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Topic: Universal quantifier

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	Universal quantification -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		The resulting statement is a universally quantified statement, and we have universally quantified over the predicate.
		In (Any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity) symbolic logic, the universal quantifier (typically "∀") is the symbol used to denote universal quantification.
		In the universal quantification, on the other hand, the natural numbers are mentioned explicitly.
	www.absoluteastronomy.com /encyclopedia/u/un/universal_quantification.htm (749 words)

	Universal quantification - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-08)
		Further information on using domains of discourse with quantified statements can be found in the Quantification article.
		But in particular, note that if you wish to restrict the domain of discourse to consist only of those objects that satisfy a certain predicate, then for universal quantification, you do this with a logical conditional.
		Universal Quantification With Skolemization As Evidenced In Chinese and English
	encyclopedia.worldsearch.com /universal_quantification.htm (558 words)

	Quantification - Wikipedia, the free encyclopedia
		The two fundamental kinds of quantification in predicate logic are universal quantification and existential quantification.
		The traditional symbol for the universal quantifier is "∀", a rotated letter "A", which stands for the word "all".
		Quantifiers have scope and a variable x is free if it is not within the scope of a quantification for that variable.
	en.wikipedia.org /wiki/Quantifier (2083 words)

	plstuff
		Quantifier negation is a necessary process (in many cases) in the construction of formal proofs of validity in predicate logic.
		If a universal statement is given, then it is obvious that every x (or y or z or whatever individual variable is indicated by the universal quantifier) is referred to in the statement.
		Universal generalization cannot be done in a case in which you are dealing with some known individual or even some unknown individual.
	pegasus.cc.ucf.edu /~stanlick/plstuff.htm (2888 words)

	Synopses of Topics - Quantifiers
		Universal quantifiers are those that are used to specify the scope to which a variable is restricted and indicating that the predicate which follows should be considered for variables in that scope.
		This leads us to consider existential quantifiers which are used to indicate that the predicate which follows applies to at least one value of the variable within the indicated scope.
		The existential quantifier is expressed as there exists, for some, for at least one or similar phrases usually combined with such that after the scope of the variable and just before the predicate.
	math.usask.ca /emr/quan.html (652 words)

	QUANTIFIER - Definition
		Universally quantified means "for all values" (written with an inverted A, LaTeX \forall) and existentially quantified means "there exists some value" (written with a reversed E, LaTeX \exists).
		To be unambiguous, the set to which the values of the variable belong should be specified, though this is often omitted when it is clear from the context (the "universe of discourse").
		In logic programming this usually means that it is actually universally quantified.
	www.hyperdictionary.com /dictionary/quantifier (160 words)

	Introduction to Logic Chapter 12 -- True or False (Site not responding. Last check: 2007-10-08)
		In quantifier logic, the lower case letter c (denoting, say, Chris) is an individual variable.
		The universal quantifier maybe dropped from a statement in a proof because of the principle that any substitution instance whatsoever may be validly inferred from a universally quantified proposition.
		The reason we may remove an existential quantifier from a proposition in a proof, then go ahead and generalize over it again (in effect, creating an "all" statement from a "some" statement) is that we chose a previously unused individual constant, which in turn stands for any individual at all.
	cwx.prenhall.com /copi/chapter12/truefalse1/deluxe-content.html (427 words)

	Tuesday, February 15
		S[a/x] n+i+1 (Ax.S) universal quantifier introduction This only works if a is a variable which does not occur outside the block (and so, for example, does not occur in S).
		Q existential quantifier elimination, lines n+i+j This only works if a is a variable which does not occur outside the block (and so, for example, does not occur in Q).
		The logic could be modified so that it would apply to nonempty universes of discourse (systems of logic, called ``free logics'' which apply to possibly empty universes of discourse are studied) but it seems fairly harmless (and is technically convenient) to take Something exists to be a logical truth.
	math.boisestate.edu /~holmes/M387syllabus/node30.html (1432 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		But the singular universal quantifiers still remain their traditional denotation because they are different from takkei in that they are not compatible with a collective reading.
		Though this definition does not work for the singular universal quantifiers, moiN and tak, because their syntactic and semantic behaviors are very different from those of definite plurals, this definition works for the plural universal quantifier takkei, which does share the same behavior with (definite) plurals.
		First, the singular universal quantifiers are not compatible with a collective reading, but the plural universal quantifier is. If both kinds of universal quantifiers denote a set of entities, then it is difficult to explain why one kind allows for a collective interpretation but the other does not.
	www.shakespeare.uk.net /journal/2_1/Wu2_1.doc (15618 words)

	Unit 11 (Site not responding. Last check: 2007-10-08)
		When determining scope, see whether there is a parenthesis between the quantifier and the rest of the sentence.
		All occurrences of the variable being quantified that fall under the scope are BOUND occurrences of that variable.
		All occurrences of variables that do not fall under the scope of their respective quantifier are FREE occurrences of the variable.
	www.pitt.edu /~belnap/phil0500/prob11.htm (197 words)

