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	Encyclopedia :: encyclopedia : Universal quantification (Site not responding. Last check: 2007-11-02)
		In predicate logic, universal quantification is an attempt to formalise the notion that something (a logical predicate) is true for everything, or every relevant thing.
		In symbolic logic, the universal quantifier (typically "∀") is the symbol used to denote universal quantification.
		Quantification in general is covered in the article quantification, while this article discusses universal quantification specifically.
	www.hallencyclopedia.com /topic/Universal_quantification.html (556 words)

	Universal quantification
		In predicate logic and technical fields that depend on it, universal quantification is an attempt to formalise the notion of something being true for all things, or all things of a certain type.
		In our example, the universe of discourse was originally the set of natural numbers; later we changed it to the set of even prime numbers.
		It's not necessary for the universe of discourse to be a set in terms of formal set theory, and universal quantification can be used in logical theories that don't make any reference to sets.
	www.ebroadcast.com.au /lookup/encyclopedia/fo/For_all.html (1057 words)

	Universal quantification - Wikipedia, the free encyclopedia
		This is a single statement using universal quantification.
		Generally, then, the negation of a propositional function's universal quantification is an existential quantification of that propositional function's negation; symbolically,
		Universal generalization concludes the propositional function must be universally true if it is true for any arbitrary element of the Universe of Discourse.
	en.wikipedia.org /wiki/Universal_quantification (905 words)

	Universal quantification (Site not responding. Last check: 2007-11-02)
		Category:Logic In predicate logic, universal quantification is an attempt to formalise the notion that something (a logical predicate) is true for everything, or every relevant thing.
		In symbolic logic, we use the universal quantifier "∀" (an upside-down letter "A" in a sans-serif font) to indicate universal quantification.
		These worthy men did not even know that they had despised not infallible, but their opinion of a beginner's work is far more but if they are long unanimous in holding him cheap, he is warned, or he has the makings of a Browning.
	universal-quantification.kiwiki.homeip.net (692 words)

	Quantification Summary
		In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things.
		The two fundamental kinds of quantification in predicate logic are universal quantification and existential quantification.
		The first variable-based treatments of quantification in formal logic did not appear until the 19th century, although term logic treats quantification in a manner that is closer to how quantifiers appear in natural language, and is less suited to formal analysis.
	www.bookrags.com /Quantification (3348 words)

	JOHAN50 (Site not responding. Last check: 2007-11-02)
		In this diagram, A stands for universal quantification ("all"), E for universal negative quantification ("no"), I for existential quantification ("some") and O for negated universal quantification ("not all").
		The negative quantifiers E and O are dispensible due to the universal presence of negation.
		Assuming that merger of negation and universal quantifiers is not a likely source of lexical items corresponding to the O corner of the Square of Opposition, there is still another avenue which we must explore.
	odur.let.rug.nl /~hoeksema/docs/j50.htm (4073 words)

	Tutorial 4 (Site not responding. Last check: 2007-11-02)
		Universal Quantification: P(x) is true for all values of x in the universe of discourse.
		P(x) to denote the universal quantification of P(x).
		Universe of Discourse: The universe of discourse specifies all the possible values of x for a propositional function P(x).
	www.cs.concordia.ca /~dsrg/soen342/tutorial4 (165 words)

	[No title]
		Quantification Quantification converts a propositional function into a proposition by binding a variable to a set of values..
		Defn: The universal quantification of P(x) is the proposition "P(x) is true for all values of x in the universe of discourse." The notation (x P(x) denotes the universal quantification of P(x), and is expressed as for every x, P(x).
		Defn: The existential quantification of P(x) is the proposition "There exists an element in the universe of discourse such that P(x) is true." The notation (x P(x) denotes the existential quantification of P(x), and is expressed as there is an x such that P(x) is true.
	www.cs.pitt.edu /~litman/courses/cs441/ch1-3.doc (753 words)

	JOT: Journal of Object Technology - The Theory of Classification
		-calculus and notions of universal [4, 5] and function-bounded quantification [6, 7].
		Universal quantification was adopted independently by Girard [4] and Reynolds [5] as a way of introducing type parameters, variables which range over types (ie which receive types as their bound value).
		F-bounded quantification was a revolutionary discovery, because it captured exactly the kind of polymorphism present in object-oriented languages, in which methods apply to families of types sharing a minimum common structure.
	www.jot.fm /issues/issue_2003_05/column2 (3108 words)

