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Original Paper
Normal derivability in modal logic
Article first published online: 28 SEP 2005
DOI: 10.1002/malq.200410054
Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1521-3870/asset/cover.gif?v=1&s=3df32dbed8d9153ac6eafe1eaa786854b9b48345 "Mathematical Logic Quarterly")
Additional Information
How to Cite
von Plato, J. (2005), Normal derivability in modal logic. Mathematical Logic Quarterly, 51: 632–638. doi: 10.1002/malq.200410054
Publication History
- Issue published online: 28 SEP 2005
- Article first published online: 28 SEP 2005
- Manuscript Revised: 5 SEP 2005
- Manuscript Accepted: 5 SEP 2005
- Manuscript Received: 20 JUL 2004
- Abstract
- References
- Cited By
Keywords:
- Normalization;
- modal logic
Abstract
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. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)