	1From Semantic Representations (Site not responding. Last check: 2007-10-08)
		We want the evaluation of the quantifiers exists and all to be taken care of by the rough algorithms in (4) and (5), respectively, which ensure that only the individuals satisfying the restriction are considered when evaluating the assertion.
		Thus the existentially quantified semantic representation in example (15.b and c) is transformed into the SELECT subquery in example (15.d) which encodes a set expression corresponding to the lefthand side of (14.b).
		To summarize, the table DUAL is used to encode yes/no-questions, the existential quantifier may be eliminated and the universal quantifier is encoded by means of the MINUS operator.
	www.ida.liu.se /~g-robek/nodalida93/nodalida93/NODA93-12/NODA93-12.html (1762 words)

	Categorical Statements (Site not responding. Last check: 2007-10-08)
		The logical terms 'all' and 'some' are referred to as the "universal quantifier" and the "existential quantifier".
		The universal negative is often expressed in English as "no Ss are Ps", and the existential negative as "not all Ss are Ps".
		For the remainder of the interpretation, use "don't exist" if the quantifier is universal ('all', 'only' or 'no'), "do exist" if it is existential ('not all', 'not only', or 'some').
	www.uncg.edu /phi/catstmts.htm (1248 words)

	Thomas Sturm: Activities: ACA02: talks: Matiyasevich (Site not responding. Last check: 2007-10-08)
		In fact, presented in [Davis53] technique was not a genuine elimination of bounded universal quantifiers, rather it was a method for changing the order of existential and bounded universal quantifiers and of gluing together two consecutive universal quantifiers.
		Since bounded universal quantifiers can be easily simulated by loops in computer programs, these techniques for constructing Diophantine representations can be also viewed as methods for elimination of bounded universal quantifiers (for details see [Matiyasevich93]).
		All known today techniques for elimination of bounded universal quantifiers lead to at least exponential growth of complexity of (minimal) witnesses but no intrinsic reasons for such growth are known.
	www.fmi.uni-passau.de /~sturm/activities/ACA02/talks/Matiyasevich (1305 words)

	Peter Suber, "Predicate Logic Terms and Symbols"
		The universal quantifier lacks existential import; it is non-committal.
		More precisely, a variable is only bound by a quantifier on the same letter; hence "x" is bound in "(x)Mx" but not in "(y)Mx", even though it is inside the scope of the quantifier in both cases.
		For example, in "(x)Ax x)Bx" the "x" in "Bx" is free with respect to the universal quantifier, bound with respect to the existential quantifier.
	www.earlham.edu /~peters/courses/log/terms3.htm (1736 words)

	Children's Universal Success with Quantification (Site not responding. Last check: 2007-10-08)
		If salience were the critical factor, then children's non-adult behavior would be consistent with the conclusion that children and adults assign different linguistic representations to sentences with the universal quantifier.
		The groups were asked to respond to different linguistic constructions containing the universal quantifier, as illustrated in (2)-(3).
		To satisfy the felicity conditions for (2), there was a Smurf who do not choose an apple or a jewel in the situation; in the situation for (3), there was a character, in addition to the Smurfs, and there were more than apples and bananas for them to choose.
	www.wam.umd.edu /~lu/abstracts/quantification.htm (481 words)

	Calixto Aguero-Bautista dissertation: abstract (Site not responding. Last check: 2007-10-08)
		In particular, the thesis argues that in a constituent question with a universal quantifier, syntactic reconstruction of the wh-phrase below the quantifier is the source of scope ambiguities.
		The second part of the thesis argues that reconstruction is necessary for PL-readings, because such interpretations are a particular case of variable binding in which the universal quantifier binds an implicit variable in one of the copies of the wh-phrase, which is analyzed as a skolemized choice function as in Kratzer's (1998) theory of indefinites.
		In addition, by comparing the interaction of overtly displaced wh-phrases with quantifiers, on the one hand, and the interaction of wh in situ and universal quantifiers, on the other, I have argued that whereas overtly moved wh-phrases move in successive cyclic fashion, wh-phrases in situ do not get their scope via successive cyclicity.
	web.mit.edu /mitwpl/dissertations/aguero_bautista.abstract.html (431 words)

	CG: 9.1 Blank referents (Existential quantifier)
		This quantifier just means "there exists a", and is part of predicate logic.
		The other quantifier is the universal quantifier,, meaning "for all".
		It is the opposite of the existential quantifier.
	www.huminf.aau.dk /cg/Module_I/1102.html (108 words)

	Universal Quantification is Strong in Children (Site not responding. Last check: 2007-10-08)
		Crucially, (5) is the adult interpretation and (6) is the interpretation peculiar to child grammar, the interpretation for non adult responses to (1) in contexts in which there is a donkey which is not ridden by any boy.
		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.
		The groups were asked to respond to different linguistic constructions containing the universal quantifier, as illustrated in (8)-(9).
	www.wam.umd.edu /~lu/abstracts/Upenn2.htm (1092 words)

