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Topic: Disjunction elimination

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	Disjunction (Stanford Encyclopedia of Philosophy)
		Disjunction is a binary truth-function, the output of which is a sentence true if at least one of the input sentences (disjuncts) is true, and false otherwise.
		q is the disjunction of p and q, and is pronounced as ‘pea vel queue’ or ‘pea vee queue’ or ‘pea or queue’.
		In this case, p and q are the disjuncts of the disjunction.
	plato.stanford.edu /entries/disjunction (2954 words)

	Disjunction elimination: Definition and Links by Encyclopedian.com
		Disjunction Elimination From wff s of the form (φ ∨ ψ), (φ...
		...because exclusive disjunction is a modification of ordinary (inclusive) disjunction, which is...
		In propositional calculus disjunction elimination is the inference that, if A or B is true, and both A and B entail C, then we may justifiably infer C. For example, it's true that either I'm inside or I'm outside.
	www.encyclopedian.com /di/Disjunction-elimination.html (204 words)

	mmtheorems3 - Metamath Proof Explorer
		Elimination of disjunction by denial of a disjunct.
		Inference adding a left disjunct to both sides of a logical equivalence.
		Inference adding a right disjunct to both sides of a logical equivalence.
	metamath.planetmirror.com /mpegif/mmtheorems3.html (308 words)

	Wednesday, February 2
		Q ~P ~Q --------- disjunction elimination 1 -------- disjunction elimination 2 Q P I think that Grantham calls these rules of disjunctive syllogism.
		Q These are not the same as Grantham's rules of disjunction introduction, but Grantham's rules are special cases, and I allow use of the same names for his rules: Q P ----- disjunction introduction 2 ----- disjunction introduction 1 (special case) (special case) P
		P disjunction elimination 2, lines 2,1 so we have the rules P ~ ~ P -------- double negation introduction ------- double negation elimination ~ ~ P P The ability to derive these rules is another advantage of our strong disjunction introduction rules.
	math.boisestate.edu /~holmes/M387syllabus/node24.html (433 words)

	Or
		A disjunction's ultimate interpretation is based on its potential informativeness, where the interpretation of the disjunctive utterance having the smallest number of true conditions is considered most informative.
		The Disjunctive Modus Ponens problem presented conjunctions in two ways: In one problem, the and was explicit in the minor premise (There is a P and a Q); in the other problem, the conjunction was implicit (two premises were presented as There is a P; There is a Q).
		Whereas one disjunct in (#4) is enough to infer the consequent, one conjunct in (#8) is not.
	www.isc.cnrs.fr /nov/Or.htm (10514 words)

	Papers in elementary proof theory 1998--2002. \\ A reasoned bibliography\\ Sara Negri and Jan von Plato
		It has been a widespread belief that this is impossible, that ``cut elimination fails in the presence of axioms.'' Unaware of this, we found a way of converting universal axioms into sequent calculus rules and proved that Gentzen's cut elimination extends to these, with no cuts left even on atomic formulas.
		All elimination rules are written in the way of disjunction elimination, with an arbitrary consequence.
		General elimination rules of item 9 are applied to linear logic which gives a calculus with no sequent calculus style features (e.g., no rule of weakening), and with no anomalies for derivations in normal form.
	www.helsinki.fi /~negri/ptpub.html (2135 words)

	Single Elimination Tournament Bracket (Site not responding. Last check: 2007-11-03)
		Gaussian elimination 1:, '''Gaussian elimination ''' or '''Gauss-Jordan elimination ''', named after Carl Friedrich Gauss and Wi 9: ity theorycomputational complexity of Gaussian elimination is Big O notationO(''n''³), that 11: ern.
		Double negative elimination 1: he propositional calculus, '''double negative elimination ''' is a rule that states that double negative 21: These two rules andmdash; double negative elimination and introduction andmdash; can be restated as follo 39: The double negative elimination rule is true in classical logic, but in int
		Elimination reaction 1: cule decreases by two (this is known as reductive elimination).
	www.relativeaccess.com /File/43708-Single.Elimination.Tournament.Brack... (900 words)

