Correspondence between Normalization of CND and Cut-Elimination of LKT
نویسنده
چکیده
We study the correspondence between normalization of two well-known constructive classical logic, namely CND (Parigot 92) and LKT (Danos-Joinet-Schellinx 93). For this, we develop term calculi. We then show translation from CND to LKT and show the simulation theorem; the normalization of CND can be simulated by cut-elimination of LKT. Furthermore, we argue that the translation can be considered as a general form of call-by-name CPS-translation. We also consider the isomorphism between CND and m-cut free fragment of LKT based on Santo's idea(Santo 2000). keywords: Constructive Classical Logic, Classical Natural Deduction, LKT, CPS-translation, classical proof theory.
منابع مشابه
A CPS-Transform of Constructive Classical Logic
We show that the cut-elimination for LKT, as presented in Danos et al.(1993), simulates the normalization for classical natural deduction(CND). Particularly, the denotation for CND inherits the one for LKT. Moreover the transform from CND proof (i.e., Parigot's -term) to LKT proof can be considered as a classical extension to call-by-name (CBN) CPS-transform.
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