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| {{other uses|Negation (disambiguation)|NOT gate}}
| | The ac1st16.dll error is annoying plus pretty common with all kinds of Windows computers. Not just does it make the computer run slower, yet it may equally prevent we from using a variety of programs, including AutoCAD. To fix this problem, we should utilize a simple system to cure all the potential issues which cause it. Here's what you have to do...<br><br>Document files enable the consumer to input data, images, tables plus alternative ingredients to enhance the presentation. The only issue with this structure compared to alternative file types including .pdf for example is its ability to be readily editable. This means which anyone viewing the file may change it by accident. Also, this file formatting will be opened by other programs but it refuses to guarantee which what we see in the Microsoft Word application might still become the same when we see it utilizing another system. However, it is nonetheless preferred by many computer consumers for its ease of use plus attributes.<br><br>Of course, the next logical step is to get these false entries cleaned out. Fortunately, this really is not a difficult task. It is the 2nd thing we should do when you noticed your computer has lost speed. The first will be to make sure there are no viruses or severe spyware present.<br><br>The way to fix this issue is to first reinstall the program(s) causing the mistakes. There are a lot of different programs that employ this file, yet one might have placed their own faulty version of the file onto the system. By reinstalling any programs that are causing the error, you will not just enable the PC to run the system correctly, but a fresh file can be placed onto a system - leaving a computer running because smoothly as possible again. If you try this, and find it refuses to work, then we should look to update the program & any software we have on your PC. This will likely update the Msvcr71.dll file, allowing the computer to read it correctly again.<br><br>Use a [http://bestregistrycleanerfix.com/system-mechanic iolo system mechanic]. This can search the Windows registry for 3 kinds of keys that can definitely hurt PC performance. These are: duplicate, lost, plus corrupted.<br><br>Although I constantly utilize the latest adaptation of browser, occasionally different extensions plus plugins become the cause of errors with my browser and the system. The same is the story with my browser that was crashing frequently potentially due to the Flash player error.<br><br>Why this is important, is considering most 'dumb' registry products really delete these files without even knowing. They simply browse from a registry plus try plus find the most issues possible. They then delete any files they see fit, plus considering they are 'dumb', they don't really care. This means which when they delete a few of these vital system files, they are actually going to cause a LOT more damage than wise.<br><br>So in summary, when comparing registry cleaning, make sure the 1 we choose offers you the following.A backup plus restore facility, quickly surgery, automatic deletion facility, start-up administration, an convenient technique of contact plus a money back guarantee. |
| {{no footnotes|date=March 2013}}
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| {{Use dmy dates|date=September 2010}}
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| In [[logic]], '''negation''', also called '''logical complement''', is an [[operation (mathematics)|operation]] that essentially takes a [[proposition]] ''p'' to another proposition "not ''p''", written ''¬p'', which is interpreted intuitively as being true when ''p'' is false and false when ''p'' is true. Negation is thus a unary (single-argument) [[logical connective]]. It may be applied as an operation on [[proposition]]s, [[truth value]]s, or [[interpretation (logic)|semantic values]] more generally. In [[classical logic]], negation is normally identified with the [[truth function]] that takes ''truth'' to ''falsity'' and vice versa. In [[intuitionistic logic]], according to the [[Brouwer–Heyting–Kolmogorov interpretation]], the negation of a proposition ''p'' is the proposition whose proofs are the refutations of ''p''.
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| ==Definition==
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| No agreement exists as to the possibility of defining negation, as to its logical status, function, and meaning, as to its field of applicability..., and as to the interpretation of the negative judgment, (F.H. Heinemann 1944).<ref name=Horn>{{cite book |last=Horn |first=Laurence R |date=2001 |title=A NATURAL HISTORY OF NEGATION |url=http://emilkirkegaard.dk/en/wp-content/uploads/A-natural-history-of-negation-Laurence-R.-Horn.pdf |location=Stanford University |chapter=Chapter 1 |page=1 |publisher=CLSI Publications |isbn=1-57586-336-7 |accessdate=29 Dec 2013 }}</ref>
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| ''Classical negation'' is an [[logical operation|operation]] on one [[logical value]], typically the value of a [[proposition]], that produces a value of ''true'' when its operand is false and a value of ''false'' when its operand is true. So, if statement ''A'' is true, then ''¬A'' (pronounced "not A") would therefore be false; and conversely, if ''¬A'' is true, then ''A'' would be false.
