The Admissible Rules of BD2 and GSc

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Abstract

The Visser rules form a basis of admissibility for the intuitionistic propositional calculus. We show how one can characterize the existence of covers in certain models by means of formulae. Through this characterization, we provide a new proof of the admissibility of a weak form of the Visser rules. Finally, we use this observation, coupled with a description of a generalization of the disjunction property, to provide a basis of admissibility for the intermediate logics BD2 and GSc.
Original languageEnglish
Pages (from-to)325-353
Number of pages29
JournalNOTRE DAME JOURNAL OF FORMAL LOGIC
Volume59
Issue number3
DOIs
Publication statusPublished - 2018

Keywords

  • admissible rules
  • intermediate logics
  • intuitionistic logic
  • universal model

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