The Admissible Rules of BD2 and GSc

Jeroen P. Goudsmit

doi:10.1215/00294527-3838972

The Admissible Rules of BD2 and GSc

Jeroen P. Goudsmit

VU SBE Executive Education

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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 language	English
Pages (from-to)	325-353
Number of pages	29
Journal	NOTRE DAME JOURNAL OF FORMAL LOGIC
Volume	59
Issue number	3
Early online date	2 Aug 2017
DOIs	https://doi.org/10.1215/00294527-3838972
Publication status	Published - 2018

Funding

Support by the Netherlands Organization for Scientific Research under grant 639.032.918 is gratefully acknowledged. The author would like to thank the anonymous referee for their helpful comments.

Funders	Funder number
Netherlands Organization for Scientific Research	639.032.918

Keywords

admissible rules
intermediate logics
intuitionistic logic
universal model

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The Admissible Rules of BD2 and GSc

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