MELL in the calculus of structures
نویسنده
چکیده
Gentzen’s sequent calculus is a tool to study properties of logics independently of semantics. The main property is cut-elimination which entails the subformula property and consistency. It is also the basis of methods of automated deduction. Although the sequent calculus is very appropriate for classical logic, it raises some concerns in dealing with more refined logics like linear logic. An example is the global behaviour of the promotion rule. The calculus of structures is a recent development that is able to overcome those difficulties without losing the ability of performing a cut-elimination proof. Moreover, the cut rule can be reduced to its atomic form in the same way as the identity axiom can. In this paper I will carry out the exercise of describing the multiplicative exponential fragment of linear logic in the calculus of structures. We get the following advantages over the sequent calculus representation: no non-deterministic splitting of the context in the times rule, a local rule for promotion, a modular proof for the cut-elimination theorem, and a decomposition theorem for derivations and proofs.
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عنوان ژورنال:
- Theor. Comput. Sci.
دوره 309 شماره
صفحات -
تاریخ انتشار 2003