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Regular representation Regular representation In mathematics, and in particular the theory of group representations, the regular representation of a group "G" is the linear representation afforded by the group action of "G" on itself by translation. One distinguishes the left regular representation λ given by left translation and the right regular representation ρ given by the inverse of right translation. Finite groups. For a finite group "G", the left regular representation λ (over a field "K") is a linear representation on the "K"-vector space "V" freely generated by the elements of "G", i. e. they can be identified with a basis of

Regular representation

V. Given "g" ∈ "G", λ is the linear map determined by its action on the basis by left translation by "g", i.e. For the right regular representation ρ, an inversion must occur in order to satisfy the axioms of a representation. Specifically, given "g" ∈ "G", ρ is the linear map on "V" determined by its action on the basis by right translation by "g", i.e. Alternatively, these representations can be defined on the "K"-vector space "W" of all functions . It is in this form that the regular representation is generalized to topological groups such as Lie groups. The

Regular representation

specific definition in terms of "W" is as follows. Given a function and an element "g" ∈ "G", and Significance of the regular representation of a group. Every group "G" acts on itself by translations. If we consider this action as a permutation representation it is characterised as having a single orbit and stabilizer the identity subgroup {"e"} of "G". The regular representation of "G", for a given field "K", is the linear representation made by taking this permutation representation as a set of basis vectors of a vector space over "K". The significance is that while the permutation representation

Regular representation

doesn't decompose – it is transitive – the regular representation in general breaks up into smaller representations. For example, if "G" is a finite group and "K" is the complex number field, the regular representation decomposes as a direct sum of irreducible representations, with each irreducible representation appearing in the decomposition with multiplicity its dimension. The number of these irreducibles is equal to the number of conjugacy classes of "G". The above fact can be explained by character theory. Recall that the character of the regular representation χ"(g)" is the number of fixed points of "g" acting on the regular representation

Regular representation

V. It means the number of fixed points χ"(g)" is zero when "g" is not "id" and |"G"| otherwise. Let "V" have the decomposition ⊕"a""V" where "V"'s are irreducible representations of "G" and "a"'s are the corresponding multiplicities. By character theory, the multiplicity "a" can be computed as formula_5 which means the multiplicity of each irreducible representation is its dimension. The article on group rings articulates the regular representation for finite groups, as well as showing how the regular representation can be taken to be a module. Module theory point of view. To put the construction more

Regular representation

abstractly, the group ring "K"["G"] is considered as a module over itself. (There is a choice here of left-action or right-action, but that is not of importance except for notation.) If "G" is finite and the characteristic of K doesn't divide |"G"|, this is a semisimple ring and we are looking at its left (right) ring ideals. This theory has been studied in great depth. It is known in particular that the direct sum decomposition of the regular representation contains a representative of every isomorphism class of irreducible linear representations of "G" over "K". You can say

Regular representation

that the regular representation is "comprehensive" for representation theory, in this case. The modular case, when the characteristic of "K" does divide |"G"|, is harder mainly because with "K"["G"] not semisimple, a representation can fail to be irreducible without splitting as a direct sum. Structure for finite cyclic groups. For a cyclic group "C" generated by "g" of order "n", the matrix form of an element of "K"["C"] acting on "K"["C"] by multiplication takes a distinctive form known as a "circulant matrix", in which each row is a shift to the right of the one above (in cyclic order, i.e.

Regular representation

with the right-most element appearing on the left), when referred to the natural basis When the field "K" contains a primitive n-th root of unity, one can diagonalise the representation of "C" by writing down "n" linearly independent simultaneous eigenvectors for all the "n"×"n" circulants. In fact if ζ is any "n"-th root of unity, the element is an eigenvector for the action of "g" by multiplication, with eigenvalue and so also an eigenvector of all powers of "g", and their linear combinations. This is the explicit form in this case of the abstract result that over an

Regular representation

algebraically closed field "K" (such as the complex numbers) the regular representation of "G" is completely reducible, provided that the characteristic of "K" (if it is a prime number "p") doesn't divide the order of "G". That is called "Maschke's theorem". In this case the condition on the characteristic is implied by the existence of a "primitive" "n"-th root of unity, which cannot happen in the case of prime characteristic "p" dividing "n". Circulant determinants were first encountered in nineteenth century mathematics, and the consequence of their diagonalisation drawn. Namely, the determinant of a circulant is the

Regular representation

product of the "n" eigenvalues for the "n" eigenvectors described above. The basic work of Frobenius on group representations started with the motivation of finding analogous factorisations of the group determinants for any finite "G"; that is, the determinants of arbitrary matrices representing elements of "K"["G"] acting by multiplication on the basis elements given by "g" in "G". Unless "G" is abelian, the factorisation must contain non-linear factors corresponding to irreducible representations of "G" of degree > 1. Topological group case. For a topological group "G", the regular representation in the above sense should be replaced by a suitable

Regular representation

space of functions on "G", with "G" acting by translation. See Peter–Weyl theorem for the compact case. If "G" is a Lie group but not compact nor abelian, this is a difficult matter of harmonic analysis. The locally compact abelian case is part of the Pontryagin duality theory. Normal bases in Galois theory. In Galois theory it is shown that for a field "L", and a finite group "G" of automorphisms of "L", the fixed field "K" of "G" has ["L":"K"] = |"G"|. In fact we can say more: "L" viewed as a "K"["G"]-module is the regular representation. This

Regular representation

is the content of the normal basis theorem, a normal basis being an element "x" of "L" such that the "g"("x") for "g" in "G" are a vector space basis for "L" over "K". Such "x" exist, and each one gives a "K"["G"]-isomorphism from "L" to "K"["G"]. From the point of view of algebraic number theory it is of interest to study "normal integral bases", where we try to replace "L" and "K" by the rings of algebraic integers they contain. One can see already in the case of the Gaussian integers that such bases may not exist: "a" +

Regular representation

bi and "a" − "bi" can never form a Z-module basis of Z["i"] because 1 cannot be an integer combination. The reasons are studied in depth in Galois module theory. More general algebras. The regular representation of a group ring is such that the left-hand and right-hand regular representations give isomorphic modules (and we often need not distinguish the cases). Given an algebra over a field "A", it doesn't immediately make sense to ask about the relation between "A" as left-module over itself, and as right-module. In the group case, the mapping on

