sperm length of males and spermathecal duct length of females. The size of male testis was also positively correlated with female spermathecae size. Additionally, females with larger spermathecae are better able to produce spermicidal secretion. This cryptic female choice betters their ability to influence paternity over their offspring. These covariances are an example of an “evolutionary arms race”. This suggests that each sex evolves certain traits to undermine the beneficial traits of the other, resulting in the coevolution of male and female reproductive systems of "S. stercoraria."

Lifecycle.

The eggs that the female lays on the dung hatch into larvae after 1–2 days, depending on temperature. The larvae quickly burrow into the dung for protection and feed on it. At 20 °C, larvae undergo three molts over five days, during which they grow exponentially. After growth, larvae spend another five days emptying their stomachs before pupation, where no additional body mass is gained. After 10–20 days, the larvae burrow into the soil around and beneath the dung and pupate. The time needed for the juvenile flies to emerge can vary from 10 days at 25 °C to 80 days at 10 °C or less. The smaller females typically emerge a few days before the males. The fitness of the resulting juveniles is greatly dependent on the quality of the dung in which they were placed. Factors affecting dung quality include water content, nutritional quality, parasites, and drugs or other chemicals given to the animal. Yellow dung flies are anautogenous. To become sexually mature and produce viable eggs or sperm, they must feed on prey to acquire sufficient proteins and lipids. Females under nutritional stress will have higher rates of egg mortality and less survival of offspring to adult emergence. "S. stercoraria" females can then produce four to 10 clutches in their lifetimes. The adults are active throughout much of the year in most moderate climates.

Phenology.

Yellow dung fly viability depends strongly on the environment. In warmer climates, a sharp population decline often occurs in the summer, when the temperatures increase above 25 °C. Meanwhile, no population decline is seen in colder climates, such as Iceland, Finland, and northern England, and high elevations. Additionally, the number of generations per year varies with altitude and latitude, typically between two and four overlapping generations. The end of winter synchronizes the first emergence in March, and the overwinter generations are produced in the fall. In northern Europe, where the mating season is shorter, only one or two generations can be expected.

Phenotypic plasticity.

Yellow dung flies have extremely variable phenotypes - body size and development rate in particular. Proximate causes of variation include juvenile nutrition, temperature, predation, and genetic variation. Much phenotypic plasticity in yellow dung flies is a result of food (dung) availability in the larval stage, which is often mediated by conspecific competition. Less dung results in more competitors, and more drying results in decreased growth rate and adult body size. Additionally, when exposed to constant temperatures in a laboratory setting, higher temperatures during growth yield smaller flies. Egg volume, but not clutch size, also decreases with increasing temperature. Giving merit to the hypothesis that constraints on physiological processes at the cellular level account for temperature-mediated body size, studies have also shown that "S. stercoraria" body size varies via gene-by-environment interactions. Different cell lines vary significantly in growth, development, and adult body size in response to food limitation.

Geographic variation.

"S. stercoraria's" phenotype has been shown to vary seasonally, latitudinally, and altitudinally as a result an adaptive response to time constraints on development due to temperature changes. In the fall, as the temperature cools, the flies are able to increase development rate, so they can achieve the necessary, albeit smaller than average, size. Furthermore, "S. stercoraria" development rate increases with increasing latitude. This is likely an adaptive response to shorter mating seasons. Body size, but not development rate, vary with altitude. Dung flies are larger at higher altitudes as a result of colder temperatures.

Reasons behind phenotypic plasticity.

Larger yellow dung flies have a competitive advantage. Therefore, body size plasticity must be a survival mechanism. Offspring of large adults still survive under food limitations, despite needing more nutrients for a longer development. Thus, the observed growth plasticity is a result of altering body chemistry and not differing survival rates of offspring from small and large parents. Plastic development rate and body size are effective at avoiding premature death, meaning "S. stercoraria" adopts a strategy of being small and alive over large and dead. Smaller flies have an advantage in stressful environmental situations, due to larger dung flies needing more energy. Additionally, low genetic differentiation exists between yellow dung fly populations, likely due to extensive gene flow, as "S. stercoraria" is able to travel great distances. When species are unable to adapt through genetics, phenotypic plasticity is the most viable option to adjust to changing environments. Yellow dung flies develop in extremely variable environments, with pat drying, dung availability, and larval competition hindering survival. Therefore, phenotypic plasticity allows "S. stercoraria" to adjust development according to unpredictable ecological situations without genetic adaptation.

