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	Negation - Wikipedia, the free encyclopedia
		It is an operation needed chiefly in logic, mathematics, and grammar.
		In logic, logical negation is a unary logical operator that reverses the truth value of its operand.
		Algebraically, logical negation corresponds to the complement in a Boolean algebra (for classical logic) or a Heyting algebra (for intuitionistic logic).
	www.wikipedia.org /wiki/Negation (1159 words)

	Negation -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		Negation, in its most basic sense, changes the (Click link for more info and facts about truth value) truth value of a statement to its opposite.
		It is an operation needed chiefly in (The branch of philosophy that analyzes inference) logic, (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, and (Studies of the formation of basic linguistic units) grammar.
		Algebraically, logical negation corresponds to the complement in a (A system of symbolic logic devised by George Boole; used in computers) Boolean algebra (for classical logic) or a (Click link for more info and facts about Heyting algebra) Heyting algebra (for intuitionistic logic).
	www.absoluteastronomy.com /encyclopedia/n/ne/negation.htm (895 words)

	NEGATION FACTS AND INFORMATION
		In classical_logic, double negation means affirmation; i.e., the statements ''p'' and ~(~''p'') are logically equivalent.
		Algebraically, logical negation corresponds to the ''complement'' in a Boolean_algebra (for classical logic) or a Heyting_algebra (for intuitionistic logic).
		In computer_science, as in mathematics negation, is used to prove the logic of a statement.
	www.palfacts.com /negation (1057 words)

	Logical Negation Philosophy - (Site not responding. Last check: 2007-10-22)
		Logical negation is bi-polar: either a statement is true, or...
		The logical negation of the proposition p, is NOT...
		The semantical analysis of logical negation discloses the roots of the ominous...
	philosophy.fmqg.com /index.php?k=logical-negation-philosophy (902 words)

	Science Fair Projects - Multi-valued logic
		In classical logic, this property is "truth": In a valid argument, the truth of the derived proposition is guaranteed because the application of valid steps preserves the property.
		Fuzzy logics were introduced by Lotfi Zadeh as a formalization of vagueness; i.e., the phenomenon that a predicate may apply to an object not absolutely, but to a certain degree, and that there may be borderline cases.
		Gödel in 1932 showed that intuitionistic logic is not a finitely-many valued logic, and defined a system of Gödel logics intermediate between classical and intuitionistic logic; such logics are known as intermediate logics.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Multi-valued_logic (778 words)

	Negation article - Negation truth value logic mathematics grammar Logic mathematics Grammar - What-Means.com (Site not responding. Last check: 2007-10-22)
		For example, ~p can be defined as p → F, where → is material implication and F is absolute falsehood.
		But in classical logic, we get a further identity: p → q can be defined as ~p ∨ q, where ∨ is logical disjunction.
		Nouns as well as verbs can be grammatically negated, by the use of a negative adjective (There is no walrus.
	www.what-means.com /encyclopedia/Not (520 words)

	The Meanings of Logical Constants
		The meanings of logical constants are determined by the role these constants play in reasoning, whereas the meanings of non-logical predicates are not to the same extent determined by the role such predicates play in reasoning.
		I still think the meanings of logical constants arise from their roles in reasoning, but these roles are not determined by relevant logical implications.
		P logically excludes N(P) N(P) logically excludes P. These rules express the truth conditions for negative propositions in exactly the way in which the rules for disjunction in a multiple conclusion logic express the truth conditions of disjunctive propositions.
	www.nyu.edu /gsas/dept/philo/courses/concepts/meaning.html (3173 words)

	6 EXPRESSIONS (Site not responding. Last check: 2007-10-22)
		A logical constant expression is a logical expression in which each primary is a logical constant, the symbolic name of a logical constant, a relational expression in which each primary is a constant expression, or a logical constant expression enclosed in parentheses.
		However, execution of a function reference in the expression e of a logical IF statement (11.5) is permitted to affect entities in the statement st that is executed when the value of the expression e is true.
		A constant expression is an arithmetic constant expression (6.1.3), a character constant expression (6.2.3), or a logical constant expression (6.4.4).
	www.fortran.com /F77_std/rjcnf-6.html (3597 words)