Regular representation

basis elements "g" of "K"["G"] defined by taking the inverse element gives an isomorphism of "K"["G"] to its "opposite" ring. For "A" general, such a structure is called a Frobenius algebra. As the name implies, these were introduced by Frobenius in the nineteenth century. They have been shown to be related to topological quantum field theory in 1 + 1 dimensions by a particular instance of the cobordism hypothesis. Regular representation In mathematics, and in particular the theory of group representations, the regular representation of a group "G" is the linear representation afforded by the group action of "G" on

Regular representation

Francis Pym Francis Pym Francis Leslie Pym, Baron Pym, (13 February 1922 – 7 March 2008) was a British Conservative politician who served in various Cabinet positions in the 1970s and 1980s, including Foreign, Defence and Northern Ireland Secretary, and Leader of the House of Commons. He was Member of Parliament (MP) for Cambridgeshire (South East Cambridgeshire after 1983) from 1961 to 1987. Pym was made a life peer in 1987. Early life. Pym was born at Penpergwm Lodge, near Abergavenny in Monmouthshire. His father, Leslie Pym, was also an MP, while his grandfather, the Rt Revd Walter Pym, was Bishop of Bombay

Francis Pym

. He was not a direct descendant of the 17th-century parliamentarian John Pym as has been commonly held (see Pym's own published family history), but a collateral descendant. He was educated at Eton, before going on to Magdalene College, Cambridge. For much of the Second World War, Pym served in North Africa and Italy as a captain and regimental adjutant in the 9th Lancers. He was mentioned in despatches twice, awarded the Military Cross, and ended his military service as a major. Pym was a managing director and landowner before he went into politics. Political career. Pym entered politics

Francis Pym

as a member of Herefordshire County Council in 1958. He contested Rhondda West without success in 1959 and entered Parliament in 1961 at a by-election as MP for Cambridgeshire. He held the seat until 1983, and thereafter was MP for South East Cambridgeshire until 1987. He was an opposition whip from 1964 and served under Edward Heath as Government Chief Whip (1970–1973) and Northern Ireland Secretary (1973–1974), and Margaret Thatcher as Defence Secretary (1979–1981), Leader of the House of Commons and Lord President of the Council (1981–1982). He became foreign secretary during the Falklands War in 1982 following Lord

Francis Pym

Carrington's resignation, but was removed by Thatcher the following year after her second election victory. Pym was a leading member of the "wets", Conservative MPs sceptical of Thatcherism. During the 1983 general election campaign he said on the BBC's "Question Time" that "Landslides don't on the whole produce successful governments". This was publicly repudiated by Thatcher and he was sacked after the election. Shortly afterwards, he launched a pressure group called Conservative Centre Forward to argue for more centrist, one-nation policies but with Thatcher at the height of her powers, it was unsuccessful. He stood down

Francis Pym

at the 1987 election and was created a life peer as Baron Pym (of Sandy in the County of Bedfordshire) on 9 October 1987. He was the author of , published in 1984 after he left the government. The book is a guide to the Wets' opposition to Thatcher's leadership style and politics. He was portrayed by Jeremy Child in the 2002 BBC production of Ian Curteis's "The Falklands Play", by Julian Wadham in the 2011 film "The Iron Lady" and by Guy Siner in the fourth series of "The Crown". Personal life. Pym died in Sandy, Bedfordshire, on

Francis Pym

7 March 2008 after a prolonged illness, aged 86. He was survived by his wife, Valerie (1929–2017), whom he married on 25 June 1949, and their four children. Francis Pym Francis Leslie Pym, Baron Pym, (13 February 1922 – 7 March 2008) was a British Conservative politician who served in various Cabinet positions in the 1970s and 1980s, including Foreign, Defence and Northern Ireland Secretary, and Leader of the House of Commons. He was Member of Parliament (MP) for Cambridgeshire (South East Cambridgeshire after 1983) from 1961 to 1987. Pym was made a life peer in 1987. Early life. Pym was

Francis Pym

Phocion Phocion Phocion (; "Phokion"; c. 402 – c. 318 BC; nicknamed The Good ("ὁ χρηστός")) was an Athenian statesman and strategos, and the subject of one of Plutarch's "Parallel Lives". Phocion was a successful politician of Athens. He believed that extreme frugality was the condition for virtue and lived in accord with this; consequently, he was popularly known as "The Good." Further, people thought that Phocion was the most honest member of the Athenian Assembly. However, within this chamber, Phocion's tendency to strong opposition relegated him to a solitary stand against the entire political class. Nonetheless, by both his individual

Phocion

prestige and his military expertise, which was acquired by the side of Chabrias, Phocion was elected strategos numerous times, with a record 45 terms in office. Thus, during most of his 84 years of life, Phocion occupied the most important Athenian offices. In the late 320s, when Macedon gained complete control of Athens (under Antipater), though somewhat compromised, Phocion defended both the urban center and its citizens. He even refused to comply with some dishonorable requests of the enemy. However, his stance put Phocion in opposition to both Polyperchon, the regent of Macedon, and most free Athenians. Polyperchon sent him

Phocion

back to Athens, where he was sentenced to death for treason by the then-restored popular assembly. Early life. Phocion's grandfather was perhaps the trierarch Phocion who was killed at the Battle of Cynossema in 411 BC. During his youth, Phocion sought to study liberal notions. He was both Plato's pupil and Xenocrates' friend. Through such philosophical education, Phocion was of virtuous moral character and he used to give prudent advice. This academic training left its mark upon him, but it was as a soldier rather than as a philosopher that he first came to notice. His austere

Phocion

lifestyle. The Athenians recognized that Phocion was honest and he was respected as such. He had a reserved demeanor; he was never seen either laughing or weeping. Indeed, he appeared quite severe, and was often feared by those meeting him for first time. Phocion believed that the frugality proved his own virtue. He was never seen at the public baths. Both on the Athenian streets and on campaign, he walked around wearing a simple tunic and without shoes. He only made an exception in extreme cold, wearing a cloak, so other soldiers said that Phocion gave a meteorological indication. Throughout

Phocion

his life Phocion lived in a home which was humble, with spare decoration, located at the neighborhood, southward from the Acropolis. His wife baked their everyday bread and cooked their everyday meals herself, and Phocion drew water, pumping it with his own hands. Phocion was first married to a woman whose father was a maker of clay statues. His second wife was famous in Athens for her humility. Once she said that her sole adornment was Phocion's twentieth strategos appointment. Phocion's son was Phocus. During his youth he became licentious and addicted to partying and wine, so Phocion