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| The [[truth table]] of ''¬p'' is as follows: | |
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| {| class="wikitable"
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| |+ Truth table of ¬p
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| ! style="width:35px;background:#aaaaaa;" | p
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| ! style="width:35px" | ¬p
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| |-
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| | True || False
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| |-
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| | False || True
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| |}
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| Classical negation can be defined in terms of other logical operations. For example, ¬''p'' can be defined as ''p'' → ''F'', where "→" is [[logical consequence]] and ''F'' is absolute falsehood. Conversely, one can define ''F'' as ''p'' & ¬''p'' for any proposition ''p'', where "&" is [[logical conjunction]]. The idea here is that any [[contradiction]] is false. While these ideas work in both classical and intuitionistic logic, they do not work in [[Brazilian logic]], where contradictions are not necessarily false. But in classical logic, we get a further identity: ''p'' → ''q'' can be defined as ¬''p'' ∨ ''q'', where "∨" is [[logical disjunction]]: "not ''p'', or ''q''".
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| Algebraically, classical negation corresponds to [[Complement (order theory)|complementation]] in a [[Boolean algebra (structure)|Boolean algebra]], and intuitionistic negation to pseudocomplementation in a [[Heyting algebra]]. These algebras provide a [[algebraic semantics (mathematical logic)|semantics]] for classical and intuitionistic logic respectively.
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| ==Notation==
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| The negation of a proposition ''p'' is notated in different ways in various contexts of discussion and fields of application. Among these variants are the following:
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| {| class="wikitable"
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| |- style="background:paleturquoise"
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| ! style="text-align:center" | Notation
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| ! Vocalization
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| |-
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| | style="text-align:center" | ¬''p''
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| | not ''p''
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| |-
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| | style="text-align:center" | −''p''
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| | not ''p''
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| |-
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| | style="text-align:center" | ~''p''
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| | not ''p''
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| |-
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| | style="text-align:center" | ''Np''
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| | en ''p''
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| |-
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| | style="text-align:center" | <math>p'\!</math>
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| | ''p'' prime,<br/> ''p'' complement
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| |-
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| | style="text-align:center" | <math>\bar{p}</math>
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| | ''p'' bar,<br/> bar ''p''
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| |-
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| | style="text-align:center" | <math>!p\!</math>
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| | bang ''p''<br/>not ''p''
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| |-
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| |}
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| In [[Set_theory#Basic_concepts|Set Theory]] \ is also used to indicate 'not member of': U \ A is the set of all members of U that are not members of A.
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| No matter how it is notated or [[List of logic symbols|symbolized]], the negation ¬''p'' / −''p'' can be read as "it is not the case that ''p''", "not that ''p''", or usually more simply (though not grammatically) as "not ''p''".
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| ==Properties==
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| ===Double negation===
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| Within a system of [[classical logic]], double negation, that is, the negation of the negation of a proposition ''p'', is [[logically equivalent]] to ''p''. Expressed in symbolic terms, ¬¬''p'' ⇔ ''p''. In [[intuitionistic logic]], a proposition implies its double negation but not conversely. This marks one important difference between classical and intuitionistic negation. Algebraically, classical negation is called an [[involution (mathematics)|involution]] of period two.
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| However, in [[intuitionistic logic]] we do have the equivalence of ¬¬¬''p'' and ¬''p''. Moreover, in the propositional case, a sentence is classically provable if its double negation is intuitionistically provable. This result is known as [[Glivenko's theorem]].
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| ===Distributivity===
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| [[De Morgan's laws]] provide a way of [[distributivity|distributing]] negation over [[logical disjunction|disjunction]] and [[logical conjunction|conjunction]] :
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| :<math>\neg(a \vee b) \equiv (\neg a \wedge \neg b)</math>, and
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| :<math>\neg(a \wedge b) \equiv (\neg a \vee \neg b)</math>.
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| ===Linearity===
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| In [[Boolean algebra (logic)|Boolean algebra]], a linear function is one such that:
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| If there exists a<sub>0</sub>, a<sub>1</sub>, ..., a<sub>n</sub> <math>\in</math> {0,1} such that
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| f(b<sub>1</sub>, ..., b<sub>n</sub>) = a<sub>0</sub> ⊕ (a<sub>1</sub> <math>\land</math> b<sub>1</sub>) ⊕ ... ⊕ (a<sub>n</sub> <math>\land</math> b<sub>n</sub>), for all b<sub>1</sub>, ..., b<sub>n</sub> <math>\in</math> {0,1}.
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| Another way to express this is that each variable always makes a difference in the [[truth-value]] of the operation or it never makes a difference. Negation is a linear logical operator.