	Remark: Quantifier Force. (Site not responding. Last check: 2007-10-08)
		If an existential quantifier is within the scope of a negation, it will behave as a universal quantifier and will be treated accordingly.
		A quantifier that behaves as a universal, even if it is syntactically an existential, is said to have universal force.
		Similarly, it can happen that a universal quantifier will have existential force if it is within the scope of an explicit or implicit negation--in this case, its variable will be replaced by a skolem term during skolemization.
	www.ai.sri.com /hpkb/snark/getting-started/node17.html (110 words)

	Luciano Floridi
		Universal quantifiers can be eliminated only via the instantiation of old constants, i.e.
		In the search for a contradiction, it is possible to repeat the elimination of the universal quantifier via the instantiation of another old constant which has already occurred in
		The repeatability of the elimination of the universal quantifiers ensures that making the tactical moves in the previous order may not be more elegant or economical, but is certainly more likely to lead to the discovery of contradictions than other strategies.
	www.wolfson.ox.ac.uk /~floridi/hstrategy.htm (820 words)

	[No title]
		Eliminate existential quantifiers(Skolemization): a) the general rule for eliminating an existential quantifier from a formula is to replace each occurrence of its existentially quantified variable by a (NEW) Skolem function whose arguments are those universally quantified variables that are bound by universal quantifiers whose scope include the scope of the existential quantifier being eliminated.
		Eliminate universal quantifiers Since all the variables in the wff we use must be within the scope of a quantifier, we are assured that all the variables remaining at this step are universally quantified.
		Furthermore, the order of universal quantification is unimportant, so we may eliminate the explicit occurrence of universal quantifiers and assume, by convention, that all variables in the matrix are universally quantified.
	www.cs.wisc.edu /~gerson/07FOL6.PPT (869 words)

	Phil 174 Logical Terms Chapter 4 (Site not responding. Last check: 2007-10-08)
		The scope of a quantifier tagged with a variable x is the expression written after the quantifier that is governed by the quantifier.
		This English structure is: quantifier + subject + predicate, where the quantifier is one of the words "all" (or "every"), "some," "no," and where the subject is an expression that is not either the word "thing" or "things".
		An instance with respect to the name a of a quantified sentence is the result of deleting the quantifier of the sentence and at the same time replacing all the occurrences of the individual variable in question throughout the sentence by occurrences of the selected name a.
	www.luc.edu /faculty/avande1/logic/defs-chap4.htm (1435 words)

	Phil 121.10 GWU Spg 03 Note#10, Pt. 3 (Site not responding. Last check: 2007-10-08)
		A variable that is not quantified is called 'free' or 'unbound', because for a variable to be quantified is for it to be 'bound' within the scope of a quantifier having that same letter.
		In each of (ii-c)-(vi-c), we were given a universal premise and, via a second premise, we were also told the proper name of an object said to exist in the universe of discourse.
		And by that use, by that assumption, we are entitled to derive that the predication of the universal wff in (1) applies to 'a'.
	home.gwu.edu /~stiv/p121p03n10p3.htm (4722 words)

	PredicateLogic - PineWiki
		To do this, we bind the variables using quantifiers, which state whether the claim we are making applies to all values of the variable (universal quantification), or whether it may only apply to some (existential quantification).
		The universal quantifier ∀ (pronounced "for all") says that a statement must be true for all values of a variable within some universe of allowed values (which is often implicit).
		So if you are trying to make a statement true, you should think of the universal quantifier as the enemy (the adversary in algorithm analysis) who says "nya-nya: try to make this work, bucko!", while the existential quantifier is the friend who supplies the one working response.
	pine.cs.yale.edu /pinewiki/PredicateLogic (1092 words)

	Philosophy 222:Class IX
		The rule UG (universal generalization): If we have a free variable in a statement form, we can put a universal quantifier in front of it (with appropriate parentheses), and change the variable to be same as in the quantifier.
		The reasoning behind EI is as follows: An existentially quantified statement says that the statement is true of something, that is, of at least one thing.
		I had to look ahead a bit to see that I would end up with a universal quantifier (in line 9) to know that I should use a variable with UI instead of a name.
	mywebpages.comcast.net /reasoning/symlogic/classes/class9.htm (1336 words)

	Quantifiers (Site not responding. Last check: 2007-10-08)
		Quantifiers permit the use of variables in deduction rules.
		They are used to point to variable nodes, indicating for which values of the variable node the rule holds.
		SNePS 2 uses restricted quantification, which means that every quantified expression must have a restriction as well as a scope.
	www.cs.buffalo.edu /~jsantore/snepsman/node40.html (59 words)

	CSC242 HW 4 (Site not responding. Last check: 2007-10-08)
		In order to do this, if an existential quantifier does not occur within the scope of a universal quantifier, simply drop the quantifier and replace all occurrences of the quantifier variable by a new constant.
		If an existential quantifier is within the scope of any universal quantifiers, there is the possibility that the value of one of the existential variables depends on the values of the associated universal variables.
		Instead, the general rule is to drop the existential quantifier and to replace the associated variable by a term formed from a new function symbol applied to the variables associated with the enclosing universal quantifiers.
	www.cs.rochester.edu /u/bayliss/csc242/logic.html (552 words)

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