Disjunction property and complexity of substructural logics

Authors:
Rostislav Horík;Kazushige Terui
Affiliations:
Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou ví 2, 182 07 Prague 8, Czech Republic;Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

We systematically identify a large class of substructural logics that satisfy the disjunction property (DP), and show that every consistent substructural logic with the DP is PSPACE-hard. Our results are obtained by using algebraic techniques. PSPACE-completeness for many of these logics is furthermore established by proof theoretic arguments.