Admissible rules in the implication–negation fragment of intuitionistic logic

Petr Cintula,George Metcalfe

doi:10.1016/j.apal.2010.09.001

Admissible rules in the implication–negation fragment of intuitionistic logic

Petr Cintula, George Metcalfe

https://doi.org/10.1016/j.apal.2010.09.001

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Journal: Annals of Pure and Applied Logic	Publication Date: Oct 12, 2010
Citations: 47	License type: elsevier-specific: oa user license

Affiliation: Czech Academy of Sciences, Institute of Computer Science, University of Bern

#Intermediate Logics #Finite Basis + Show 8 more

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Abstract

Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic IPC and its consistent axiomatic extensions (intermediate logics). A Kripke semantics characterization is given for the (hereditarily) structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of IPC form a PSPACE-complete set and have no finite basis.

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