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Topic: Existential quantifier

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Quantification

	Existential quantification - Wikipedia, the free encyclopedia
		In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain.
		It may seem obvious that the phrase "and so on" is meant to include all natural numbers, and nothing more, but this wasn't explicitly stated, which is essentially the reason that the phrase couldn't be interpreted formally.
		In symbolic logic, we use the existential quantifier "∃" (a backwards letter "E" in a sans-serif font) to indicate existential quantification.
	en.wikipedia.org /wiki/Existential_quantifier (541 words)

	Quantification - Wikipedia, the free encyclopedia
		The corresponding symbol for the existential quantifier is "∃", a rotated letter "E", which stands for the word "exists".
		It has three elements: A mathematical specification of a class of objects via syntax, a mathematical specification of various semantic domains and the relation between the two, which is usually expressed as a function from syntactic objects to semantic ones.
		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)

	The Mercury Language Reference Manual - Existential types (Site not responding. Last check: 2007-10-08)
		For an existentially quantified type variable, the situation is the converse: the callee must determine the value of the type variable, and all callers must be defined so as to work for all types which are an instance of the called procedure's declared type.
		Note that an existentially typed procedure is not allowed to have different types for its existentially typed arguments in different clauses (even mode-specific clauses) or in different subgoals of a single clause; however, the same effect can be achieved in other ways (see see section Some idioms using existentially quantified types).
		Construction and deconstruction of existentially quantified data types are inverses: when constructing a value of an existentially quantified data type, the "existentially quantified" functor acts for purposes of type checking like a universally quantified function: the caller will determine the values of the type variables.
	www.cs.mu.oz.au /research/mercury/information/doc-release/reference_manual_11.html (1627 words)

	PlanetMath: quantifier
		A quantifier is a logical symbol which makes an assertion about the set of values which make one or more formulas true.
		While these are the most common quantifiers (in particular, they are the only quantifiers appearing in classical first-order logic), some logics use others.
		This is version 9 of quantifier, born on 2002-08-25, modified 2005-09-05.
	planetmath.org /encyclopedia/Quantifier.html (678 words)

	plstuff
		Quantifier negation is a necessary process (in many cases) in the construction of formal proofs of validity in predicate logic.
		Thus, a general rule with existential instantiation is that one must always existentially instantiate to "something new." The "something new" is some new unknown represented by a different letter than was used in the first case.
		Existential instantiation therefore proceeds from knowledge of the ascription of a property to some known individual, from the ascription of a property to an arbitrarily selected individual, or from the ascription of a property to an unknown, that it is true that something has that property.
	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)

	Introduction to Logic Chapter 12 -- True or False (Site not responding. Last check: 2007-10-08)
		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 rule of EG (existential generalization) is used to justify this inference: 1.
		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)

	[No title]
		This quantifier might be explicitly provided, as in the case of existential predicates, or might be implicit, as in the case of activity verbs, where an existential closure operator quantifies over the event variable.
		She follows Diesing’s (1992) Mapping Hypothesis, according to which variables in the VP are mapped onto the nuclear scope and are subject to existential closure, whereas variables outside the VP are mapped onto the restrictor and are bound by the generic quantifier.
		The quantifier binds the variables to the left of the semicolon (x in this case), and variables to the right of the semicolon (y) are bound by existential closure.
	www.bgu.ac.il /~arikc/nals.doc (7434 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.
		It does not have existential import (we made no commitment to the existence of the object called 'a') and it stands for _any_ object in the universe of discourse, however many objects there might be in that universe (even were there none).
		Yet, the existential quantifier is non-truth-functional, and so by constructing (7) we have made a new simple, opaque to the simple we saw in (6).
	home.gwu.edu /~stiv/p121p03n10p3.htm (4722 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)

	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)

	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)

	Peter Suber, "Predicate Logic Terms and Symbols"
		By convention, the existential quantifier has existential import; that is, it asserts the existence of something.
		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)