Parasites and diseases.

Since "S. stercoraria" is a synanthropic fly, it does carry the risk of passively contaminating human food with various pathogens, molds, or yeasts.  Some sexually transmitted diseases of insects are known, particularly in Coleoptera. Similar diseases have also been studied in "S. stercoraria". Many of these sexually transmitted diseases are from multicellular ectoparasites (mites), protists, or the fungus "Entomophthora muscae". These are frequently responsible for either sterilizing or killing the host fly.

Predators.

Besides being an easy meal for a great many bird and bat species, they are also preyed upon by other insects. Much competition exists between larvae of different species within a dung pat. Other insect species may also use the pats as hunting grounds. These include robber flies and clown beetles.

Use as a model organism.

Like "Drosophila melanogaster", the yellow dung fly is an ideal model organism due to its short lifespan and susceptibility to various experimental manipulations. Initial interest in yellow dung flies came from their potential as biocontrol agents against pest flies around livestock. In the past 40 years alone, many studies have used "S. stercoraria" to research topics such as sperm competition, mating behavior, sexual conflict, reproductive physiology, thermal biology, and genetics. In particular, research on yellow dung flies has contributed greatly to understanding of multiple mating systems and sperm competition.  Recently, "S. stercoraria" was approved as a standard required test species for ecotoxicological testing. This includes evaluating the residues of veterinary drugs in livestock dung. Yellow dung flies are a key part of decomposing waste in pastures, which is key to preventing the spread of endoparasites and returning nutrients to the soil. The species’ diet also serves to reduce the abundance of pest flies. To test a chemical's toxicity, the chemical is mixed with bovine faeces, to which yellow dung fly eggs are added. Then, endpoints, such as sex and number of emerged adult flies, retardation of emergence, morphological change, and developmental rate, are measured and analyzed to determine toxicity. A great deal of research has been done on the effects of avermectins on populations of "S. stercoraria". Avermectins are used to control endoparasites in livestock. The resulting dung contains drug residues that can have unintentional adverse effects on yellow dung fly populations, such as increased mutations and decreased offspring viability. If the use of such drugs in agriculture is not carefully monitored, considerable economic losses could occur.

Scathophaga stercoraria, commonly known as the yellow dung fly or the golden dung fly, is one of the most familiar and abundant flies in many parts of the Northern Hemisphere. As its common name suggests, it is often found on the feces of large mammals, such as horses, cattle, sheep, deer, and wild boar, where it goes to breed. The distribution of "S. stercoraria" is likely influenced by human agriculture, especially in Northern Europe and North America. The Scathophaga are integral in the animal kingdom due to their role in the natural decomposition of dung in fields. They are also very important in the scientific world due to their short lifecycles and susceptibility to experimental manipulations, thus have contributed significant knowledge about animal behavior.

Výkalnice hnojní ("Scathophaga stercoraria") je štíhlá hnědožlutá moucha s poměrně dlouhýma nohama a jedním párem středně dlouhých, u kořene nažloutých křídel. Samci jsou pokryti žlutavými až zlatavými chloupky, samice nejsou tolik do žluta, jsou méně ochlupené a méně nápadné. Mimo zimy jsou aktivní po celý rok a nejsou ani tak závislé na prostředí, jako na čerstvém trusu kopytníků, do kterého stejně jako všichni ostatní příslušníci čeledi výkalnicovitých kladou vajíčka a ve kterém se vyvíjí jejich larvy.


History.

