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Topic: Disjunction introduction

Related Topics

Disjunctive syllogism

Classical logic

Principle of explosion

Prima facie

	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 (2967 words)

	Study Four
		The rule that covers the relation between conjunction and disjunction is simply this: The denial of a conjunction is equivalent to (equal to) a disjunction of the denials of the propositions.
		And, the denial of a disjunction is equivalent to a conjunction of the denials of the propositions.
		The rule is: An implication is equivalent to a disjunction consisting of the denial of the antecedent as one disjunct and the consequent of the implication as the other disjunct.
	www2.sjsu.edu /logic/study4.htm (2753 words)

	Learn more about Propositional calculus in the online encyclopedia. (Site not responding. Last check: 2007-10-22)
		The first eight are non-hypothetical, meaning that they do not involve hypothetical reasoning: specifically, the introduction of hypothetical premises is not used; the last two rules are hypothetical.
		Introducing a hypothesis means adding a wff to a derivation not originally present as a premise; discharging the hypothesis means eliminating the wff justifiably--any wffs correctly derived from the hypothesis justify the introduction of the hypothesis after the fact.
		With wffs and rules of inference, it's possible to derive wffs; the derivation is a valid argument form, while the derived wff is known as a lemma.
	www.onlineencyclopedia.org /p/pr/propositional_calculus.html (480 words)

	Gettier problem - Wikipedia, the free encyclopedia
		Smith therefore (justifiably) concludes (by the rule of disjunction introduction) that "Jones owns a Ford, or Brown is in Barcelona", even though Smith has no knowledge whatsoever about the location of Brown.
		The JTB account is then criticized for trying to get the factivity of knowledge "on the cheap," by replacing an irreducible notion of factivity with the conjunction of some of the properties that accompany it (in particular, truth and justification).
		Of course, the introduction of irreducible primitives into a philosophical theory is always a controversial move (some would say a sign of desperation), and such anti-reductionist accounts are unlikely to please those who have other reasons to hold fast to the method behind JTB+G accounts.
	www.marylandheights.us /project/wikipedia/index.php/Gettier_problem (1749 words)

	Wednesday, February 2
		Implication introduction 2 (modus tollens) has not been forgotten, but it is not needed as a basic rule (it can be derived from the others, and we'll see how to do this).
		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)

	Richard Gilbert (Site not responding. Last check: 2007-10-22)
		The idea of disjunction can be equally applied to poetry in general; what is significant for haiku particularly are those types of disjunction used, whether there may be consistent disjunctive styles, and the frequency of occurrence and quality of instances occurring in a single haiku, versus poems in other genres.
		Importantly, disjunction is not, strictly speaking, paradox or juxtaposition, because the effects are not cognitively dualistic—the alchemy is that of impossibles, not polarities.
		Disjunction has at least three arresting qualities: centrifugal force (the reader is thrown out of the poem and image, even out of language), gravitational force (the reader is drawn into interior contemplation), and misreading as meaning (a falling out of, and recovery of meaning).
	www.worldhaikureview.org /3-2/essay_rgilbert.shtml (9811 words)

	Brief introduction to logic (Site not responding. Last check: 2007-10-22)
		My intent here is to give a brief introduction to only one aspect of the study of logic so that the reader may better understand the principles described in my book.
		Disjunction is usually formed by placing the word "or" between two simple statements.
		And their disjunction is not false unless all these propositions are false.
	www.sirus.com /users/mjake/Brief.html (7793 words)

	Andrews. To Truth through Proof. (Site not responding. Last check: 2007-10-22)
		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).
	gtps.math.cmu.edu /cebrown/notes/tttp.html (6301 words)

	Lionheart Chronicles \| "et in Arcadia ego..."
		And although the Disjunction was brief, there was time for all manner of spiritkind to come into our world.
		The spiritkind soon discovered they had no essence of their own and were forced into either parasitic or symbiotic relationships with what they found around them.
		While the introduction of spirits and magic into humans in some cases created creatures like the troll or goblin, some spirits developed a symbiotic relationship with their human hosts.
	www.rpgplanet.com /lionheart/guide-races.shtml (788 words)

	October 23, 2003
		The idea behind conditional introduction is that, to prove a conditional sentence, we can assume its antecedent (for the sake of argument) and prove on that assumption that its consequent follows.
		Conditional introduction sanctions the inference from our proof of 5 (from 1, 2 and 4) to the conclusion that 3 follows from 1 and 2.
		The rule of conditional introduction tells us that to prove a conditional sentence, we should assume its antecedent (for the sake of argument) and prove on that assumption that its consequent follows.
	www.albany.edu /~amu78/hdt_9.html (1335 words)

