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

5 pagesPublished: 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