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A Note on Extensions: Admissible Rules via Semantics

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Logical Foundations of Computer Science (LFCS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7734))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Utrecht University, Janskerkhof 13a, 3512BL, Utrecht, The Netherlands

    Jeroen Goudsmit

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  1. Jeroen Goudsmit
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Editors and Affiliations

  1. Computer Science, CUNY Graduate Center, 365 Fifth Avenue, 10016, New York, NY, USA

    Sergei Artemov

  2. Department of Mathematics, Cornell University, 545 Malott Hall, 14853, Ithaca, NY, USA

    Anil Nerode

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Goudsmit, J. (2013). A Note on Extensions: Admissible Rules via Semantics. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2013. Lecture Notes in Computer Science, vol 7734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35722-0_15

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  • DOI: https://doi.org/10.1007/978-3-642-35722-0_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35721-3

  • Online ISBN: 978-3-642-35722-0

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