However, many statisticians are persuaded by the work of Bruno de Finetti that only one kind of mathematical uncertainty is needed and thus fuzzy logic is unnecessary.

However, the line between ' recuperation ' and ' détournement ' can become thin ( or at least very fuzzy ) at times, as Naomi Klein points out in her book No Logo.

However, Husig et al., 2005 argue that front-end not need to be fuzzy, but can be handled in a structured manner.

However the construction of such boundary, diachronically, is not always transparent, but rather fuzzy ; and on the other hand it reflects a tension of maintaining the boundary.

However, powerful intermediate empires such as the Parthians and Kushans kept the two Eurasian flanking powers permanently apart and mutual awareness remained low and knowledge fuzzy.

However, usually the computer scientist Lotfi A. Zadeh is credited with inventing the specific idea of a " fuzzy concept " in his seminal 1965 paper on fuzzy sets, because he gave a formal mathematical presentation of the phenomenon.

However, fuzzy concepts may also occur in scientific, journalistic, programming and philosophical activity, when a thinker is in the process of clarifying and defining a newly emerging concept which is based on distinctions which, for one reason or another, cannot ( yet ) be more exactly specified or validated.

However, " The Boy Who Knew Too Much " was one of the few episodes in which technical issues still remained ; for example, Bart and Lisa's image was fuzzy toward the beginning, and the episode featured for the last time " some of the hand drawn dimensions that would be eliminated once the show switched over to digital compositing and desktop cartoon creation ".

However, expressing these properties as axioms requires use of second-order logic.

However Prolog is not particularly user friendly and is an order of logic away from human logic.

However, if one finds one single black swan, deductive logic admits the conclusion that the statement that all swans are white is false.

However, inclinations towards deeming hair texture " adaptively trivial " may root in certain cultural value judgments more than objective logic.

However, the new geopolitical logic of the Cold War made possible that the former enemy Italy, a hinge-country between Western Europe and the Mediterranean, and now a new, fragile democracy threatened by the proximity of the Iron Curtain and the presence of a strong Communist party, was considered by the USA as an important ally for the Free World, and received under the Marshall Plan US $ 1, 204 million from 1947 to 1951.

However, more expressive languages are likely to require more complex logic and algorithms to construct equivalent inferences.

However, even simple systems based on this simple logic can be used to represent data that is well beyond the processing capability of current computer systems: see computability for reasons.

However, the first proposal to use the clausal form of logic for representing computer programs was made by Cordell Green ( 1969 ).

However, later in antiquity, the propositional logic developed by the Stoics was no longer understood.

However, advances in propositional logic were still made after Frege.

However, in the 1930s Gödel's incompleteness theorems convinced many mathematicians that mathematics cannot be reduced to logic alone, and Karl Popper concluded that " most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently.

However, because the intuitionistic notion of truth is more restrictive than that of classical mathematics, the intuitionist must reject some assumptions of classical logic to ensure that everything he proves is in fact intuitionistically true.

However, Principia Mathematica required, in addition to the basic axioms of type theory, three further axioms that seemed to not be true as mere matters of logic, namely the axiom of infinity, the axiom of choice, and the axiom of reducibility.

However, the I / O devices needed more electronic logic to manage their own word count and transfer address registers.

However, the enthymeme based upon logic ( especially, based upon the syllogism ) was viewed as the basis of rhetoric.

However, since the time of Aristotle, logic has also changed, for example, Modal logic has undergone a major development which also modifies rhetoric.

However, in the 19th century, with the development of historical-comparative linguistics, linguists began to realize the sheer diversity of human language, and to question fundamental assumptions about the relationship between language and logic.

However, logic does not deal with truth in the absolute sense, as for instance a metaphysician does.