	The Meanings of Logical Constants
		The second and third give elimination rules for conjunction in the sense that they allow a consequence not containing conjunction to be derived from a conjunctive statement.
		But, given the second elimination rule, it is enough to show that P and the other premises logically imply N(P), for in that case they imply anything.
		I have not been able to respond to all her worries, To mention one point, she argued forcefully that the meanings of the logical constants might be determined holistically in the sense that, for example the meaning of disjunction might be affected by whether classical negation was present.
	www.nyu.edu /gsas/dept/philo/courses/concepts/meaning.html (3173 words)

	Andrews. To Truth through Proof. (Site not responding. Last check: 2007-11-03)
		System F of first-order logic is introduced in the usual way (with disjunction, negation, and universal quantification as primitive)--except he allows propositional, function and relation variables over which we cannot quantify.
		Andrew's System G operates with disjunctions (not with sequents)--deriving theorems from "not A or A" (with A atomic) using "introduction" style rules (double negation, conjunction, universal generalization, and existential generalization) and alpha-beta.
		Here we derive wff's (including an "empty disjunction" wff which may stand for "false" or nothing if used with a disjunction) starting from a given set S of wff's by the rules: Disjunction (for rearranging disjunctions), simplification [factoring], substitution, cut, negation elimination, conjunction elimination, and universal instantiation (by simply removing the quantifier).
	www.andrew.cmu.edu /user/cebrown/notes/tttp.html (6301 words)

	Propositional calculus Summary
		Of the three connectives for conjunction, disjunction, and implication (∧, ∨, and →), one can be taken as primitive and the other two can be defined in terms of it and negation (¬).
		Axioms OR-1 and OR-2 correspond to "disjunction introduction." The relation between OR-1 and OR-2 reflects the commutativity of the disjunction operator.
		which is conjunction elimination, one of the ten inference rules used in the first version (in this article) of the propositional calculus.
	www.bookrags.com /Propositional_calculus (4189 words)

	Disjunctive syllogism - Wikipedia, the free encyclopedia
		A disjunctive syllogism, also known as modus tollendo ponens (literally: mode which, by taking away, affirms) is a valid, simple argument form:
		The reason this is called "disjunctive syllogism" is that, first, it is a syllogism--a three-step argument--and second, it contains a disjunction, which means simply an "or" statement.
		Note that the disjunctive syllogism works whether 'or' is considered 'exclusive' or 'inclusive' disjunction.
	en.wikipedia.org /wiki/Disjunctive_syllogism (346 words)

	CIS 301 Captain's log
		Disjunction elimination in proofs of properties of finite sets.
		Taking a cue from the proof rules for conjunction, an elimination rule and an introduction rule for universal quantification was presented.
		Taking a cue from the proof rules for disjunction, an introduction rule for existential quantification was presented.
	www.cis.ksu.edu /~tamtoft/CIS301/Fall02/log.html (1500 words)

	logic-classes-nov2
		P - P v Q introduces a disjunction where there was not one before, by means of a valid inference.
		The idea is that if we assume a disjunction and we can make two sub-derivations, one deriving something from one disjunct and the other deriving the same thing from the other, then we can derive that something, thus eliminating the OR.
		And unlike the rules for the other operators, the introduction and elimination rules are very similar.
	www.arts.ualberta.ca /~amorton/logic04/logic-classes-nov2.html (2443 words)

	NDRio 2001 - Invited Lecturer
		Prawitz 1965 gave a translation that instead produced cut-free derivations.
		It is shown that by writing all the elimination rules of natural deduction in the manner of disjunction elimination, with an arbitrary consequence, isomorphism between normal derivations and cut-free derivations is achieved.
		Likewise, it is shown that Prawitz' translation contains an implicit process of cut elimination.
	www.inf.puc-rio.br /nd/plato.html (93 words)

	Official List of Rules and Theorems
		Notice that an ``introduction'' rule is a rule for proving a goal with the appropriate top-level connective or quantifier, while an ``elimination'' rule is a rule for using a premise or previous conclusion with that the appropriate top-level connective.
		Q ~P ~Q ------- ------- disjunction elimination Q P proof by cases: this is a derived rule but again a basic part of our toolkit.
		Q disjunction introduction (refer to whole box) derived rules: P Q ----- ----- disjunction introduction (Grantham) P
	math.boisestate.edu /~holmes/M387syllabus/node46.html (1231 words)

