Normal derivability in modal logic

Mathematical Logic Quarterly 51 (6):632-638 (2005)
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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

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Jan Von Plato
University of Helsinki

Citations of this work

Proof Theory for Modal Logic.Sara Negri - 2011 - Philosophy Compass 6 (8):523-538.
Normal derivability in classical natural deduction.Jan Von Plato & Annika Siders - 2012 - Review of Symbolic Logic 5 (2):205-211.
Sketch of a Proof-Theoretic Semantics for Necessity.Nils Kürbis - 2020 - In Nicola Olivetti, Rineke Verbrugge & Sara Negri (eds.), Advances in Modal Logic 13. Booklet of Short Papers. Helsinki: pp. 37-43.

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References found in this work

Natural deduction with general elimination rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.
A Problem of Normal Form in Natural Deduction.Jan von Plato - 2000 - Mathematical Logic Quarterly 46 (1):121-124.

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