	Lojban Reference Grammar: Chapter 15
		Logical negation is bi-polar: either a statement is true, or it is false.
		This negation uses the same “ke” and “ke'e” delimiters (the “ke'e” is always elidable at the end of a selbri) that are used in tanru.
		Negations made with “na'e” or “na'eke” also include within their scope any sumti attached to the brivla or tanru with “be” or “bei”.
	xahlee.org /lojban/hrefgram/chapter15.html (7551 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		For this reason, we believe that logical negation is a key feature for a reasoning system that is to handle a knowledge base of any significant size.
		Such inference is sound, when it succeeds for ground X, but it is not logically complete in the general case, for unbound X. This is demonstrated by Prolog's not returning a binding for X in such cases.
		One of the techniques which PTTP uses to achieve its level of generality is to employ negation, not as an operator, but in the form of individually negated predicates, i.e., for each predicate p(X), the negation of the predicate is expressed as a predicate, not_p(X).
	www.cs.nmsu.edu /~tson/ASP2001/XSBneg.doc (2347 words)

	logical negation symbol - a Whatis.com definition
		The logical negation symbol is used in Boolean algebra to indicate that the truth value of the statement that follows is reversed.
		The simplest use of a negation symbol is with a single sentence.
		The negation symbol is often found within, or preceding, complex logical statements.
	whatis.techtarget.com /gDefinition/0,294236,sid44_gci843775,00.html (217 words)

	Logic Programming Course -- Negation
		Negation in logic is a standard unary operation that evaluates to true when its argument is false and to false otherwise.
		Although at first glance this interpretation of the semantics of this predicate might appear similar to negation in logic, in actual fact it implements a different form of negation known as negation as failure.
		Hence, in logic programming unlike in first order logic, the double negation of a predicate is not equivalent that predicate.
	www.cs.sfu.ca /CC/SW/Prolog/Notes/negation.html (467 words)

	IEEE 754R committee minutes from May 23, 2002
		There may appear to be two ways to write the logical negation of a predicate, one using NOT explicitly and the other reversing the relational operator.
		For example, the logical negation of (X = Y) may be written (NOT X = Y) or (X ?<> Y); in this case both expressions are functionally equivalent to (X != Y).
		If it is important to have the complete set of predicates, quiet and signaling, it is possible to implement them using a small subset of the predicates plus a standard logical negation which does not alter the signal behavior of the predicate to be negated.
	grouper.ieee.org /groups/754/meeting-minutes/02-05-23.html (3729 words)

	Logical Instructions in Assembly Language
		Logical instructions typically work on a bit by bit basis, although some processors use the entire contents of the operands as whole flags (zero or not zero input, zero or negative one output).
		Typical logical operations include logical negation or logical complement (NOT), logical and (AND), logical inclusive or (OR or IOR), and logical exclusive or (XOR or EOR).
		Logical tests are a comparison of a value to a bit string (or operand treated as a bit string) of all zeros.
	www.osdata.com /topic/language/asm/logicop.htm (765 words)

	COMPUTER SCIENCE TECHNICAL REPORT ABSTRACTS (Site not responding. Last check: 2007-10-22)
		We address the issue of endowing a logical framework with a logically justified notion of negation.
		Since negation-as-failure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgements, we adapt the idea of elimination of negation from Horn logic to a fragment of higher-order hereditary Harrop formulae.
		As this is in general not possible, we restrict ourselves to a fragment in which clause complementation is viable and that has proven to be expressive enough for the practice of logical frameworks.
	reports-archive.adm.cs.cmu.edu /anon/2000/abstracts/00-175.html (233 words)

	Elimination of Negation in a Logical Framework - Momigliano (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Abstract: We address the issue of endowing a logical framework with a logically justified notion of negation.
		Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae cannot directly express negative information, although negation is a useful specification tool.
		Since negation-as-failure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgments, we adapt the idea of elimination of negation from Horn logic to a fragment...
	citeseer.ist.psu.edu /315125.html (556 words)

	Not Operator
		Performs logical negation on a Boolean expression, or bitwise negation on a numeric expression.
		This example uses the Not operator to perform logical negation on a Boolean expression.
		This example uses the Not operator to perform logical negation of the individual bits of two numeric expressions.
	www.nedcomp.nl /support/origdocs/dotnetsdk/vblr7net/vaoprnot.htm?ntp=1 (213 words)

	Negation : Logical not (Site not responding. Last check: 2007-10-22)
		For instance, if p denotes the statement "today is Saturday", then its negation ~p is the statement "today isn't Saturday".
		Nevertheless, ~~~p and ~p are logically equivalent even intuitionistically.
		What educated man.html">man it is quite uncertain whether he will accomplish an ordinary task, make sure, on almost every day, of a decent amount of produced same degree and continuance of strain will produce is not a priori thread of uniform quality: but a very clever man, by very.
	www.termsdefined.net /lo/logical-not.html (379 words)

	Negation - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-22)
		A Natural History of Negation (Center for the Study of Language and Information - Lecture Notes)
		The Expression of the Inexpressible in Eugenio Montale's Poetry: Metaphor, Negation, and Silence.(Book Review) : An article from: The Modern Language Review
		Negation: A Notion in Focus (Perspectives in Analytical Philosophy, Bd 7)
	encyclopedia.worldsearch.com /negation.htm (602 words)

