A New S4 Classical Modal Logic in Natural Deduction

Journal of Symbolic Logic 71 (3):799 - 809 (2006)
Abstract
We show, first, that the normalization procedure for S4 modal logic presented by Dag Prawitz in [5] does not work. We then develop a new natural deduction system for S4 classical modal logic that is logically equivalent to that of Prawitz, and we show that every derivation in this new system can be transformed into a normal derivation
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Sara Negri (2011). Proof Theory for Modal Logic. Philosophy Compass 6 (8):523-538.
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John Thomas Canty (1964). A Natural Deduction System for Modal Logic. Notre Dame Journal of Formal Logic 5 (3):199-210.
John Hawthorn (1990). Natural Deduction in Normal Modal Logic. Notre Dame Journal of Formal Logic 31 (2):263-273.
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