Complexity of Admissible Rules in the Implication-Negation Fragment of Intuitionistic Logic

5 pages•Published: March 25, 2013

Abstract

The goal of this paper is to study the complexity of the set of admissible rules of the implication-negation fragment of intuitionistic logic IPC. Surprisingly perhaps, although this set strictly contains the set of derivable rules (the fragment is not structurally complete), it is also PSPACE-complete. This differs from the situation in the full logic IPC where the admissible rules form a co-NEXP-complete set.

Keyphrases: admissible rules, computational complexity, intuitionistic logic

In: Andrei Voronkov, Geoff Sutcliffe, Matthias Baaz and Christian Fermüller (editors). LPAR-17-short. short papers for 17th International Conference on Logic for Programming, Artificial intelligence, and Reasoning., vol 13, pages 30-34.

Links:	https://easychair.org/publications/paper/HJc
	https://doi.org/10.29007/cll3

BibTeX entry

@inproceedings{LPAR-17-short:Complexity_Admissible_Rules_Implication,
  author    = {Petr Cintula and George Metcalfe},
  title     = {Complexity of Admissible Rules in the Implication-Negation Fragment of Intuitionistic Logic},
  booktitle = {LPAR-17-short. short papers for 17th International Conference on Logic for Programming, Artificial intelligence, and Reasoning.},
  editor    = {Andrei Voronkov and Geoff Sutcliffe and Matthias Baaz and Christian Fermüller},
  series    = {EPiC Series in Computing},
  volume    = {13},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/HJc},
  doi       = {10.29007/cll3},
  pages     = {30-34},
  year      = {2013}}

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