	[No title]
		According to the logic we have constructed, the sentence Paul sang and danced is true if Paul sang on Tuesday and danced on Wednesday, but this interpretation doesn’t correspond to my intuition about the meaning of the sentence.
		Propositional logic predicts that these sentences can be conjoined in either order, but English insists on an iconic relation between the order of events and their conjunction.
		Propositional negation is commonly translated into ordinary English by the circumlocution it is not the case that.
	www.ku.edu /~pyersqr/Ling331/Kearns2.htm (3432 words)

	MathViews - Language Structure
		The logical and relational operators yield a 0 if the specified relation is false and a 1 if the relation is true.
		is a matrix, then the logical negation operates on each element individually, following the rule stated above.
		The logical negation operator does not support complex numbers and complex matrices.
	www.mathwizards.com /techinfo/man/mathv04.htm (3433 words)

	CSL 2000: Abstract for Paper 78 (Site not responding. Last check: 2007-10-22)
		Logical frameworks with a logic programming interpretation as hereditary Harrop formulae cannot express directly negative information, although negation is a useful specification tool.
		Since negation-as-failure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgments, we adapt the idea of elimination of negation introduced by Sato & Tamaki for Horn logic to a fragment of higher-order HHF.
		This entails finding a middle ground between the Closed World Assumption required by negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.
	www.tcs.informatik.uni-muenchen.de /csl2000/Abstracts/78.html (121 words)

	C Programming: Precendence Examples
		And I thought that the Logical Not was only once step higher than the logical and, why is the logical not at a higher precedence than Multiplication???
		(j andand k) // logical and is higher precedent than logical or.
		(j = j + 1) // unary preincrement is higher precentent that logical or.
	www.experts-exchange.com /Programming/Programming_Languages/C/Q_21335749.html (549 words)

	RE: [nn] logical negation in rules? (Site not responding. Last check: 2007-10-22)
		Maybe in reply to: Skip Montanaro: "[nn] logical negation in rules?"
		Reply: Skip Montanaro: "RE: [nn] logical negation in rules?"
		ScreenOS 5.x has the negate option in the policy/rule statement.
	www.qorbit.net /nn/Nov-2003/1386.html (196 words)

	Elimination of Negation in a Logical Framework - Momigliano (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [12] cannot express directly negative information, although negation is a useful speci cation tool.
		Since negationas -failure does not t well in a logical framework, especially one endowed with hypothetical and parametric judgments, we adapt the idea of elimination of negation introduced in [17] for Horn logic to a fragment of higher-order HHF.
		51 A framework for dening logics (context) - Harper, Honsell et al.
	citeseer.ist.psu.edu /306713.html (575 words)

	R-functions
		Expressed another way, for every formal logical sentence (i.e., for every Boolean function), one may construct a corresponding R-function using R-conjunction, R-disjunction, and R-negation, whose sign is determined by the truth table of the logical sentence.
		The logical disjunction \/ and conjunction /\ operations can respectively be accomplished in the usual case by performing intersection and union operations.
		Depending on the particular form of the R-conjunction, R-disjunction, and R-negation chosen to construct the corresponding R-function (i.e., depending on the “family” from which the R-functions are chosen), a rich variety of differential properties may be obtained.
	sal-cnc.me.wisc.edu /Research/meshless/R-functions/R-functions.html (472 words)

	Logical Symbols
		Although traditional categorical logic can be used to represent and assess many of our most common patterns of reasoning, modern logicians have developed much more comprehensive and powerful systems for expressing rational thought.
		We'll begin our study of symbolic logic with the propositional calculus, a formal system that effectively captures the ways in which individual statements can be combined with each other in interesting ways.
		The five logical operators are all truth-functional connectives; the truth or falsity of each compound statement formed by using them is wholly determined by the truth-value of the component statements and the meaning of the connective.
	www.philosophypages.com /lg/e10a.htm (999 words)

	[nn] logical negation in rules? (Site not responding. Last check: 2007-10-22)
		Next in thread: David Klein: "RE: [nn] logical negation in rules?"
		Maybe reply: David Klein: "RE: [nn] logical negation in rules?"
		Is there a way to logically negate an element of a rule as there is in
	www.qorbit.net /nn/Nov-2003/1385.html (167 words)

	Awareness, Negation and Logical Omniscience (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Abstract: General Epistemic Logics su#er from the problem of logical omniscience, which is that an agent's knowledge and beliefs are closed under implication.
		Based on the notion of awareness, we introduce two kinds of negations: general negation and strong negation.
		23 On epistemic logic and logical omniscience (context) - Vardi - 1986
	citeseer.lcs.mit.edu /589540.html (405 words)

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