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== '''[[Formal fuzzy logic]]''' ==
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'''Fuzzy logic''' is a relatively new chapter of formal logic whose aim is to formalize the reasonings involving predicates that are vague in nature (as an example ''small'', ''near'', ''similar''). An example of such kind of reasoning is
==Footnotes==
 
: ''If a tomato is red, then the tomato is ripe. Since this tomato is very red, this tomato is very ripe.''
 
Further examples of reasonings involving vague predicates are in the item ''[[Paradoxes and fuzzy logic]]'' and in the section ''Fuzzy logic with no truth-functional semantics''. The main tool for fuzzy logic is the notion of a ''[[fuzzy subset]]'' since a vague predicate is interpreted by a fuzzy subset. Notice that in literature the name ''"fuzzy logic"'' also denotes a large series of topics based on an informal usage of the notion of a fuzzy subset and which are usually devoted to applications.
 
As a matter of fact, fuzzy logic is an evolution and an enlargement of [[multi-valued logic]] since all the definitions and results in the literature on multi-valued logic are also considered in fuzzy logic. In particular, as in multi-valued logic, the starting point is a fixed ''valuation structure'', i.e. a bounded [[lattice (order)|lattice]] ''L'' equipped with suitable operations to interpret the logical connectives. The minimum 0 means ''''False'''', the maximum 1 means ''''True'''', the remaining elements are interpreted as intermediate truth values. The following is the main class of valuation structures (see Hájek 1998, Novák et al. 1999 and Gottwald 2005) corresponding to the connectives <math>\wedge</math> and <math>\rightarrow </math>.
 
''[[Formal fuzzy logic|.... (read more)]]''
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Latest revision as of 10:19, 11 September 2020

Napoleon (Napoleon Bonaparte or, after 1804, Napoleon I, Emperor of the French) was a world historic figure and dictator of France from 1799 to 1814. He was the greatest general of his age--perhaps any age, with a sure command of battlefield tactics and campaign strategies, As a civil leader he played a major role in the French Revolution, then ended it when he became dictator in 1799 and Emperor of France in 1804 He modernized the French military, fiscal, political legal and religious systems. He fought an unending series of wars against Britain with a complex, ever-changing coalition of European nations on both sides. Refusing to compromise after his immense defeat in Russia in 1812, he was overwhelmed by a coalition of enemies and abdicated in 1814. In 1815 he returned from exile, took control of France, built a new army, and in 100 days almost succeeded--but was defeated at Waterloo and exiled to a remote island. His image and memory are central to French national identity, but he is despised by the British and Russians and is a controversial figure in Germany and elsewhere in Europe.

The Trail of Napoleon - J.F. Horrabin - Map.jpg

Rise to Power

Once the Revolution had begun, so many of the aristocratic officers turned against the Revolutionary government, or were exiled or executed, that a vacuum of senior leadership resulted. Promotions came very quickly now, and loyalty to the Revolution was as important as technical skill; Napoleon had both. His demerits were overlooked as he was twice reinstated, promoted, and allowed to collect his back pay. Paris knew him as an intellectual soldier deeply involved in politics. His first test of military genius came at Toulon in 1793, where the British had seized this key port. Napoleon, an acting Lieutenant-Colonel, used his artillery to force the British to abandon the city. He was immediately promoted by the Jacobin radicals under Robespierre to brigadier-general, joining the ranks of several brilliant young generals. He played a major role in defending Paris itself from counter-revolutionaries, and became the operational planner for the Army of Italy and planned two successful attacks in April 1794. He married Josephine (Rose de Beauharnais) in 1796, after falling violently in love with the older aristocratic widow.[1]

Footnotes

  1. Englund pp 63-73, 91-2, 97-8