eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2013-09-02
197
214
10.4230/LIPIcs.CSL.2013.197
article
Annotation-Free Sequent Calculi for Full Intuitionistic Linear Logic
Clouston, Ranald
Dawson, Jeremy
Goré, Rajeev
Tiu, Alwen
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex annotations to guarantee soundness and cut-elimination. We give a simple and annotation-free display calculus for FILL which satisfies Belnap’s generic cut-elimination theorem. To do so, our display calculus actually handles an extension of FILL, called Bi-Intuitionistic Linear Logic (BiILL), with an ‘exclusion’ connective defined via an adjunction with par. We refine our display calculus for BiILL into a cut-free nested sequent calculus with deep inference in which the explicit structural rules of the display calculus become admissible. A separation property guarantees that proofs of FILL formulae in the deep inference calculus contain no trace of exclusion. Each such rule is sound for the semantics of FILL, thus our deep inference calculus and display calculus are conservative over FILL. The deep inference calculus also enjoys the subformula property and terminating backward proof search, which gives the NP-completeness of BiILL and FILL.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol023-csl2013/LIPIcs.CSL.2013.197/LIPIcs.CSL.2013.197.pdf
Linear logic
display calculus
nested sequent calculus
deep inference