Admissible rules in the implication-negation fragment of intuitionistic logic |
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Authors: | Petr Cintula George Metcalfe |
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Institution: | a Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodarenskou vezi 2, 182 07 Prague 8, Czech Republicb Mathematics Institute, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland |
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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 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 form a PSPACE-complete set and have no finite basis. |
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Keywords: | 03B20 03B22 03B55 |
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