	CS157: Problem Set 4
		for disjunction, => for implication, A for universal quantification, and E for existential quantification.
		An elimination or restriction strategy is compatible with a proof method if and only if it is possible to prove the same conclusions with the strategy as without.
		If the answer is "not compatible", give an example of a set of premises and a conclusion for which Ordered Resolution and the strategy fail to prove the conclusion, while Ordered Resolution alone succeeds in proving the conclusion.
	logic.stanford.edu /classes/cs157/2005/problems/ps4.html (423 words)

	Startup guide for Bertie3 or Twootie (Site not responding. Last check: 2007-11-03)
		Disjunction ("either...or") is symbolized with the lowercase letter "v" (as in "victory"), directly above the space bar.
		The natural deduction system uses the connective followed by "i" or "e" (or "I" or "E") for "introduction" or "elimination" respectively.
		Premises in the proof are justified with a "P", and auxiliary assumptions in a conditional proof with "A".
	www.ucc.uconn.edu /~wwwphil/startup.htm (532 words)

	Semantic versus syntactic branching
		The standard disjunction elimination rule, also called syntactic branching rule, will create one branch on which p is true and one branch on which q is true.
		For example, if the cut formula is [](-[](pq)-[](pr)), then creating one branch on which this true and a second one on which it is false, might actually create a tableaux with a higher number of branches than the one we obtain using syntactic branching.
		To investigate the effect of these two variants of disjunction elimination we compare two tableaux-based systems which are identical except that one system uses semantic branching while the other one uses syntactic branching.
	www.csc.liv.ac.uk /~ullrich/mdp/section5.html (610 words)

	Third lecture
		The key to seeing the relationship between the reduction rules and the semantical explanations of the elimination rules is this: to verify a proposition by putting a proof of yours that it is true into practice corresponds to reducing a natural deduction to introductory form and deleting the last inference.
		If you want the elimination rule for conjunction to exhibit the same pattern as the elimination rules for falsehood, disjunction, and existence, it should be formulated differently, but, in its standard formulation, it reads as follows.
		And, as you see, I have again chosen the usual formulation of the elimination rule for the universal quantifier rather than the one which is patterned upon the elimination rules for falsehood, disjunction, and existence.
	www.hf.uio.no /ifikk/filosofi/njpl/vol1no1/meaning/node4.html (6576 words)

	Disjunctions Disjunctive Syllogism, vI and vE
		Our first rule, one that we shall call disjunctive syllogism (DS) allows us, when given any disjunction p v q and the negation of one of the disjuncts, to add the other disjunct as a line.
		The important point to remember is that the one of the lines to which this rule applies must be a disjunction.
		Our or elimination rule (vE) is one form of a rule that is sometimes called 'constructive dilemma'.
	www.thelogiccourse.com /bluestorm/disjunctionset.html (858 words)

	Maggie Johnson
		Disjunction Introduction: Form P, infer P v Q
		Conjunction Elimination: allows us to assert Pi of a conjunctive sentence P1^…^Pi^…^Pn which we have already derived in our proof.
		Disjunction Introduction: allows us to go from a sentence Pi to any disjunction where Pi is among the disjuncts, say P1 v…v Pi v … v Pn.
	cse.stanford.edu /classes/cs103a/h11Proofs2.htm (288 words)

	CIS 301 Captain's log
		Please send e-mail to the TA (varsha@cis.ksu.edu) if you have not received e-mail from her yet or if you have added the class recently.
		Today's coverage: Rules for implication elimination and introduction, modus tollens and several examples.
		October 24: Natural deduction proofs in predicate logic: rules for for all introduction and elimination, and existential introduction and elimination; examples.
	www.cis.ksu.edu /~ab/Courses/301/fall01/log.html (755 words)