	Conjunction, Negation, and Disjunction
		The logical operations of conjunction, negation, and disjunction (alteration) are discussed with respect to their truth-table definitions.
		Truth Functionality: In order to know the truth value of the proposition which results from applying an operator to propositions, all that need be known is the definition of the operator and the truth value of the propositions used.
		Disjunction (or as it is sometimes called, alternation) is a connective which forms compound propositions which are false only if both statements (disjuncts) are false.
	philosophy.lander.edu /logic/conjunct.html (875 words)

	Paraconsistent logic Information
		The semantic clauses for negation and disjunction are given as follows (the other logical connectives can be defined in the usual ways):
		It is easy to check that this valuation constitutes a counterexample to both explosion and disjunctive syllogism.
		As one can verify, LP preserves most other inference patterns that one would expect to be valid, such as De Morgan's laws and the usual introduction and elimination rules for negation, conjunction, and disjunction.
	www.bookrags.com /wiki/Paraconsistent_logic (1711 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 and ~Q (however you prove this) ~P negation introduction, previous box Double Negation These are derived rules, but they are really part of our basic toolbox.
		Q ~P ~Q ------- ------- disjunction elimination Q P proof by cases: this is a derived rule but again a basic part of our toolkit.
	math.boisestate.edu /~holmes/M387syllabus/node46.html (1231 words)

	UA-spec (text)
		Structural elements are associated with the help of operations (disjunction, conjunction, junction, and subjunction) and are considered in different contexts (structural, abstract, relational, and modal).
		This document could be divided into two names base (consists of abstract and intro) and desc (consists of intro and defs).
		(base) [abstract (desc) [introduction] (base) defs] (desc) or (base) [abstract introduction] (desc) [introduction defs] Let's examine various variants of associating these two names with the help of different operations.
	www.mail-archive.com /www-talk@w3.org/msg00027.html (1575 words)

	Principle of explosion - Open Encyclopedia (Site not responding. Last check: 2007-10-22)
		Explosion is based on several of the fundamental formal properties of disjunction, the logical operator corresponding to the English "or".
		Subscribers to paraconsistent logics reject the above reasoning, usually citing the invalidity of either disjunction introduction or disjunctive syllogism.
		Dialetheism, one particular paraconsistent logic, rejects the argument in order to accept certain instances of P ∧ ¬P.
	open-encyclopedia.com /Principle_of_explosion (166 words)

	Strategy for Proofs
		Check whether there is a disjunctive statement among the premises.
		If the goal is part of a disjunction, chances are good you will be using disjunction-elimination.
		This will often indicate the introduction rule by which you will introduce the conclusion.
	www.unc.edu /~tparent/Strategy4Proofs.htm (679 words)

	Prolog programming
		Moving down, the predicate "disjunction" is defined as follows.
		Between them, these two clauses define disjunction to be terms whose tree diagrams have internal nodes of degree 2 labelled by
		The formula is in conjunctive normal form, in the sense that it is a conjunction of disjunctions.
	www.dcs.warwick.ac.uk /~mju/CS205/prolog3.html (1120 words)

	The Meanings of Logical Constants
		This difference between conjunction and disjunction can be avoided by giving up appeal to rules of natural deduction in favor of rules of a `sequent calculus'.
		So, we can state introduction and elimination rules of natural deduction for negation, but clearly these rules are not simply restatements of the truth conditions of negated propositions.
		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)

	Non-disjunction of chromosome 18 -- Bugge et al. 7 (4): 661 -- Human Molecular Genetics
		It increases with maternal age and has been hypothesized to involve two steps: an unfavourable chiasma distribution at diplotene in fetal life followed by age-dependent deterioration of the mechanism for meiotic disjunction, which is most severe for tetrads with susceptible distributions of chiasmata (4).
		It leads to normal disjunction and is the rule in the species where it occurs, demonstrating a mechanism for regular disjunction that does not depend on crossing over.
		For chromosome 18 we have examined the frequency of normal disjunction from nullichiasmate tetrads by reconstruction of the chiasma distribution from crossovers in normal meiosis and compare this with the distribution from transitions in non-disjunction.
	hmg.oxfordjournals.org /cgi/content/full/7/4/661 (6151 words)

	Fitch Rule Summary
		Instructions for use: You can cite any prior sentence available and create a disjunction containing as one conjunct the prior line cited and as another disjunct any sentence you like.
		Types of sentences you must cite: Must cite one disjunction, a subproof for each disjunct within that disjunction, and nothing else.
		Instructions for use: Cite a disjunction, create a subproof for each disjunct that begins with each disjunct in turn.
	www.ocf.berkeley.edu /~brianwc/courses/logic/rulesummary.html (774 words)

	prop1
		Thus, John is in class even though Jane is outside is symbolized as P and Q. a compound made of two simpler propositions, called disjuncts.
		There are two types of disjunctions, or two ways to interpret a disjunction.
		Thus, for our purposes, a disjunction is true if and only if at least one of its disjuncts are true.
	www.olemiss.edu /courses/logic/prop1.htm (538 words)