Phocion

sent him off to Sparta (which was famous for frugal lifestyles) for a period. Early military service to Athens. The young Phocion enrolled with Chabrias' armies, in many campaigns, gaining much experience. Chabrias esteemed him highly because Phocion helped to compensate for his turbulent personality. Reciprocally, Phocion was commended for the chief actions of his campaigns, and thus gained much fame among the Athenians. In 376 BC, Phocion's participation was crucial in the Athenian naval victory of Naxos, where he commanded the leading left wing. Since it was the first clear Athenian victory since the Peloponnesian War, the Athenians

Phocion

greatly honoured its military leaders. The battle took place on the main day of the Eleusinian Mysteries and was remembered for years. After Chabrias died, Phocion took care of his family and particularly of his son, Ctesippus. However, Phocion could barely cope with Ctesippus' rather slow character. At last he exclaimed "O Chabrias, did ever a man show so much gratitude as I do in putting up with your son" Role in the Athenian Assembly. Publicly, Phocion was recognized as the most austere and wisest Athenian politician. However, in the Athenian Assembly, he had an attitude of opposition to most

Phocion

of his peers, and criticism from Phocion was often unpopular within the chamber. Once, an oracle was brought from Delphi. It said that one man would confront the rest of the politicians, whose opposing stand would be homogeneous. Phocion then rose, exclaiming: "I am that person who disagrees." Once, after Phocion was applauded by the chamber he asked his friends: "Have I unwittingly said something vile?" (Οὐ δὴ που κακόν τι λέγων ἐμαυτὸν λέληθα?) Demosthenes called him "the chopper of my speeches." On another occasion, Phocion spoke but was not heeded and not permitted to continue. He said: "You may

Phocion

compel me to act against my wishes, but you shall never force me to speak against my judgment." On the other hand, Phocion never harmed anyone he disliked. Indeed, he was so kind that he helped a political rival if he was in some difficulty. Additionally, Phocion was unhappy that Athenian public functions had become split between two groups. Whereas the politicians dealt eminently with civilian matters, military issues were attended to exclusively by the generals. He campaigned for Athens to regain its old tradition, with politicians who could manage both sets of affairs. Parrying the eloquence of his opponents

Phocion

, Phocion resorted both to wise concepts and pithy sayings, which were famous in antiquity. Yet he avoided demagogic style and his tone was harsh and demanding, with few embellishments. Another distinguishing quality was that Phocion compressed many ideas into short phrases. Before any presentation, he spent much time considering how to shorten it. One of his friends said "You seem to be thinking about something, Phocion", and he replied "Yes, I am considering whether I can shorten the speech I am going to make." Anecdotes. When someone made a joke about his severe visage, and some of the local politicians

Phocion

he was not on good terms with laughed in response, he remarked, "My frown never yet made any of you sad, but these jolly men have given you plenty of sorrow." Demosthenes once said to Phocion that he might be killed some day, if the people became irrational. Phocion responded: "Yes; however, they would kill you if they came to their senses." On an occasion when Phocion was being heavily attacked by the entire assembly, he requested Archibiades, a man who liked imitating the Spartan lifestyle, to support his stand. However, the man took the popular side, declaring against Phocion

Phocion

as well. Phocion then grabbed his Spartan-style beard, saying, "It's time for you to shave." Another assemblyman, Aristogeiton, was famous because he usually called for war. However, when a muster was called he happened to appear wearing bandages around his legs and walking with a cane. Phocion got up and shouted to the enrolling officer: "Put down Aristogeiton too, as lame and unfit for service." Some time afterward, Aristogeiton was jailed and at his request, Phocion visited him often. His friends criticized him for it, but he replied: "Come on! There is no better place to visit Aristogeiton

Phocion

." During a boundary dispute with Thebes, Phocion urged negotiations, while most Athenians called for war. He argued, "You had better carry on the contest with the weapons you use best: your tongues." Polyeuctos, an out-of-shape Athenian politician, once made a speech advocating war with Philip II of Macedon, stopping repeatedly to drink water and catch his breath. During one such pause Phocion remarked, "Here is a fine man to lead us into war. What do you think he'll do when he is carrying his shield and armor to meet the enemy, if giving a speech has nearly

Phocion

killed him with exhaustion?" Record-breaking strategos. Although Phocion never canvassed the Athenians for it, he was appointed strategos a record-breaking 45 times. Sometimes he did not attend the election meetings of the Agora and the people were forced to seek him afterward. However, he accepted the appointment on every occasion. Management of the Second Athenian League. Phocion was sent to the Aegean Sea by Chabrias, to collect the regional tributes for the Second Athenian League. As representatives of Athens were unpopular among their 'subject' allies, Phocion had been issued 20 warships. However, he declined to bring them along

Phocion

, commenting that "if he was being sent to fight the islanders he would need a larger force, but if he was visiting them as allies, one ship was enough." So he departed just with his own trireme. At each city, Phocion negotiated each fee so diplomatically that he returned home with a large allied fleet, which protected their treasury. The allies even organized colourful parades in his honour. Military service to Persia in Cyprus. Between 351–349 BC, Phocion helped the Persian Emperor Artaxerxes III to subdue the Cypriot rebellion. Campaign in Euboea against Macedonia. In 349 BC, Philip II of

Phocion

Macedon invaded Euboea and established many local tyrants. Phocion went there with a small force, expecting to win over the Euboeans by diplomatic means. But Philip had organised a strong bribe network which corrupted the local politicians. Phocion established his camp on a hill outside the city of Tamynae, and ordered his men to ignore those who neglected their duties because of Macedonian bribes. He explained: "They are useless to us and furthermore, they will get in the way of those that are loyal." In 348 BC, with Macedonian support, the Euboean general Callias brought his armies to attack the

Phocion

camp. Phocion decided to offer many religious sacrifices before battle, until the gods were favourable. However such activities demanded much time, and the forces of the Euboean mercenaries attacked the enemy, their general thinking Phocion was a coward and hoping to force his hand. The Athenian cavalry was ill-disciplined, and not wishing to remain idle, raced out to meet the enemy, but with no formation and in scattered groups, so that they were easily beaten and routed. The Euboeans defeated the mercenaries and they began ravaging the Athenian camp. After Phocion could interpret his sacrifices favorably (or alternatively to

Phocion

draw the enemy in), he led his main lines into battle while the enemy where surging up the palisade thinking they had defeated Phocion's forces. This resulted in Phocion cutting down and routing the enemy forces. Just with his best men while the main body of the army rallied some of the previously dispersed troops, Phocion engaged the enemy's chief divisions, in a ferocious battle. Phocion was victorious but then freed the captured enemies, fearing the Athenians might treat them too harshly. Subsequently, Phocion captured the fort of Zaretra, which was at Euboea island's narrowest portion. Then

