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Normal derivability in modal logic

✍ Scribed by Jan von Plato

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 89 KB
Volume: 51
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200410054

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✦ Synopsis

The standard rule of necessitation in systems of natural deduction for the modal logic S4 concludes A from A whenever all assumptions A depends on are modal formulas. This condition prevents the composability and normalization of derivations, and therefore modifications of the rule have been suggested. It is shown that both properties hold if, instead of changing the rule of necessitation, all elimination rules are formulated in the manner of disjunction elimination, i. e. with an arbitrary consequence.

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