	The Philosophical Computer - Introduction
		This book is an introduction, entirely by example, to the possibilities of using computer models as tools in philosophical research in general and in philosophical logic in particular.
		Figure 5 is a portrait of conjunction: the value colors on its axes combine in conjunction to give the values at points of intersection.
		When we put the two images side by side it becomes obvious that they have a certain symmetry: the symmetry standardly captured by speaking of disjunction and conjunction as dual operators.
	www.sunysb.edu /philosophy/faculty/pgrim/intro.html (3241 words)

	NTU Info Centre: Propositional calculus (Site not responding. Last check: 2007-10-22)
		; Conjunction Elimination: From any wff (φ ∧ ψ), we may infer φ and ψ ; Disjunction Introduction: From any wff φ, we may infer (φ ∨ ψ) and (ψ ∨ φ), where ψ is any wff.
		; Disjunction Elimination: From wffs of the form (φ ∨ ψ), (φ → χ), and (ψ → χ), we may infer χ.
		Axiom AND-3 corresponds to "conjunction introduction." 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.
	www.nowtryus.com /article:Propositional_calculus (2726 words)

	CIS 301 Captain's log (Site not responding. Last check: 2007-10-22)
		Before next time: read the introduction of LPL (the text book), start playing with the software, and preferably start reading a bit of Chap 1.
		Elimination and introduction rule for the identity predicate.
		Disjunction elimination corresponds to "proof by cases"; negation introduction corresponds to "proof by contradiction".
	www.cis.ksu.edu /~tamtoft/301/log.html (1966 words)

	Constructive Mathematics (Stanford Encyclopedia of Philosophy)
		A natural — although, as we shall see, not the unique — interpretation of this disjunction is that not only does (at least) one of the statements P, Q hold, but also we can decide which one holds.
		It is on these interpretations of disjunction and existence that mathematicians have built the grand, and apparently impregnable, edifice of classical mathematics which serves a foundation for the physical, the social, and (increasingly) the biological sciences.
		Secondly, there is a model theory (Kripke models) in which it can be shown that LPO is not derivable in Heyting arithmetic — that is, Peano arithmetic using the computational interpretation of the connectives and quantifiers that we state in more detail in the next section (Bridges and Richman 1987, Chapter 7).
	plato.stanford.edu /entries/mathematics-constructive (6377 words)

	CS206: Formal Methods in Computer Science (Site not responding. Last check: 2007-10-22)
		Introduction to a class of predicate logic formula for which satisfiability checking is decidable (computable): the Bernays-Schonfinkel class, a simple algorithm for checking satisfiability of this class of sentences, and illustrations
		Introduction to Herbrand Universe and Lowenheim-Skolem Theorem on existence of countable models of satisfiable predicate logic sentences.
		Introduction to Herbrand's Theorem on unsatisfiability of predicate logic sentences.
	www.cse.iitb.ac.in /~supratik/courses/cs206 (1707 words)

	80.07.04: Logic and Set Theory
		To negate a conjunction or disjunction of two or more simple statements we negate each of the simple statements and then change all of the connectives from disjunction’s to conjunctions and all of the conjunctions to disjunction’s.
		To this point we have discussed simple statements, negations, conjunctions, disjunction’s and conditional statements all of which are statements that are either true or false but not both.
		A short chapter containing a brief introduction to set theory and logic as well as the importance of these areas in the elementary school.
	www.cis.yale.edu /ynhti/curriculum/units/1980/7/80.07.04.x.html (3651 words)

	Propositionally Logical Conclusions - Rules - OR-Introduction
		Note that only one part of the disjunction is a nessesary premise.
		Germany is located in Asia or the Internet is very fast or the distance between Earth and Moon is less than the height of Mount Everest or Finland is situated in Northern Europe or rain falls.
		We see that the new parts in the constructed disjunction have really not be in a sensible context to the given premise.
	www.informatik.htw-dresden.de /~logic/conclusions/rule5.html (185 words)

	Propositional Logic [Internet Encyclopedia of Philosophy] (Site not responding. Last check: 2007-10-22)
		Abelard, for example, seems to have been the first to differentiate clearly exclusive from inclusive disjunction (discussed below), and to suggest that inclusive disjunction is the more important notion for the development of a relatively simple logic of disjunctions.
		The truth-function for an operator can be represented as a table, each line of which expresses a possible combination of truth-values for the simpler statements to which the operator applies, along with the resulting truth-value for the complex statement formed using the operator.
		The form of reasoning exemplified in step 5 is called disjunctive syllogism, and involves deducing one disjunct of a disjunction on the basis of the disjunction and the negation of the other disjunct.
	www.iep.utm.edu /p/prop-log.htm (8796 words)

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