Phocion

, he returned to Athens. Campaign to repel Philip II from Byzantium. With his armies, Philip II reached the Dardanelles, expecting successively to seize Chersonesus, Perinthus, and Byzantium. The Athenians sent Chares to confront him but the Greek colonies reacted negatively to him, as usual. Consequently, the force could do nothing except roam around the region. The Athenians were so angry that they wanted to cancel the expedition. Phocion interceded, saying: "You shouldn't be angry at our allies. You should blame our generals, because of whom we are feared even by those who need us most." Then, in 339 BC

Phocion

, Phocion was sent to the region. To Phocion's good fortune, it transpired that Leon, a personal friend from the academy and a Byzantine well known for his courage, personally guaranteed the Athenian's good faith. Thus, particularly there, the new expedition was amicably received and, even though Phocion had planned to camp outside the walls, was welcomed into the city, where the Athenian soldiers acted with exemplary discipline and courtesy. The Athenian soldiers also fought bravely, defending the site. Then, Phocion attacked the Macedonians around the region, liberating many cities, which expelled their Macedonian garrisons. Eventually, Macedonia was forced

Phocion

to withdraw from the region (temporarily, as it turned out). However, Phocion was wounded so he returned to Athens. Secretly, the Megarians requested military help from Phocion, who arrived with his army and was warmly received. He erected two long walls, from Megara to the seaport of Nisaea. The Megarians felt so safe that they allied with Athens. Confrontation with Macedonia. Subjection of Athens by Philip II. Regarding Macedonia, Phocion's moderate stand was to avoid a confrontation which might be catastrophic for Athens. Although he had been successful in his campaigns against it, he had come to view Macedon

Phocion

as a rising power, and to doubt the wisdom of an Athenian foreign policy too strongly opposed to it. However, the Athenians preferred the firebrand orators who desired war. Among them were Demosthenes, Lycurgus, and Hypereides. They were particularly emboldened because Athens seemed to have sufficient military power. Philip, on the other hand, preferred not to go to war with Athens; he hoped instead the Athenians would consent to put their strong navy at his disposal for use against Persia. Phocion was touring the Aegean colonies when Athens commanded its generals to confront Philip. He came back and addressed the

Phocion

assembly, opposing this course of action. A lawyer asked him if he was defying the people's will, and Phocion responded: "Yes, even though I know that if there is war I will be your boss, and if there is peace you will be mine." Unfortunately, Athens could not be persuaded to reverse its decision. When the strategy to be used against Philip came under discussion, the question arose as to whether it would be better to engage in battle close to home or at a distance. Phocion advised, "Let us not ask where we should fight, but how we

Phocion

may win. That will be the way to keep war at a distance. If we are beaten in a distant battle, it will soon be at our doors." In the event, Athens and her allies suffered a crushing defeat at Chaeronea, in 338 BC. Then the Athenian aristocracy supported the nomination of Phocion for strategos, and the Areopagus passed it. Phocion delayed the inevitable garrisoning of defeated Athens as long as possible. Initially, he favored negotiating directly with Philip, who he thought could be expected to be lenient, and opposed having Athens join a congress of Greek states and be

Phocion

forced to accept Macedonia's common terms of peace, which were not yet known. Demades, however, offered a contrary motion, and the Athenians approved it. They soon regretted their decision, since at the congress Philip obliged the Athenians to provide him with both ships and cavalry. When the Athenians expressed remorse, Phocion said: "I was opposed to the motion, fearing this. Now the deed is done, and we must make the best of it. We shouldn't be without hope, though. Our ancestors suffered similar episodes of subjection, but they carried on, and because of that both Athens and Greece

Phocion

as a whole survived." Later, after Philip died (336 BC), Phocion banned all celebratory sacrifice, saying: "The army which defeated us at Chaeronea has lost just one man." Relations with Alexander. When the new Macedonian king, Alexander, was about to attack Thebes, Demosthenes protested impudently. Phocion interceded, with some lines of Homer: "Foolhardy man, why provoke one whose temper is already savage? Why provoke this Macedonian who is full of limitless ambition? When there is a holocaust on our borders, do you wish to spread the flames to our city as well, by provoking him further? My whole object in

Phocion

taking up the burdens of this office is to prevent this, and I shall not allow my fellow citizens to destroy themselves, even if they wish it." Thebes was destroyed and Alexander demanded the handover of the most anti-Macedonian Athenians, among whom was Demosthenes. The assembly called upon Phocion repeatedly by name until he stood on his feet. Beside him, Phocion called Nicocles, his best friend, saying: "We have been brought to a pass. I would deliver Nicocles if they might request it. We must reduce the wrath of our conqueror, rather than oppose him." Nonetheless, the Athenian Assembly

Phocion

passed a decree denying the demand. Then, when Alexander refused to see other Athenian ambassadors, Phocion was sent. As Phocion had been regarded as a respectable person by Philip, his son received him attentively, listening to his proposals. Alexander was persuaded to relent in his demand for the opposing Athenian politicians (even though they were enemies of Phocion as well). Indeed, Alexander asked for advice and Phocion said: "If Macedonia wishes peace, it should abandon the war. If Macedonia desires glory, it should turn against Persia, instead of oppressing Greece." Eventually, Phocion was favored by the king, even over many

Phocion

Macedonians. After Alexander defeated the Persian Emperor Darius III, Phocion was among the few individuals who were saluted with the word "greetings" by the king in his correspondence. During this period, Phocion maintained his policy of peace. Alexander made a request for a number of Athenian warships which Phocion supported, saying: "You should either possess superior strength or side with those that do." Athenian rebellion and the Lamian War against Antipater. In 323 BC, rumors of Alexander's death reached Athens. Phocion feared any hasty reaction and he commented: "If he is dead now, he will be dead tomorrow as

Phocion

well. We must be cautious before celebrating." The Macedonian leaders began fighting for the crown; Antipater was the candidate with the best prospects. The Athenians hastened to rebel against Macedonia. Leosthenes, the rebel leader, shared the charge of strategos with Phocion. This was the beginning of the Lamian War although, as always, Phocion opposed it. Leosthenes inquired about which historical achievements Phocion had attained. Phocion responded: "Do you think it is nothing then that our citizens are all buried at home in their own tombs?" Other assemblymen asked him whether the military preparations were enough or not. Phocion said: "They

