MELL in the calculus of structures

✍ Scribed by Lutz Straßburger

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 591 KB
• Volume: 309
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(03)00240-8

✦ Synopsis

The calculus of structures is a new proof theoretical formalism, like natural deduction, the sequent calculus and proof nets, for specifying logical systems syntactically. In a rule in the calculus of structures, the premise as well as the conclusion are structures, which are expressions that share properties of formulae and sequents. In this paper, I study a system for MELL, the multiplicative exponential fragment of linear logic, in the calculus of structures. It has the following features: a local promotion rule, no non-deterministic splitting of the context in the times rule and a modular proof for the cut elimination theorem. Further, derivations have a new property, called decomposition, that cannot be observed in any other known proof theoretical formalism.