From Display Calculi to Deep Nested Sequent Calculi: Formalised for Full Intuitionistic Linear Logic

  • Jeremy E. Dawson
  • Ranald Clouston
  • Rajeev Goré
  • Alwen Tiu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8705)


Proof theory for a logic with categorical semantics can be developed by the following methodology: define a sound and complete display calculus for an extension of the logic with additional adjunctions; translate this calculus to a shallow inference nested sequent calculus; translate this calculus to a deep inference nested sequent calculus; then prove this final calculus is sound with respect to the original logic. This complex chain of translations between the different calculi require proofs that are technically intricate and involve a large number of cases, and hence are ideal candidates for formalisation. We present a formalisation of this methodology in the case of Full Intuitionistic Linear Logic (FILL), which is multiplicative intuitionistic linear logic extended with par.


Proof System Logical Rule Proof Theory Structural Rule Sequent Calculus 
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Copyright information

© IFIP International Federation for Information Processing 2014

Authors and Affiliations

  • Jeremy E. Dawson
    • 1
  • Ranald Clouston
    • 2
  • Rajeev Goré
    • 1
  • Alwen Tiu
    • 3
  1. 1.Research School of Computer ScienceAustralian National UniversityAustralia
  2. 2.Department of Computer ScienceAarhus UniversityDenmark
  3. 3.School of Computer EngineeringNanyang Technological UniversitySingapore

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