	Universal Quantification is Strong in Children
		A second problem of this approach is that it assumes that the same semantic universal which holds in adult language (namely that determiners are conservative) is violated in child grammar.
		Another consequence of the proposal by Drozd and van Loosbroek (1999) is that children should accept a sentence like (1) in a context in which one boy is not riding a donkey in the interpretation in (6).
		To satisfy the felicity conditions for (8), there was a Smurf who do not choose an apple or a jewel in the situation; in the situation for (9), there was a character, in addition to the Smurfs, and there were more than apples and bananas for them to choose.
	www.ling.umd.edu /lu/abstracts/Upenn2.html (1092 words)

	Universal Quantification With Skolemization as Evidenced from Chinese and English Reference & Research Book News - ... (Site not responding. Last check: 2007-11-02)
		Universal quantification with skolemization as evidenced in Chinese and English.
		The revised definition of EVERY requires a variable in the scope of the universal quantifier word, she says, because the skolem function facilitates the paired reading by linking the choice of the value for y with the choice of the value for x.
		The study is based on her 1996 doctoral dissertation in linguistics for the University of Pennsylvania.
	www.findarticles.com /p/articles/mi_m0QLQ/is_3_20/ai_n15394847 (157 words)

	Logic terms and concepts : Thomas Alspaugh : UCI
		Free occurrences of the variable in the subformula of the quantification are bound by the quantifier.
		A quantifier is used to make an assertion about the application of a formula to every object in the domain: either that the formula is true for every object in the domain (a universal quantification) or that it is true for some object in the domain (an existential quantification).
		A universal quantification is written as ∀x (F); occasionally this notation is seen ∀x.F, but it is obsolete (see dot).
	www.isr.uci.edu /~alspaugh/logic/logicConcepts.html (4121 words)

	Universal Quantification
		The universal quantifiers over role terms with set constructors, or role names, which are related to other role names via some propositional axioms, must be decomposed into their atomic components.
		Decomposed quantifications over the same roles can be comprised into one single quantification.
		Universal quantification over role fillers interact in a relatively simple way with the arithmetic expressions over role terms.
	www-texdev.ics.mq.edu.au /OHLBACH/mdla/node6.html (162 words)

	CS 540 Lecture Notes: First-Order Logic
		Universal quantification corresponds to conjunction ("and") in that
		Existential quantification corresponds to disjunction ("or") in that
		Remove universal quantification symbols by first moving them all to the left end and making the scope of each the entire sentence, and then just dropping the "prefix" part.
	www.cs.wisc.edu /~dyer/cs540/notes/fopc.html (1984 words)

	CSC 205 Lecture Notes Week 6 and 7
		The universal and existential quantifiers have their standard logical meanings, but will be applied in specific ways, as upcoming examples illustrate.
		Universal and existential quantification are two ways to state mulitple conditions in a single expression.
		The potential problem with unbounded quantification is that the body of the universal quantifier may not have the correct value in an unbounded range, and hence the value of the entire quantifier expression may be false when we expect it to be true.
	www.csc.calpoly.edu /~gfisher/classes/205/lectures/6-7.html (8605 words)

	Chapter Ten
		Arranging affirmative and negative universal propositions and affirmative and negative existential propositions on a square of opposition clarifies their relationships.
		From the substitution instance of a propositional function with respect to the name of any arbitrarily selected individual, one may validly infer the universal quantification of that propositional function.
		From the existential quantification of a propositional function, we may infer the truth of its substitution instance with respect to any individual constant (other than y) that occurs nowhere earlier in the context.
	puffin.creighton.edu /yuan/logic/Outline/LogicCh10.htm (1089 words)

	Euler Diagrams and Quantified Expressions
		One kind of quantification is called universal quantification and the other existential.
		The next figure on the lower left shows the diagram that corresponds to what your text refers to as the "Universal Negative," namely, the statement "No A are B." Again, the quantified statements that correspond to this case are shown at the bottom.
		And, since we are not asked to prove a universal statement, we have replaced the universal quantification with a single constant, K
	www.rci.rutgers.edu /~cfs/305_html/Deduction/EulerDiags.html (942 words)

	Universal Quantification with Skolemization as Evidenced in Chinese and English
		This book makes a contribution to the study of universal quantification, scoping properties of indefinites in Chinese, semantic properties of the Chinese adverb dou and a number of conjunction and additive words, and event semantics.
		It is mainly concerned with the revision of the formal definition of universal quantification and in order to do so, it delves deeply into the semantics of dou and in the structuring of (Davidsonian) events.
		The Mandarin element dou is generally regarded as a universal quantifier, but Shi-Zhe Huang shows that that is only part of the story, since dou may also occur in contexts with no universal quantification.
	www.mellenpress.com /mellenpress.cfm?bookid=6174&pc=9 (778 words)

