Disjunction introduction - Revision history

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en>Graham87: 1 revision from :nost:Disjunction introduction: import old edit from the Nostalgia Wikipedia, see User:Graham87/Import

2013-07-06T11:06:15Z

1 revision from nost:Disjunction introduction: import old edit from the Nostalgia Wikipedia, see User:Graham87/Import

← Older revision		Revision as of 13:06, 6 July 2013
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			'''Disjunction introduction''' or '''addition'''<ref>Hurley</ref><ref>Moore and Parker</ref><ref>Copi and Cohen</ref> is a simple [[validity\|valid]] [[argument form]], an [[immediate inference]] and a [[rule of inference]] of [[propositional calculus\|propositional logic]]. The rule makes it possible to introduce [[logical disjunction\|disjunctions]] to [[formal proof\|logical proofs]]. It is the [[inference]] that if ''P'' is true, then ''P or Q'' must be true.

			:Socrates is a man.
			:Therefore, either Socrates is a man or pigs are flying in formation over the English Channel.

			The rule can be expressed as:
			:<math>\frac{P}{\therefore P \or Q}</math>

			where the rule is that whenever instances of "<math>P</math>" appear on lines of a proof, "<math>P \or Q</math>" can be placed on a subsequent line.

			Disjunction introduction is controversial in [[paraconsistent logic]] because in combination with other rules of logic, it leads to [[Principle of explosion\|explosion]] (i.e. everything becomes provable). See [[Paraconsistency#Tradeoff\|Tradeoffs in Paraconsistent logic]].

			== Formal notation ==
			The ''disjunction introduction'' rule may be written in [[sequent]] notation:

			: <math>P \vdash (P \or Q)</math>

			where <math>\vdash</math> is a [[metalogic]]al symbol meaning that <math>P \or Q</math> is a [[logical consequence\|syntactic consequence]] of <math>P</math> in some [[formal system\|logical system]];

			and expressed as a truth-functional [[tautology (logic)\|tautology]] or [[theorem]] of propositional logic:

			:<math>P \to (P \or Q)</math>

			where <math>P</math> and <math>Q</math> are propositions expressed in some formal system.

			== References ==
			{{reflist}}

			{{DEFAULTSORT:Disjunction Introduction}}
			[[Category:Rules of inference]]
			[[Category:Paraconsistent logic]]
			[[Category:Theorems in propositional logic]]

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2012-03-10T21:48:25Z

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