Some general results about proof normalization

Logica Universalis 4 (1):1-29 (2010)
Abstract
In this paper, we provide a general setting under which results of normalization of proof trees such as, for instance, the logicality result in equational reasoning and the cut-elimination property in sequent or natural deduction calculi, can be unified and generalized. This is achieved by giving simple conditions which are sufficient to ensure that such normalization results hold, and which can be automatically checked since they are syntactical. These conditions are based on basic properties of elementary combinations of inference rules which ensure that the induced global proof tree transformation processes do terminate.
Keywords Formal systems  proof tree transformation  weak andstrong normalization  cut-elimination  rewriting
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DOI 10.1007/s11787-010-0011-4
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Proofs and Types.Jean-Yves Girard - 1989 - Cambridge University Press.

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