Minimality of the correctness criterion for multiplicative proof nets

نویسنده

  • Denis Béchet
چکیده

Received Almost a decade ago, Girard invented linear logic with the notion of proof-net. Proof-nets are special graphs built from formulas, links and boxes. However, not all nets are proof-nets. Firstly, they must be well constructed (we say that such graphs are proof-structures). Secondly, a proof-net is a proof-structure that corresponds to a sequential proof. It must verify a correctness criterion. One may wander what this static criterion means for cut-elimination. We prove that every not-correct proof-structure (without cut) can be put in an environment where reductions lead to two kinds of wrong basically conngurations: deadlocks and disconnected proof-structures. Thus, this proof says that there does not exist a bigger class than proof-nets of proof-structures where normalization does not lead to very bad conngurations.

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عنوان ژورنال:
  • Mathematical Structures in Computer Science

دوره 8  شماره 

صفحات  -

تاریخ انتشار 1998