A new S4 classical modal logic in natural deduction
暂无分享,去创建一个
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. ?
[1] Andrea Masini,et al. 2-Sequent Calculus: Intuitionism and Natural Deduction , 1993, J. Log. Comput..
[2] Alex K. Simpson,et al. The proof theory and semantics of intuitionistic modal logic , 1994 .
[3] Valeria de Paiva,et al. On an Intuitionistic Modal Logic , 2000, Stud Logica.
[4] G. Bellin. A system of natural deduction for GL , 2008 .
[5] Gunnar Stålmarck,et al. Normalization theorems for full first order classical natural deduction , 1991, Journal of Symbolic Logic.