	[No title]
		You are reasonably sure that what you are trying to prove (either as a final or an intermediate step) follows from either side of the disjunction.
		In order to use Disjunction elimination, you will introduce two subproofs.
		Each subproof begins with the assumption that one of the sides of the disjunction is true.
	www.courses.psu.edu /phil/phil012_pam208/0221.doc (494 words)

	[No title]
		A disjunction is true as long as one of the disjuncts is true.
		We can show both that if it is the left disjunct, we can derive the conclusion and that if it is the right disjunct, we can derive the conclusion.
		So, it doesn’t matter which disjunct is actually the true one (or they both could be true), as long as we have showed that the conclusion can be derived in either case.
	www.cs.brandeis.edu /~jlittman/SummerLogic/lectureNotes/June14.doc (1434 words)

	Elimination of micronucleated cells by apoptosis after treatment with inhibitors of microtubules -- Decordier et al. 17 ...
		Elimination of micronucleated cells by apoptosis after treatment with inhibitors of microtubules -- Decordier et al.
		Elimination of micronucleated cells by apoptosis after treatment with inhibitors of microtubules
		that apoptosis contributes to the elimination of cells with
	mutage.oxfordjournals.org /cgi/content/abstract/17/4/337 (555 words)

	[No title]
		If the column under the main connective (the last one you fill in) is entirely true, then the sentence is a Tautology.
		Proof by cases is called disjunction elimination, and it is very powerful.
		The way it works is to break the sentence into all possible cases.
	www.stanford.edu /~pedregal/ConceptTree/test.xml (965 words)

	lotf.info - Disjunction elimination (Site not responding. Last check: 2007-11-03)
		In Logic Propositional disjunction elimination is the inference that; if "A or B" is true; and A entails C; and B entails C; then we may justifiably infer C
		The reasoning is simple: since at least one of the statements A and B is true; and since either of them would be sufficient to entail C; C is certainly true.
		During his lifetime he was involved in almost 200 movies, expecially comedies, where he demonstrated his great elegance and his fine sense of humour.
	lotf.info /6624 (255 words)

	Startup guide for Bertie3
		Probably the biggest barrier to overcome is to learn what keys to press for logic symbols.
		So ">I" is Conditional Introduction, "vE" is Disjunction Elimination, "Vi" is Universal Introduction, and so on.
		Primary assumptions in the derivation are justified with a "P", and auxiliary assumptions in a subderivation are justified with "A".
	classes.colgate.edu /pgregory/phil325/startup.html (1793 words)

	Coq.Logic.ProofIrrelevance
		This is a proof in the pure Calculus of Construction that classical logic in Prop + dependent elimination of disjunction entails proof-irrelevance.
		Since, dependent elimination is derivable in the Calculus of Inductive Constructions (CCI), we get proof-irrelevance from classical logic in the CCI.
		The Calculus of Inductive Constructions (CCI) enjoys dependent elimination, hence classical logic in CCI entails proof-irrelevance.
	coq.inria.fr /library/Coq.Logic.ProofIrrelevance.html (432 words)

	disjunction - OneLook Dictionary Search
		Disjunction : A Glossary of Mathematical Terms [home, info]
		Phrases that include disjunction: exclusive disjunction, disjunction and existence properties, disjunction drive, disjunction elimination, disjunction introduction, more...
		Words similar to disjunction: disconnectedness, disconnection, disjuncture, more...
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=disjunction (252 words)

	Workflow automation: overview and research issues
		Negation Elimination ( EMBED Equation.DSMT4 ): EMBED Equation.DSMT4 Conditional Introduction ( EMBED Equation.DSMT4 ): Given a derivation of a wff EMBED Equation.DSMT4 from a hypothesis EMBED Equation.DSMT4 , discharge the hypothesis and infer EMBED Equation.DSMT4 .
		Disjunction Elimination ( EMBED Equation.DSMT4 ): From a wff of the form EMBED Equation.DSMT4 , EMBED Equation.DSMT4 , EMBED Equation.DSMT4 , infer EMBED Equation.DSMT4 .
		Disjunctive Syllogism (DS): EMBED Equation.DSMT4 Theorem Introduction (TI): Any substitution instance of a theorem may be introduced at any line of a proof.
	math.arizona.edu /~ksimic/ming.doc (6614 words)

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