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| ===Self dual===
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| In [[Boolean algebra (logic)|Boolean algebra]] a self dual function is one such that:
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| f(a<sub>1</sub>, ..., a<sub>n</sub>) = ~f(~a<sub>1</sub>, ..., ~a<sub>n</sub>) for all a<sub>1</sub>, ..., a<sub>n</sub> <math>\in</math> {0,1}. Negation is a self dual logical operator.
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| ==Rules of inference==
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| There are a number of equivalent ways to formulate rules for negation. One usual way to formulate classical negation in a [[natural deduction]] setting is to take as primitive rules of inference ''negation introduction'' (from a derivation of ''p'' to both ''q'' and ¬''q'', infer ¬''p''; this rule also being called ''[[reductio ad absurdum]]''), ''negation elimination'' (from ''p'' and ¬''p'' infer q; this rule also being called ''ex falso quodlibet''), and ''double negation elimination'' (from ¬¬''p'' infer ''p''). One obtains the rules for intuitionistic negation the same way but by excluding double negation elimination. | |
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| Negation introduction states that if an absurdity can be drawn as conclusion from ''p'' then ''p'' must not be the case (i.e. ''p'' is false (classically) or refutable (intuitionistically) or etc.). Negation elimination states that anything follows from an absurdity. Sometimes negation elimination is formulated using a primitive absurdity sign ⊥. In this case the rule says that from ''p'' and ¬''p'' follows an absurdity. Together with double negation elimination one may infer our originally formulated rule, namely that anything follows from an absurdity.
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| Typically the intuitionistic negation ¬''p'' of ''p'' is defined as ''p''→⊥. Then negation introduction and elimination are just special cases of implication introduction ([[conditional proof]]) and elimination ([[modus ponens]]). In this case one must also add as a primitive rule ''ex falso quodlibet''.
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| ==Programming==
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| As in mathematics, negation is used in [[computer science]] to construct logical statements.
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| <source lang="cpp"> | |
| if (!(r == t))
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| {
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| /*...statements executed when r does NOT equal t...*/
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| }
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| </source>
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| The "<code>!</code>" signifies logical NOT in [[B (programming language)|B]], [[C Programming Language|C]], and languages with a C-inspired syntax such as [[C++]], [[Java (programming language)|Java]], [[JavaScript]], [[Perl]], and [[PHP]]. "<code>NOT</code>" is the operator used in [[ALGOL 60]], [[BASIC programming language|BASIC]], and languages with an ALGOL- or BASIC-inspired syntax such as [[Pascal programming language|Pascal]], [[Ada programming language|Ada]], [[Eiffel (programming language)|Eiffel]] and [[Seed7]]. Some languages (C++, Perl, etc.) provide more than one operator for negation. A few languages like [[PL/I]] and [[Ratfor]] use <code>¬</code> for negation. Some modern computers and [[operating systems]] will display <code>¬</code> as <code>!</code> on files encoded in [[ASCII]]. Most modern languages allow the above statement to be shortened from <code>if (!(r == t))</code> to <code>if (r != t)</code>, which allows sometimes, when the compiler/interpreter is not able to optimize it, faster programs.
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| In computer science there is also ''bitwise negation''. This takes the value given and switches all the [[binary numeral system|binary]] 1s to 0s and 0s to 1s. See [[bitwise operation]]. This is often used to create [[signed number representations|ones' complement]] or "<code>~</code>" in C or C++ and [[two's complement]] (just simplified to "<code>-</code>" or the negative sign since this is equivalent to taking the arithmetic negative value of the number) as it basically creates the opposite (negative value equivalent) or mathematical complement of the value (where both values are added together they create a whole).
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| To get the absolute (positive equivalent) value of a given integer the following would work as the "<code>-</code>" changes it from negative to positive (it is negative because "<code>x < 0</code>" yields true)
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| <source lang="cpp">
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| unsigned int abs(int x)
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| {
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| if (x < 0)
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| return -x;
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| else
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| return x;
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| }
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| </source>
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| To demonstrate logical negation:
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| <source lang="cpp">
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| unsigned int abs(int x)
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| {
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| if (!(x < 0))
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| return x;
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| else
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| return -x;
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| }
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| </source>
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| Inverting the condition and reversing the outcomes produces code that is logically equivalent to the original code, i.e. will have identical results for any input (note that depending on the compiler used, the actual instructions performed by the computer may differ).
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| This convention occasionally surfaces in written speech, as computer-related [[slang]] for ''not''. The phrase <code>!voting</code>, for example, means "not voting".
