词条 | Disjunction elimination |
释义 |
In propositional logic, disjunction elimination[1][2] (sometimes named proof by cases, case analysis, or or elimination), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof. It is the inference that if a statement implies a statement and a statement also implies , then if either or is true, then has to be true. The reasoning is simple: since at least one of the statements P and R is true, and since either of them would be sufficient to entail Q, Q is certainly true. An example in English: If I'm inside, I have my wallet on me. If I'm outside, I have my wallet on me. It is true that either I'm inside or I'm outside. Therefore, I have my wallet on me. It is the rule can be stated as: where the rule is that whenever instances of "", and "" and "" appear on lines of a proof, "" can be placed on a subsequent line. Formal notationThe disjunction elimination rule may be written in sequent notation: where is a metalogical symbol meaning that is a syntactic consequence of , and and in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: where , , and are propositions expressed in some formal system. See also
References1. ^{{cite web|url=https://proofwiki.org/wiki/Rule_of_Or-Elimination |title=Archived copy |accessdate=2015-04-09 |deadurl=yes |archiveurl=https://web.archive.org/web/20150418093657/https://proofwiki.org/wiki/Rule_of_Or-Elimination |archivedate=2015-04-18 |df= }} {{DEFAULTSORT:Disjunction Elimination}}2. ^http://www.cs.gsu.edu/~cscskp/Automata/proofs/node6.html 2 : Rules of inference|Theorems in propositional logic |
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