However, using this 9-valued logic (< tt > U </ tt >,< tt > X </ tt >,< tt > 0 </ tt >,< tt > 1 </ tt >,< tt > Z </ tt >,< tt > W </ tt >,< tt > H </ tt >,< tt > L </ tt >,< tt >-</ tt >) instead of simple bits ( 0, 1 ) offers a very powerful simulation and debugging tool to the designer which currently does not exist in any other HDL.

However, vacuous truth also appears in, for example, intuitionistic logic in the same situations given above.

However, it is well known that sentences of this kind cannot be interpreted in first-order logic, where individual variables stand for individual things.

However, formal logic makes no such guarantee if any premise is false, the conclusion can be either true or false.

However, several important phase transitions, such as the Mott insulator-superfluid transition, are known that do not follow the Ginzburg-Landau paradigm.

However, there is still room within an originalist paradigm for stare decisis ; whenever the plain meaning of the text has alternative constructions, past precedent is generally considered a valid guide, with the qualifier being that it cannot change what the text actually says.

However, Kuhn would not recognise such a paradigm shift.

However, the growing trend ( or paradigm shift ) towards character-centered drama and naturalistic plots and settings has replaced the episodic action-adventure format that was once standard for television science fiction.

However, correspondences between Ockhamist and Nominalist philosophy / theology and literary texts from medieval to postmodern times have been discussed within the scholarly paradigm of literary nominalism.

However, in Ars Magica the " Medieval paradigm "-the collection of folk beliefs and superstitions-is correct ; this means that the beliefs and superstitions of the medieval period are existent reality: lost children are really abducted by Faeries, sickness and crop failure are caused by Demons, Angels help the righteous, and dragons and other mythical creatures exist.

" However she makes the point that " these alternative modes of knowing, which are oriented to the social benefits and sustenance needs are not recognized by the capitalist reductionist paradigm, because it fails to perceive the interconnectedness of nature, or the connection of women's lives, work and knowledge with the creation of wealth.

However, after 1973, the show changed to an entirely-live paradigm.

However, this " bad apple paradigm " is considered by some to be an " easy way out ".

However, Hymes ' ambition in a sense backfired ; the second paradigm in fact marked a further distancing of the subdiscipline from the rest of anthropology.

However, Kuhn would not recognize such a paradigm shift.

However, this change in research style ( and paradigm ) eventually ( after more than a century ) led to a theory of atomic structure that accounts well for the bulk properties of matter ; see, for example, Brady's General Chemistry.

However, many instances exist in which change in a discipline's core model of reality has happened in a more evolutionary manner, with individual scientists exploring the usefulness of alternatives in a way that would not be possible if they were constrained by a paradigm.

However, there have recently been voices claiming that " the bibliographical paradigm " is obsolete, and it is not today common in LIS.

However, the paradigm Theory of constraints was first used by Goldratt.

However, most pre-war theorists can be considered as having shared a very similar paradigm.

However, using the reflection-oriented programming paradigm, the application could be designed and written to utilize reflection in order to invoke methods in classes and without hard-coding method names.

However, recent data has resulted in a paradigm shift.

However, other researchers have contested the claims of the media effects paradigm.

However, the paradigm shift of the gene-centric view of evolution ( popularised by Richard Dawkins in The Selfish Gene ) shortly afterwards overturned this idea: mainstream views in behavioural ecology and sociobiology saw natural selection restored to Darwinian principles in terms of survival value to the individual ( and its kin ).

However, since roughly 1890, new discoveries have caused significant paradigm shifts ; the advent of quantum mechanics ( QM ), and of Einsteinian relativity ( ER ).

However, much of the research into the visuo-spatial memory construct have been conducted in accordance to the paradigm advanced by Baddeley and Hitch.

However, from the 1940s onward a new architectural paradigm, which discarded historical vocabularies and incorporated attitudes learned from Germany and from the studio of Frank Lloyd Wright, stemmed from German émigré Henry Klumb.

However, in contrast to previous approaches, which were often based on tradition or authority, modern medical guidelines are based on an examination of current evidence within the paradigm of evidence-based medicine.