	CG: 9.9.1 Quantifier
		The existential quantifier is represented either by a blank (i.e., by nothing) or by the symbol.
		Since a blank quantifier is the existential quantifier, this means that we can paraphrase this graph as "There is a cat, and there is a mat, and the cat is on the mat".
		It is also called the "universal quantifier", since it means that the referent refers to all instances of the given type.
	www.huminf.aau.dk /cg/Module_I/1302.php (332 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		If the pronoun ‘He’ in the second sentence is itself a quantifier, we would have an easy explanation as to why the second sentence expresses a general claim: the generality is a result of the presence of this quantifier in the sentence.
		If you claim that pronouns anaphoric on singular existential quantifiers can go proxy for standard Russellian descriptions or numberless descriptions in order to get the right truth conditions for donkey sentences, then you are committed to the claim that the pronouns in discourses like (1a) have readings resulting from their going proxy for numberless descriptions.
		Thus familiarity in effect constrains the s2’s quantified over in (C) (“there is an s2 such that”) in the case of 1, but not 1b. (Actually, things may have to be a bit more complicated than this to handle more complex examples.) This gives 1 the proper truth conditions and they are different from 1b’s.
	www.uscphilosophy.org /phil_global_images/people/CDQandDonkey1.doc (9263 words)

	Categorical Statements
		The logical terms 'all' and 'some' are referred to as the "universal quantifier" and the "existential quantifier".
		Existential statements say that at least one member of one class belongs to another class.
		If the quantifier is 'all' or 'not all', use the subject as is, but negate the predicate.
	www.uncg.edu /phi/catstmts.htm (1248 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).
		A technical point is that the variable x in the statement (Ax.S) that we prove is NOT local to the box and may in fact occur in S. Normally, we would not expect it to.
		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).
	math.boisestate.edu /~holmes/M387syllabus/node30.html (1432 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)

	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)

	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)

	quantifier from FOLDOC (Site not responding. Last check: 2007-10-08)
		The quantifier applies to, or binds, variables which stand as the arguments of predicates.
		The quantifier asserting, "there are some" or "there is at least one".
		For example, the natural translation of (x)Px is, "All things have property P." The "all" in the universal quantifier refers to all the objects in the domain of the interpretation (universe of discourse), not to all objects whatsoever.
	lgxserver.uniba.it /lei/foldop/foldoc.cgi?quantifier (164 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").
		If a variable is not quantified then it is a free variable.
	www.hyperdictionary.com /dictionary/quantifier (160 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)

	Disk instructions, part 3
		Other than the logical constants (&,~, the existential quantifier symbol E etc.), and parentheses, there are four kinds of symbols (which play different roles in the rules):
		The exception: This is the writing of the existential quantifier: (a) No backwards E is available, so we make do the with a straight, capital, E. (b) For the computer, the existential quantifiers must be written without the parentheses.
		You introduce, as assumption, a "typical disjunct" of your existential premiss, i.e., a formula (in this case it could be: (Pb & (y)Raby)) obtained by substituting a NEW arbitrary name for the variable.
	www.philosophy.umd.edu /Faculty/LSvenonius/ls/disk4.html (853 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.
		One thing that this means, is that when both universal and existential quantifiers appear in premises, do EI before UI.
	mywebpages.comcast.net /reasoning/symlogic/classes/class9.htm (1336 words)

	Existential quantifier (Site not responding. Last check: 2007-10-08)
		An existential quantifier is the symbol ∃ in predicate calculus.
		The unique existential quantifer is the symbol ∃!.
		All is still licensed under the GNU FDL.
	www.wordlookup.net /ex/existential-quantifier.html (258 words)

	Existential Graphs
		By an existential relation I mean any relation, R, such that anything that is R to x (where x is some particular kind of object) is nonexistent in case x is nonexistent.
		Universal quantifier: He aslo adopted Π to indicate a logical product of any number of terms, which would only be true if every one of the terms happened to be true.
		When a line of identity crosses one or more negations, the corresponding existential quantifier is asserted in the outermost area in which the line occurs.
	www.jfsowa.com /peirce/ms514.htm (11281 words)

	[No title]
		There are two quantifiers, universal (everything is such that...) and existential (at least one thing is such that...).
		Overall, there are many arguments that require quantifiers when symbolized, but to which our familiar 18 rules of reasoning cannot be applied because the quantifed wffs do not exactly fit the argument forms (patterns) of the 18 rules.
		Furthermore, the initial quantifier must "cover" or apply to the whole line; that is, the scope of the quantifier must be the whole line.
	www.philosophy.eku.edu /Williams/PHI371Web/Q-Rules.htm (999 words)

	LP: The fix command (Site not responding. Last check: 2007-10-08)
		The fix command provides a method of forward inference, which can be used to eliminate an existential quantifier from a fact in LP's logical system.
		command eliminates the unique accessible prenex-existential quantifier over the variable from the named facts and substitutes the term for all occurrences of the variable bound by that quantifier.
		The named facts must contain exactly one accessible prenex-existential quantifier over the variable (because it is not sound to instantiate two different existential quantifiers by the same term).
	nms.lcs.mit.edu /larch/LP/commands/fix.html (213 words)

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