A note on extensions: Admissible rules via semantics

Jeroen Goudsmit*

*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review


Any intermediate logic with the disjunction property admits the Visser rules if and only if it has the extension property. This equivalence restricts nicely to the extension property up to n. In this paper we demonstrate that the same goes even when omitting the rule ex falso quod libet, that is, working over minimal rather than intuitionistic logic. We lay the groundwork for providing a basis of admissibility for minimal logic, and tie the admissibility of the Mints-Skura rule to the extension property in a stratified manner.

Original languageEnglish
Title of host publicationLogical Foundations of Computer Science - International Symposium, LFCS 2013, Proceedings
Number of pages13
Publication statusPublished - 1 Dec 2013
EventInternational Symposium on Logical Foundations of Computer Science, LFCS 2013 - San Diego, CA, United States
Duration: 6 Jan 20138 Jan 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7734 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceInternational Symposium on Logical Foundations of Computer Science, LFCS 2013
Country/TerritoryUnited States
CitySan Diego, CA


  • Admissible rules
  • Disjunction property
  • Extensions of Kripke models
  • Minimal logic


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