The correspondence between cut-elimination and normalization II
نویسندگان
چکیده
منابع مشابه
Correspondence between Normalization of CND and Cut-Elimination of LKT
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...
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Cut-free proofs in Herbelin’s sequent calculus are in 1-1 correspondence with normal natural deduction proofs. For this reason Herbelin’s sequent calculus has been considered a privileged middle-point between L-systems and natural deduction. However, this bijection does not extend to proofs containing cuts and Herbelin observed that his cutelimination procedure is not isomorphic to β-reduction....
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Pairs of systems, which consist of a system of sequents and a natural deduction system for some part of intuitionistic logic, are considered. For each of these pairs of systems the property that the normalization theorem is a consequence of the cut-elimination theorem is presented.
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This paper aims to give an introduction to Type Logical Grammar (TLG) for the general linguist who may not have a background in logic or proof theory. It is shorter than book-length treatments such as Hepple 1990, Morrill 1994, Carpenter 1996, Jäger 2001, and Moot 2002, and less technical than surveys such as Moortgat 1997. What does it mean to use logic as a grammatical formalism? The short an...
متن کاملProof Fragments, Cut-Elimination and Cut-Introduction
Cut-elimination is usually presented as a set of local proof reduction steps together with a terminating strategy thus showing the existence of cut-free proofs for all provable sequents. Viewing cut-elimination as a transformation of mathematical proofs, not only the existence but also the structure and content of the cut-free proofs deserves investigation. In this paper we use proof skeletons ...
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1974
ISSN: 0003-4843
DOI: 10.1016/0003-4843(74)90011-4