Trans-X was started by Canadian musician Pascal Languirand, previously known for his albums in the ambient, cosmic and space music genres. The name comes from the 1977 Kraftwerk song "Trans-Europe Express", which Languirand thought “was catchy and reflected well the direction I wanted to take with Trans-X“. In 1982 he recruited Montreal keyboardist and programmer Steve Wyatt as the second half of the Trans-X duo. Together they recorded a demo that got Trans-X a recording contract for a single, "Vivre sur Vidéo".  Steve Wyatt played some synthesizer and did some programming on "Vivre sur Vidéo". He also composed "Digital World" and played all the instruments on the track, which was on the B-side of the single. "Digital World" can also be found on the maxi-single and on the band's debut album. Wyatt left Trans-X sometime in late 1983.  When "Living on Video" (the English version of "Vivre sur Vidéo") was released in May 1983, it was an instant hit in Canada and the single later sold two million copies and reached British and European Top ten charts on its 1985 release.  Later in 1983, Trans-X released another song "Message on the Radio" which did not make it into the charts, and Trans-X ended the year with another single, "3D-Dance". All these songs featured on the band's 1983 debut album, "Living on Video", known in Canada as "Message On The Radio". For the studio recording of the album, Anne Brosseau was hired to do backing vocals. However, she decided not to perform with Trans-X. For this reason, Montrealer Laurie Ann Gill, who performed backing vocals for synthpop group Nudimension, was recruited for promotional pictures, TV performances and touring, which she did until 1985.  In 1986, the band released their second album, which had the same title and artwork as their debut album. Different versions were released in Canada and America and the album also contained three tracks from the 1983 album, although they were remixed or re-recorded.  In 1988, Languirand decided to retire Trans-X after their third album "On My Own" failed to chart outside of Canada. After the album was released Languirand went silent for a few years and decided to continue his solo career with new age, ambient and space music instead of electronica.  In 1994, Languirand returned as Trans-X, performing live with Nadia Sohaei. Later Languirand recorded a remake of his main hit under the title "Living on Video 2003" and released "The Drag-Matic Album", produced by Michel Huygen of Neuronium. One more new version of this hit, "Living on Video 2k6" was released on 6 May 2006.  As of 2010, Languirand lives in Mexico. In early 2012, he was seen performing live with Truc Quynh, better known as "TQ", a relatively well-known Italo disco singer. With TQ, Languirand has been collaborating since at least 2004. However, on the 2010 single "I Want To Be With You Tonight", the "L. O. V. 2011" album and on the 2012 "Hi-NRG" album that was released in Mexico, Languirand was vocally accompanied by Corina Lawrence, who he worked together with from 2008 to 2015. In 2013, Languirand sang ”My Fascination” with Truc Quynh; the song became part of TQ's later album "Out of the Shadows" which was released in late 2014. Although Languirand was involved in singing that song, it was more of a spin-off than a pure Trans-X project. Over the years, Languirand became more and more interconnected with other artists, especially after 1988, by not solely working for Trans-X, but being able to do other projects. Sometimes, he lent his voice to others, sometimes he worked for others as a producer, etc.  In 2012, Luis Broc joined the band as drummer and in 2014 he was joined by Ramón Serratos in SFX, synthesis and as a DJ of the band in live performances. Both are of Mexican origin. During 2016, the band made a series of tours in South America, reaffirming the taste for the Hi-NRG genre in diverse audiences, in the initiative of "Discolocos", a documentary film (co-written, directed and produced by David Dávila Herrera) that reflects the world of the followers of the genre since the 1980s. The film features Trans-X, who also created and sang the soundtrack ("Discolocos, Vol. 1", released 2018), which has roots in classic themes from the 1980s in his tribute to the Hi-NRG and Italo disco genres, collaborating with the voices of Willie Chambers, Jessica Williams, Claudja Barry, Tobias Bernstrup, Stephan Groth, Cynthia Manley, Eskil Simonsson, Conrad Kaneshiro, Christina Criscione and J. D. Hall.  Since 2018, Mario Várguez and Aletz Franco on synths and electronic drums respectively have been live guest musicians. They are members of the Mexican electro-indie rock band Ventormenta. Also, backing vocals and dance are performed by Lily Contreras. Since 2019, Languirand has been working on a new album under Cleopatra Records.

Band members.

Current touring musicians  Former members and touring musicians

Trans-X is a Canadian 1980s synth band formed in Montreal, Quebec, Canada. They are known for their hit song "Living on Video" which charted worldwide.

Trans-X je kanadská hudební skupina, aktivní především v osmdesátých letech minulého století, jež se proslavila skladbou "Living on Video". Trans-X založil Pascal Languirand, který předtím dělal různá hudební alba různých žánrů – ambient, cosmic, space music. Poté založil duo s Montrealskou rodačkou Laurie Ann Gillovou, která utvářela celek v podobě dua Trans-X. Ann Gillová předtím zpívala pro synthpop kapelu Nudimension.