Bunched Hypersequent Calculi for Distributive Substructural Logics

18 pages•Published: May 4, 2017

Agata Ciabattoni and Revantha Ramanayake

Abstract

We introduce a new proof-theoretic framework which enhances the expressive power of bunched sequents by extending them with a hypersequent structure. A general cut-elimination theorem that applies to bunched hypersequent calculi satisfying general rule conditions is then proved. We adapt the methods of transforming axioms into rules to provide cutfree bunched hypersequent calculi for a large class of logics extending the distributive commutative Full Lambek calculus DFLe and Bunched Implication logic BI. The methodology is then used to formulate new logics equipped with a cutfree calculus in the vicinity of Boolean BI.

Keyphrases: bbi, bunched calculi, cut elimination, distributive substructural logics, dunn mints calculi, hypersequents, logic of bunched implications, separation logic, structural rules

In: Thomas Eiter and David Sands (editors). LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 46, pages 417-434.

Links:	https://easychair.org/publications/paper/sr2D
	https://doi.org/10.29007/ngp3

BibTeX entry

@inproceedings{LPAR-21:Bunched_Hypersequent_Calculi_Distributive,
  author    = {Agata Ciabattoni and Revantha Ramanayake},
  title     = {Bunched Hypersequent Calculi for Distributive Substructural Logics},
  booktitle = {LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Thomas Eiter and David Sands},
  series    = {EPiC Series in Computing},
  volume    = {46},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/sr2D},
  doi       = {10.29007/ngp3},
  pages     = {417-434},
  year      = {2017}}

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