A System of Interaction and Structure V: The Exponentials and Splitting

Alessio Guglielmi (1) , Lutz Strassburger (2)

1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
2 PARSIFAL - Proof search and reasoning with logic specifications

System NEL is the mixed commutative/non-commutative linear logic BV augmented with linear logic's exponentials, or, equivalently, it is MELL augmented with the non-commutative self-dual connective seq. System NEL is Turing-complete, it is able to directly express process algebra sequential composition and it faithfully models causal quantum evolution. In this paper, we show cut elimination for NEL, based on a property that we call splitting. NEL is presented in the calculus of structures, which is a deep-inference formalism, because no Gentzen formalism can express it analytically. The splitting theorem shows how and to what extent we can recover a sequent-like structure in NEL proofs. Together with the decomposition theorem, proved in the previous paper of the series, this immediately leads to a cut-elimination theorem for NEL.

Domaines: Logique en informatique [cs.LO]

Alessio Guglielmi, Lutz Strassburger. A System of Interaction and Structure V: The Exponentials and Splitting. Mathematical Structures in Computer Science, 2011, pp.1-22. ⟨10.1017/S096012951100003X⟩. ⟨inria-00441254v2⟩