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| ==Kripke semantics==
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| In [[Kripke semantics]] where the semantic values of formulae are sets of [[possible world]]s, negation can be taken to mean [[set-theoretic complement]]ation.{{citation needed|date=August 2012}} (See also [[possible world semantics]].)
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| ==See also==
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| * [[Logical conjunction]]
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| * [[Logical disjunction]]
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| * [[NOT gate]]
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| * [[Bitwise operation#NOT|Bitwise NOT]]
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| * [[Ampheck]]
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| * [[Apophasis]]
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| * [[Cyclic negation]]
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| * [[Double negative elimination]]
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| * [[Grammatical polarity]]
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| * [[Negation (linguistics)]]
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| * [[Negation as failure]]
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| * [[Square of opposition]]
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| * [[Binary opposition]]
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| ==References==
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| {{reflist}}
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| == Further reading ==
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| * [[Dov Gabbay|Gabbay, Dov]], and Wansing, Heinrich, eds., 1999. ''What is Negation?'', [[Kluwer]].
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| * [[Laurence R. Horn|Horn, L.]], 2001. ''A Natural History of Negation'', [[University of Chicago Press]].
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| * [[G. H. von Wright]], 1953–59, "On the Logic of Negation", ''Commentationes Physico-Mathematicae 22''.
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| * Wansing, Heinrich, 2001, "Negation", in Goble, Lou, ed., ''The Blackwell Guide to Philosophical Logic'', [[Wiley-Blackwell|Blackwell]].
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| * Marco Tettamanti, Rosa Manenti, Pasquale A. Della Rosa, Andrea Falini, Daniela Perani, Stefano F. Cappa and Andrea Moro (2008). "Negation in the brain: Modulating action representation", NeuroImage Volume 43, Issue 2, 1 November 2008, pages 358–367, http://dx.doi.org/10.1016/j.neuroimage.2008.08.004/
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| ==External links==
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| * {{springer|title=Negation|id=p/n066170}}
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| * [http://mathworld.wolfram.com/NOT.html NOT], on [[MathWorld]]
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| {{Logical connectives}}
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| {{logic}}
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| [[Category:Grammar]]
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| [[Category:Semantics]]
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| [[Category:Logical connectives]]
| |
The ac1st16.dll error is annoying plus pretty common with all kinds of Windows computers. Not just does it make the computer run slower, yet it may equally prevent we from using a variety of programs, including AutoCAD. To fix this problem, we should utilize a simple system to cure all the potential issues which cause it. Here's what you have to do...
Document files enable the consumer to input data, images, tables plus alternative ingredients to enhance the presentation. The only issue with this structure compared to alternative file types including .pdf for example is its ability to be readily editable. This means which anyone viewing the file may change it by accident. Also, this file formatting will be opened by other programs but it refuses to guarantee which what we see in the Microsoft Word application might still become the same when we see it utilizing another system. However, it is nonetheless preferred by many computer consumers for its ease of use plus attributes.
Of course, the next logical step is to get these false entries cleaned out. Fortunately, this really is not a difficult task. It is the 2nd thing we should do when you noticed your computer has lost speed. The first will be to make sure there are no viruses or severe spyware present.
The way to fix this issue is to first reinstall the program(s) causing the mistakes. There are a lot of different programs that employ this file, yet one might have placed their own faulty version of the file onto the system. By reinstalling any programs that are causing the error, you will not just enable the PC to run the system correctly, but a fresh file can be placed onto a system - leaving a computer running because smoothly as possible again. If you try this, and find it refuses to work, then we should look to update the program & any software we have on your PC. This will likely update the Msvcr71.dll file, allowing the computer to read it correctly again.
Use a iolo system mechanic. This can search the Windows registry for 3 kinds of keys that can definitely hurt PC performance. These are: duplicate, lost, plus corrupted.
Although I constantly utilize the latest adaptation of browser, occasionally different extensions plus plugins become the cause of errors with my browser and the system. The same is the story with my browser that was crashing frequently potentially due to the Flash player error.
Why this is important, is considering most 'dumb' registry products really delete these files without even knowing. They simply browse from a registry plus try plus find the most issues possible. They then delete any files they see fit, plus considering they are 'dumb', they don't really care. This means which when they delete a few of these vital system files, they are actually going to cause a LOT more damage than wise.
So in summary, when comparing registry cleaning, make sure the 1 we choose offers you the following.A backup plus restore facility, quickly surgery, automatic deletion facility, start-up administration, an convenient technique of contact plus a money back guarantee.