Abstract
In this chapter we compare and contrast the natural deduction system given in Section 2.2 to a modified version of a hybrid-logical natural deduction system given by Jerry Seligman. The chapter is structured as follows. In the first section of the chapter we describe the natural deduction systems under consideration, in particular, we define our version of Seligman’s system. In the second and third sections, we give translations of derivations backwards and forwards between the systems, and in the fourth section we devise a set of reduction rules for our version of Seligman’s system by translation of the reduction rules for the system given in Section 2.2. In the final section we discuss the results.
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A historical remark is relevant here: An analogous problem appears in connection with intuitionistic linear logic. This problem was originally solved by Benton et al. (1992, 1993), and by the author of the present book. See the account given in Braüner (1996). The same problem appears in connection with a natural deduction system for the modal logic S4, see Bierman and de Paiva (2000).
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Braüner, T. (2011). Comparison to Seligman’s Natural Deduction System. In: Hybrid Logic and its Proof-Theory. Applied Logic Series, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0002-4_4
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DOI: https://doi.org/10.1007/978-94-007-0002-4_4
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