Phocion

will be sufficient for a sprint. However, if it is to be a long race, then I fear for Athens for she has no reserves of either men, supplies or warships." Phocion was ordered to lead the military actions against Boeotia. Cleverly, he called on all Athenians under the age of 60 years to enroll. The elderly protested but Phocion responded: "This is fair! Although I am 80 years old, I will lead the attack." This calmed the people down. On the other front, Antipater retreated and he was surrounded by the Greeks, around Lamia. The Athenians were exultant. Phocion

Phocion

said: "I would have wished being the general who achieved this victory. Nonetheless, still I would have counseled as before." As more good news arrived, Phocion said: "I am wondering when the good news will end." Leosthenes soon died in fighting Macedonian forces making a sally out of besieged Lamia. A new strategos, Antiphilus, was appointed, to counterbalance Phocion. In 322 BC, Phocion hurriedly led a force of Athenians against Micion, who had disembarked at Rhamnus with an army composed of Macedonians and mercenaries. So many individuals came to him with military advice that he exclaimed, "Heracles, how many generals

Phocion

we have, and how few soldiers!" Then he attacked the enemy and utterly routed them, killing Micion. Simultaneously, the Greeks defeated the Macedonians, at Thessaly. However, Craterus brought a large army over from Asia, and the Greeks were defeated at Crannon, also in 322 BC. Antipater soon approached Athens. Demades, who was another peace advocate, was the only other Athenian leader who didn't flee. He proposed that an embassy should negotiate peace. Phocion commented: "If I had been listened to before, the Athenians wouldn't need to be discussing such things." At Thebes, both met Antipater, whose invasion of

Phocion

Attica was expected imminently. Phocion was well received. When Phocion asked Antipater to cease his advance and listen to peace proposals, Craterus protested that it was unfair that the army should sit idle in allied lands, damaging their economies, while the enemy lands could be so easily ravaged. Antipater's lone demand was the discretional surrendering of Athens. In a second encounter, at which Antipater scorned the presence of Xenocrates, Phocion heard the new Macedonian terms of peace: Phocion argued against the garrisoning unsuccessfully. However, Phocion knew its Macedonian commander, Menyllus, personally. Soon, Antipater proved that he was one of

Phocion

the worst Macedonian tyrants in history. 12,000 Athenians were disfranchised and many people were forced to migrate to Thrace. Phocion helped by securing some exiles citizenship in the Peloponnesus area. Phocion became the virtual ruler of Athens and he strove to keep the peace. By his influence, only just individuals were appointed magistrates, and people who were too rebellious weren't allowed to hold public office. However, Phocion refused when Antipater requested him to do dishonorable things, commenting: "I can't be both his friend and his flatterer." Additionally, he protected the refugee Harpalus. The aftermath of these events was

Phocion

that Phocion became quite unpopular. He was accused of delivering Athens to Antipater. The Athenians were particularly angry about the fate of Demosthenes, who had been banished, dying soon after. Phocion had been supported by him early in his political career, even in some capital trials. Thus, it seemed like a personal betrayal. Crisis of Polyperchon. In 319 BC, before his death, Antipater chose that, instead of his own son, Cassander, General Polyperchon would be the next Macedonian ruler. Soon, Cassander began conspiring against Polyperchon. Thus, Cassander disposed that, at Munychia, Nicanor replaced Menyllus, with the order of controlling Attica

Phocion

. In Athens, Phocion was accused of helping such concealments of Cassander and, by deliberately delaying military action against Nicanor, made it possible for Nicanor to take the Piraeus, but he slighted such rumors. Indeed, Phocion met Nicanor, requesting a mild treatment for the Athenians. Also, Phocion convinced Nicanor to host the local games. The Macedonian spent lavishly on the event. Athenians were divided between two parties. Phocion belonged to the oligarchic party of the rich minority, which was on Cassander's side. The majority of the citizens however supported Polyperchon, because he promised to restore democracy, allow Athenian exiles (60

Phocion

% of all Athenian citizens before the Lamian War) to return, and remove the occupying Macedonian garrison. Still as strategos, Phocion supported Nicanor openly. He spurned an insistent rumor that Nicanor would attempt invading Athens. At Piraeus, Phocion was holding a conference with Nicanor when Athenian soldiers attempted to jail the Macedonian general. Phocion helped his escape, declaring: "I don't believe that he would harm Athens although, still, I would defend him if he may wrong us." Subsequently, the Athenian Assembly commanded that Phocion should attack Nicanor, at Munychia. Initially, Phocion refused. Then, effectively, Nicanor used the troops of the

Phocion

Macedonian garrison to seize Piraeus, with Phocion's compliance. When Phocion decided to attack them, the Athenian soldiers had already rebelled against his command as strategos. In 318 BC, Polyperchon decided to realign Athenian politics in his own interests. Favoring the popular party, he restored all liberties. His son, Alexander, arrived in Athens with a Macedonian army, while Athenian exiles (more than half of the entire citizen body) returned home, expecting revenge against the politicians who had betrayed the democracy. Polyperchon expected that Phocion would be forced to leave the urban center. Moreover, the Macedonians would seize complete control of

Phocion

Athens. Phocion was immediately deposed as strategos by an informal assembly. Death sentence by the Athenian Assembly. The Athenian orator Agnonides accused Phocion of treachery, for he had refused, and then delayed, to attack Nicanor. Phocion decided to meet Polyperchon personally. Phocion gathered an entourage, composed of politicians who were well regarded by the Macedonian ruler. However, their voyage was delayed by the illness of one member. During that interval, Agnonides proposed another embassy to accuse Phocion formally before the regent, and the Athenian Assembly passed the motion. Both delegations arrived simultaneously, before the Macedonian throne, at Phocis. Although the

Phocion

regent arrested and tortured one politician of Phocion's cortege, he expected both groups to be heard out. As many people attempted to speak simultaneously, Agnonides proposed that they all be put into a single cage and taken back to Athens to decide the issue there. Polyperchon smiled at that. When Phocion started speaking, the ruler began interrupting him so annoyingly that Phocion struck the floor with his staff and refused to utter another word. Then, Polyperchon ordered the detention of Phocion and his associates; while those closest to him were also seized, most of his embassy escaped from the

Phocion

court. By a written bidding, Polyperchon announced that the treacherous prisoners would be judged by the now free people of Athens. Phocion was brought back home where he was carted straight to the place of judgment. There, he waited while a massive assembly gathered. The Athenian archons conducted the proceedings. Any Athenian could participate in it, including slaves, foreigners, and those formerly disfranchised. The letter from Polyperchon was read while the entire multitude cried out against the oligarchs, who were the enemies of freedom. Phocion demanded: "Do you wish to condemn us justly? Then, you should listen to our defense

