However, poor marketing and failure to repeat the technological advances of the first systems meant that the Amiga quickly lost its market share to competing platforms, such as the fourth generation game consoles, Apple Macintosh and IBM PC compatibles.

However, rapid technological advances and worldwide participation accelerated the completion date to 2003 ( making it a 13 year project ).

However, beyond this theoretical significance, efficient and scalable algorithms for SAT that were developed over the last decade have contributed to dramatic advances in our ability to automatically solve problem instances involving tens of thousands of variables and millions of constraints.

However, restrictive Spanish trade laws made it difficult for Cubans to keep up with the 17th and 18th century advances in processing sugar cane pioneered in British Barbados and French Saint Domingue ( Haiti ).

However, none of these parameters differ significantly from early writings of Howard and Balfour, suggesting that in fact modern composting has not made significant advances over the traditional methods that take a few months to work.

However, further experience might result in a change or even retraction of the specification before it advances.

However, Riefenstahl maintained that Goebbels was upset that she had rejected his advances and was jealous of her influence on Hitler, seeing her as an internal threat ; therefore, his diaries could not be trusted.

However, advances in VLSI have made such devices possible.

However, these wars did not result in any significant advances southwards.

However the reduction in cultivation may not have actual effects on cocaine production, as recent advances in coca growing and more efficient processing methods allow for greater cocaine yield.

However, new advances in technology have allowed for more sophisticated communication for speakers and public orators.

However, at Khe Sanh a mere 14 years later, advances in air power allowed the United States to withstand the siege.

However, he also advances a " Remedial Rights Only Theory " where a group has " a general right to secede if and only if it has suffered certain injustices, for which secession is the appropriate remedy of last resort.

However, there were elements within the RAF and the government that sought to adopt the new nuclear weaponry and advances in aviation technology to introduce more potent and effective means of conducting warfare.

However, Apple's designs included quite a few concepts that were not part of ( or were non-trivial advances to ) the prototype developed at PARC.

However the chemical convenience of having oxygen as the primary atomic weight standard became ever more evident with advances in analytical chemistry and the need for ever more accurate atomic weight determinations.

However, recent advances in mass spectrometry ( i. e. multiple-collector inductively coupled plasma mass spectrometry ) now enable the measurement of isotope ratios in heavier stable elements, such as iron, copper, zinc, molybdenum, etc.

However, Louisa May Alcott mentioned to Ralph Waldo Emerson that Thoreau's facial hair " will most assuredly deflect amorous advances and preserve the man's virtue in perpetuity.

However, with modern testing advances to more safely rule out infectious disease and by ensuring that there are no incentives offered to participate, some have argued that prisoners can now voluntarily consent to organ donation just as they can now consent to medical procedures in general.

However, there is also the risk that advances can lead to make biological weapons.

However, it is also possible that such advances could be exploited for hostile purposes, something evidenced in a small number of incidents of bioterrorism, but more particularly by the series of large-scale offensive biological warfare programmes carried out by major states in the last century.

However the advances of Padua in the 13th century finally brought the commune into conflict with Can Grande della Scala, lord of Verona.

However, the mode of technological development in the field of autonomy has mostly followed a bottom-up approach, such as hierarchical control systems, and recent advances have been largely driven by the practitioners in the field of control science, not computer science.

However, the channel did air Olivia Newton-John's 1981 video for the hit song " Physical ", which lavished camera time on male models working out in string bikinis who spurn her advances, ultimately pairing off to walk to the men's locker rooms holding hands, though the network ended the clip before the overt homosexual " reveal " ending in some airings.

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

However, in a classical context the semantics of the sequent can also ( by propositional tautology ) be expressed either as

However additional problems raise from propositional extensionality and proof irrelevance.

However, the algebraic properties of this structure are somewhat different from those of classical propositional logic in that the principle of distributivity fails.

However, by at least one line of argument, truth-conditional semantics seems to be able to capture the meaning of belief-sentences like " Frank believes that the Red Sox will win the next game " by appealing to propositional attitudes.

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, 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, 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, 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.