	Willard Van Orman Quine, Mathematical Logic
		Universal quantification corresponds roughly to ``every,'' and more precisely to the mathematician's ``for all.'' Existential quantification --- ``some,'' ``a,'' ``at least one,'' ``there exists'' --- reduces to a combination of universal quantification and negations.
		An infinity of tautologous statements about quantification are baptised ``the axioms of quantification,'' and the business of proof begins.
		If there is any difference between classes and properties, it is merely this: classes are the same when their members are the same, whereas it is not universally conceded that properties are the same when possessed by the same objects.
	cscs.umich.edu /~crshalizi/reviews/mathematical-logic (1782 words)

	Leivant. Higher Order Logic. (Site not responding. Last check: 2007-11-02)
		For example, consider the set of (codes of) sentences over a language containing 0, successor and finitely many functions which include those used to represent negation, disjunction, equality, universal quantification, and substitution in the coding of the language which are true in the standard model N of the language.
		In order to obtain a single universal quantifier, the type structure must be enriched, as in Girard's system F-omega in which forall [and exists] has the type "delta t.
		In higher order logic, eliminating detours of the form of relational universal generalization followed by a relational universal instantiation by substituting the instantiation throughout the derivation my replace one detour by larger ones.
	www.andrew.cmu.edu /user/cebrown/notes/leivant.html (4896 words)

	Symbolic Logic: Lecture Notes: University of West Georgia - Robert Lane, Ph.D.
		This rule allows you to move from a universal quantification to an instance of that quantification (hence the name “universal instantiation”).
		This implicational rule allows you to move from an existential quantification to an instance of that quantification (hence the name “existential instantiation”).
		The variable in the existential quantification must be replaced with a free variable working as an unknown.
	www.westga.edu /~rlane/symbolic/lecture17_predicatelogicproofs1.html (1240 words)

	Jalal Kawash, Writing Complex SQL Queries that Require Universal Quantifiers
		One major disadvantage of SQL is that the language does not provide a universal quantification construct.
		One major disadvantage of SQL is its lack of a universal quantification construct.
		The use of universal quantifiers to logically understand and express the for all and every phrases is more natural and more intuitive than negating existential quantifiers.
	www.cs.ubc.ca /wccce/program00/kawash/kawash.html (1031 words)

	Concept Formulae with Universal Quantifiers
		Lemma 5.4 The decomposition of the universal quantifications (Def.
		Universal quantification over an empty set is a tautology, therefore
		the universal quantifications (all parts may be empty).
	www-texdev.ics.mq.edu.au /OHLBACH/mdla/node22.html (599 words)

	Abstracts - Veneeta Dayal
		Ever introduces a type of modality that is independent of the verbal system by enforcing universal quantification over epistemic alternatives to the world of evaluation.
		The central thesis advanced here is that FC 'any' is a universal determiner whose domain of quantification is not a set of particular individuals but the set of possible individuals of the relevant kind.
		In the case of modals of necessity, the interaction between the universal force of 'any' and the particular modal base is shown to be crucial.
	www.rci.rutgers.edu /~dayal/abstr1.html (982 words)

	CSC165 2005F — Assignments
		Do not try to do an assignment at the last minute: they require creativity and investigation of different approaches, so the exact amount of time they will take you is difficult to predict.
		The statement for o(f, g) is correct: notice the the universal quantification of c.
		Do something similar here: make sure the universal property appears explicitly, and that we are negating that property to look for a counterexample.
	www.cs.toronto.edu /~gfb/csc165/2005F/assignments.shtml (1134 words)

	Rapid Detection and Quantification of Members of the Archaeal Community by Quantitative PCR Using Fluorogenic Probes -- ... (Site not responding. Last check: 2007-11-02)
		Using the prokaryotic universal and archaeon-specific primer sets and probes, the conditions for fluorogenic PCR were established
		The detection and quantification of different proportions of archaeal rDNA in heterogeneous rDNA samples were examined (Fig.
		universal probe and 54°C for the archaeal probe).
	aem.asm.org /cgi/content/full/66/11/5066 (4457 words)

	Peirce’s Philosophy of Logic
		Interestingly, he tends in this paper to deal with quantification as implicit in assertions involving the signs of inclusion and identity (e.g., 3.66); we shall see this concept (i.e., implicit quantification) emerge again—metamorphosized—a quarter of a century later in his most successful logical systems, the existential graphs.
		The third, second-intentional logic, effectively involves quantification over predicates and relations; this is a branch of logic which Peirce continued to work on and never quite finished with.
		Peirce’s discussions of the gamma graphs also involve quantification over predicates and metatheoretical and other notations; once again, we will be unable to go into the mathematical details of these notations.
	web.clas.ufl.edu /users/jzeman/csphiloflogic.htm (5515 words)

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