Phocion

." Phocion insisted: "I admit that I have wronged and deserve condemnation for my political actions. However, these other individuals don't." Some people responded that they should be condemned for being his friends. Then Phocion gave up. Subsequently, Agnonides read the condemning motion. In unison, the whole crowd rose up from their seats. Thus, Phocion and ten acquaintances were sentenced to die by drinking hemlock. Execution. They were conducted to a prison, and were harassed along the way. Someone spat on Phocion's face and he said to the archons: "You should force these people to behave." When Phocion and

Phocion

his friends had drunk the hemlock provided, not enough poison remain to execute Phocion. The executioner refused to prepare more unless he was paid 12 drachmas. Phocion remarked, "In Athens, it is hard for a man even to die without paying for it." A friend paid the executioner the extra sum on his behalf; Phocion drank his poison and died. It was May 19, 318 BC. This coincided with the traditional Athenian parade of Zeus. It was decreed that the corpse could not be buried in Attica; neither could anyone cremate it. A hired man brought it across the Megarian

Phocion

frontier. There the body was burned. Phocion's wife set up an empty tomb, brought Phocion's bones and heart home by night, and buried them there. Soon afterward, Cassander gained control of the city and placed Phocion's oligarchic party in power. The new rulers properly reburied Phocion's remains at public expense and erected a bronze statue of Phocion. The oligarchs then executed Agnonides; Phocion's son Phocus then tracked down and killed two other anti-oligarchic accusers who had fled the city. Phocion "The Good". Phocion's recognized probity bestowed on him the cognomen "The Good". Phocion

Phocion

could have been extremely wealthy, either by his offices or by the high commissions which were managed by him. Instead, he was incorruptible and led an extremely frugal lifestyle. This was despite the fact that the entire Athenian political class was quite corrupt in that epoch. Philip II offered much money to him and the Macedonian heralds mentioned the future needs of his sons. Phocion responded, "If my sons are like me, my farm, which has enabled my present eminence, will suffice for them. If, instead, they become spoiled by luxury, I will not be the individual who will be

Phocion

guilty for that." Alexander sent a delegation to Phocion to offer him 100 talents, but Phocion refused, saying: "I am an honorable man. I would not harm either Alexander's reputation or mine." Then, the king further offered him the government and possession of the cities Cius, Mylasa and Elaea. Phocion refused, but did request the release of some men enslaved at Sardis, who were promptly liberated. Soon afterward, Alexander died (323 BC). In 322 BC, Harpalus arrived at Athens from Asia, seeking refuge. He tried to give 700 talents to Phocion, who rejected this offer. Phocion warned that he

Phocion

shouldn't attempt to corrupt Athens or he would be punished. Consequently, the angry Harpalus turned the whole assembly against Phocion with his bribes. However, as Phocion kept helping him (with good will but within ethical limits), Harpalus befriended Phocion's son-in-law, Charicles. Charicles eventually accepted a lavish commission to build a tomb for Harpalus' mistress, and was investigated for corruption. Phocion refused to help him at the trial, saying: "I chose you to be my son-in-law only for honorable purposes." Phocion also refused presents from Menyllus, saying: "You are not a better man than Alexander

Phocion

, so there is no reason to accept your gifts." With his bribes, Menyllus then became a friend of Phocus. An Appraisal. Phocion was courageous, mild-mannered, and incorruptible. At the same time, Phocion is disliked by some liberal classical historians, such George Grote, for his perceived betrayal of the ideal of pan-Hellenism and Athenian independence, and indifference to the sufferings of the majority of his countrymen who were banished from their native city:It was precisely during the fifty years of Phokion's political and military influence, that the Greeks were degraded from a state of freedom, and Athens

Phocion

from ascendency as well as freedom, into absolute servitude. Insofar as this great public misfortune can be imputed to any one man, to no one was it more ascribable than to Phokion... Had he lent his influence to... direct the armed efforts,of his countrymen, the kings of Macedon might have been kept within their own limits, and the future history of Greece might have been altogether different... he did gratuitously all that Philip desired — by nullifying and sneering down the efforts of Demosthenes... The intense and unanimous wrath of the people against him... was directed... against his public policy

Phocion

. It was the last protest of extinct Grecian freedom, speaking as it were from the tomb in a voice of thunder. Phocion Phocion (; "Phokion"; c. 402 – c. 318 BC; nicknamed The Good ("ὁ χρηστός")) was an Athenian statesman and strategos, and the subject of one of Plutarch's "Parallel Lives". Phocion was a successful politician of Athens. He believed that extreme frugality was the condition for virtue and lived in accord with this; consequently, he was popularly known as "The Good." Further, people thought that Phocion was the most honest member of the Athenian Assembly. However, within this chamber, Phocion

Phocion

Bill Cash Bill Cash Sir William Nigel Paul Cash (born 10 May 1940) is a British Conservative politician who has served as a Member of Parliament (MP) since 1984. He was first elected for Stafford and then for Stone in Staffordshire in 1997. Cash is a prominent Eurosceptic. After his tenth election victory in the 2019 general election, aged 79, Cash became the oldest sitting member of the House of Commons. Cash was the founder of the Maastricht Referendum Campaign in the early 1990s, and is now the elected Chair of the House of Commons' European Scrutiny Committee. He has also served

Bill Cash

as a vice-president of the Eurosceptic pressure group Conservatives for Britain, and to this day is one of the strongest critics of the European Union from the Conservative Party. He was appointed a Knight Bachelor in the 2014 Birthday Honours for political services. Education. Cash was born in Finsbury, London, to a political family, which included seven Liberal Members of Parliament, including John Bright. He grew up in Sheffield and was educated at Stonyhurst College in Lancashire before attending Lincoln College, Oxford, where he took an MA in History. He qualified as a solicitor in 1967, and since 1979

Bill Cash

has practised as a solicitor on his own account (i.e. he is neither employed by a law firm nor is he a member of a partnership). Family. Cash married Bridget Mary (née Lee) at Wardour Castle Chapel in Wiltshire on 16 October 1965, and they have 2 sons and a daughter. His son is the journalist William Cash. Along with his wife, Bill Cash restored the now Grade I Upton Cressett Hall in the 1970s. The Hall was subsequently voted the 'Best Hidden Gem' heritage destination in the UK at the 2011 Hudson's Heritage awards. He is a distant

Bill Cash

cousin of country music singer Johnny Cash. Parliament. Cash entered Parliament in 1984, when he was elected as MP for Stafford at a by-election in May following the death of Sir Hugh Fraser. Since the 1997 election he has been MP for Stone, Staffordshire. Stone was a then newly (re-)created constituency, the previous version of which (with slightly different boundaries) had been abolished in 1950. He has been chairman of various parliamentary committees. He was elected unopposed as Chairman of the European Scrutiny Committee on 8 September 2010, and has been a member of the Select Committee on European

Bill Cash

Legislation since 1985. Cash was elected chairman of the Conservative Backbench Committee on European Affairs (1989–91). International affairs. Cash is chairman of a number of All-Party African committees, including those on Kenya and Uganda. He is also chairman of the All-Party Committee on Malaysia. He has also served as chairman on the All-Party Group for the Jubilee 2000 (1997–2000). He is chairman of the All-Party Sanitation and Water Committee (Third World) in which he works closely with Wateraid and Tearfund. He introduced the Gender Equality (International Development) Bill, 2013, which, although only 18th in the Private

Bill Cash

Members Ballot, was enacted in March 2014. Mariella Frostrup wrote in "The Times", "The new law that puts gender equality at the heart of our overseas aid policy will be as historic as the Slave Trade Act." Justine Greening, Secretary of State for International Development, wrote in "The Telegraph" blog "Yet for assiduously steering his Gender Equality in International Development Bill through Parliament over recent months, Bill Cash deserves the recognition of women everywhere. … It's also a proud legacy for a Parliamentary champion of women's rights [..] Bill Cash." The day after the Act came into force, the Prime

Bill Cash

Minister, David Cameron, told Cash in the House of Commons, "I am sure the whole House will want to join me in commending my hon. Friend on his Bill, and on his legislative achievement to get that important measure on the statute book." Euroscepticism and the Maastricht Rebellion. Cash is known as a strong Eurosceptic. He has been described by Kenneth Clarke as the most "Eurosceptic" Member of Parliament. In the book by historian Robert Blake titled "The Conservative Party: from Peel to Major", Cash is described as the leader of the Eurosceptics during the Maastricht Rebellion and as being

Bill Cash

indefatigable... a constitutional lawyer of great expertise. The 'Maastricht Rebellion' took place in the early 1990s, and reached its height in 1993. MPs belonging to the governing Conservative Party refused to support the government of John Major in the votes in the House of Commons on the issue of the implementation of the Maastricht Treaty (Treaty on European Union) in British law. It was a major event of John Major's troubled second term as Prime Minister (1992–1997). Major's party had a small majority, thus giving the relatively small number of rebels great influence: for example, there were 22

Bill Cash

rebels on the second reading of the European Communities (Amendment) Bill in May 1992, and the government's majority at the time was only 18. The rebellion (as Major later complained in his memoirs) had the support of the former Prime Minister Margaret Thatcher and Lord Tebbit. Thatcher declared in a speech in the House of Lords that she "could never have signed that Treaty" and that it was "a recipe for national suicide". In 1993, Cash founded and remains chairman of the eurosceptic European Foundation which was created during the Maastricht Rebellion, the funding for which he organised. During

Bill Cash

1994–1995 Cash was a member of the Tindemans group. He was secretary of the European Reform Forum, and has been vice-president of the Conservative Small Business Bureau. After fellow Maastricht rebel Iain Duncan Smith became leader of the Conservatives, Cash was appointed to the post of shadow Attorney General in 2001, and in 2003 he was Shadow Secretary of State for Constitutional Affairs, but he returned to the backbenches later that year after Duncan Smith was ousted as party leader. In April 2019, Cash was in favour of a "No-deal" option as a negotiating position for Britain leaving

Bill Cash

the European Union. Writing. In November 2011, Cash published a biography of John Bright, whom he described as "one of the greatest parliamentarians of all time", to coincide with the 200th anniversary of Bright's birth. The biography was received with critical acclaim: reviewer Andrew Roberts notes that Bright's legacy "was largely forgotten until this first-class, encapsulating biography". Amanda Foreman states that "Bill Cash not only breathes new life into Bright but delivers an entirely fresh view of both the man himself and his stance as the professional scourge of the upper classes... Bright's character receives[s its

Bill Cash

] full due in Cash's nuanced portrait". In addition to his historical writing, Cash has also published a number of books, pamphlets and essays on Britain's relationship with the European Union, and the Eurosceptic movement. These include: "It's the EU, Stupid" (2011), "The Challenge for the Conservative Party: The future for Britain and Europe" (2004), "Associated, Not Absorbed: The Associated European Area: a constructive alternative to a single European state" (2000), "Visions of Europe" (Duckworth, 1993) and "Against a Federal Europe: The Battle for Britain" (Duckworth, 1991). Expenses claims. On 28 May 2009, in the swirl of stories

Bill Cash

surrounding the 2009 Parliamentary Expenses scandal, it was reported that Cash had claimed £15,000 which he paid his daughter, Laetitia Cash, a prospective Conservative candidate, as rent for a Notting Hill flat, when he had a mortgaged flat of his own a few miles away, which his son Sam Cash was staying in rent-free. "It was only for a year, she was getting married, she wasn't there. My other flat wasn't round the corner, it was in Westminster. It was done through the rules", he said on "Newsnight". The following day Cash announced that he had

Bill Cash

agreed to pay the money back. Cash rejected calls for his resignation and said he was hopeful of getting a fair hearing. David Cameron was said to have ordered Cash to co-operate or risk having the Conservative whip withdrawn. Cash was cleared on appeal in February 2010 by former High Court judge and President of the Court of Appeal, the Rt Hon Sir Paul Kennedy. Cash faced a no-confidence vote by secret ballot by his constituency party on 2 July 2009. He was, however, re-selected with the support over 98% of the vote. Cash also received a

Bill Cash

personal letter of support from Conservative leader Cameron before the meeting thanking Cash for "the tireless contribution you make to the work of Parliament. You have a long record of serving your constituents with commitment and integrity." Kennedy, in his letter to Cash regarding his appeal, wrote: "In my judgment there are special reasons why it would not be fair and equitable to require repayment of any money. They are that in 2004–05 you paid rent for accommodation. Such rent was recoverable under the Rules as they existed at the time unless there was some evidence of impropriety. There is

Bill Cash

no such evidence in your case." Registered interests. As a solicitor for William Cash & Co, Upton Cresset, near Bridgnorth in Shropshire, Cash received payment of £31,800 on 25 October 2021 for 64 hours work (Registered 11 November 2021). In popular culture. Cash was portrayed by actor Richard Durden in the 2019 HBO and Channel 4 produced drama entitled "". Bill Cash Sir William Nigel Paul Cash (born 10 May 1940) is a British Conservative politician who has served as a Member of Parliament (MP) since 1984. He was first elected for Stafford and then for Stone in Staffordshire in 1997

Bill Cash

Question answering Question answering Question answering (QA) is a computer science discipline within the fields of information retrieval and natural language processing (NLP), which is concerned with building systems that automatically answer questions posed by humans in a natural language. Overview. A question answering implementation, usually a computer program, may construct its answers by querying a structured database of knowledge or information, usually a knowledge base. More commonly, question answering systems can pull answers from an unstructured collection of natural language documents. Some examples of natural language document collections used for question answering systems include: Question answering research attempts to deal with

Question answering

a wide range of question types including: fact, list, definition, "How", "Why", hypothetical, semantically constrained, and cross-lingual questions. History. Two early question answering systems were BASEBALL and LUNAR. BASEBALL answered questions about Major League Baseball league over a period of one year. LUNAR, in turn, answered questions about the geological analysis of rocks returned by the Apollo moon missions. Both question answering systems were very effective in their chosen domains. In fact, LUNAR was demonstrated at a lunar science convention in 1971 and it was able to answer 90% of the questions in its domain posed by people untrained

Question answering

on the system. Further restricted-domain question answering systems were developed in the following years. The common feature of all these systems is that they had a core database or knowledge system that was hand-written by experts of the chosen domain. The language abilities of BASEBALL and LUNAR used techniques similar to ELIZA and DOCTOR, the first chatterbot programs. SHRDLU was a highly successful question-answering program developed by Terry Winograd in the late 1960s and early 1970s. It simulated the operation of a robot in a toy world (the "blocks world"), and it offered the possibility of asking

Question answering

the robot questions about the state of the world. Again, the strength of this system was the choice of a very specific domain and a very simple world with rules of physics that were easy to encode in a computer program. In the 1970s, knowledge bases were developed that targeted narrower domains of knowledge. The question answering systems developed to interface with these expert systems produced more repeatable and valid responses to questions within an area of knowledge. These expert systems closely resembled modern question answering systems except in their internal architecture. Expert systems rely heavily on expert-constructed and

Question answering

organized knowledge bases, whereas many modern question answering systems rely on statistical processing of a large, unstructured, natural language text corpus. The 1970s and 1980s saw the development of comprehensive theories in computational linguistics, which led to the development of ambitious projects in text comprehension and question answering. One example of such a system was the Unix Consultant (UC), developed by Robert Wilensky at U.C. Berkeley in the late 1980s. The system answered questions pertaining to the Unix operating system. It had a comprehensive hand-crafted knowledge base of its domain, and it aimed at phrasing the answer to accommodate

Question answering

various types of users. Another project was LILOG, a text-understanding system that operated on the domain of tourism information in a German city. The systems developed in the UC and LILOG projects never went past the stage of simple demonstrations, but they helped the development of theories on computational linguistics and reasoning. Specialized natural language question answering systems have been developed, such as EAGLi for health and life scientists. Architecture. As of 2001, question answering systems typically included a "question classifier" module that determines the type of question and the type of answer. Question answering methods. Question answering is

Question answering

very dependent on a good search corpus—for without documents containing the answer, there is little any question answering system can do. It thus makes sense that larger collection sizes generally lend well to better question answering performance, unless the question domain is orthogonal to the collection. The notion of data redundancy in massive collections, such as the web, means that nuggets of information are likely to be phrased in many different ways in differing contexts and documents, leading to two benefits: Some question answering systems rely heavily on automated reasoning. Open domain question answering. In information retrieval, an open

Question answering

domain question answering system aims at returning an answer in response to the user's question. The returned answer is in the form of short texts rather than a list of relevant documents. The system uses a combination of techniques from computational linguistics, information retrieval and knowledge representation for finding answers. The system takes a natural language question as an input rather than a set of keywords, for example, "When is the national day of China?" The sentence is then transformed into a query through its logical form. Having the input in the form of a natural language question makes

Question answering

the system more user-friendly, but harder to implement, as there are various question types and the system will have to identify the correct one in order to give a sensible answer. Assigning a question type to the question is a crucial task, the entire answer extraction process relies on finding the correct question type and hence the correct answer type. Keyword extraction is the first step for identifying the input question type. In some cases, there are clear words that indicate the question type directly, i.e., "Who", "Where" or "How many", these words tell the system that the answers

Question answering

should be of type "Person", "Location", or "Number", respectively. In the example above, the word "When" indicates that the answer should be of type "Date". POS (part-of-speech) tagging and syntactic parsing techniques can also be used to determine the answer type. In this case, the subject is "Chinese National Day", the predicate is "is" and the adverbial modifier is "when", therefore the answer type is "Date". Unfortunately, some interrogative words like "Which", "What" or "How" do not give clear answer types. Each of these words can represent more than one type. In situations like this, other words in

Question answering

the question need to be considered. First thing to do is to find the words that can indicate the meaning of the question. A lexical dictionary such as WordNet can then be used for understanding the context. Once the question type has been identified, an information retrieval system is used to find a set of documents containing the correct keywords. A tagger and NP/Verb Group chunker can be used to verify whether the correct entities and relations are mentioned in the found documents. For questions such as "Who" or "Where", a named-entity recogniser is used to find relevant

Question answering

Person and "Location" names from the retrieved documents. Only the relevant paragraphs are selected for ranking. A vector space model can be used as a strategy for classifying the candidate answers. Check if the answer is of the correct type as determined in the question type analysis stage. An inference technique can also be used to validate the candidate answers. A score is then given to each of these candidates according to the number of question words it contains and how close these words are to the candidate, the more and the closer the better. The answer is then translated

Question answering

into a compact and meaningful representation by parsing. In the previous example, the expected output answer is "1st Oct." Mathematical question answering. An open source math-aware question answering system based on Ask Platypus and Wikidata was published in 2018. The system takes an English or Hindi natural language question as input and returns a mathematical formula retrieved from Wikidata as succinct answer. The resulting formula is translated into a computable form, allowing the user to insert values for the variables. Names and values of variables and common constants are retrieved from Wikidata if available. It is claimed that the

Question answering