A Syntactic Characterization of the Gabbay-de Jongh Logics

3 pages•Published: July 28, 2014

Abstract

Skura syntactically characterised intuitionistic propositional logic among all intermediate logics by means of a Łukasiewicz-style refutation system. Another such syntactic characterisation is given by Iemhoff in terms of admissible rules. Here we offer a bridge between these results. That is to say, we provide sufficient conditions under which admissible rules yield a refutation system fully characterising the logic. In particular, we give a characterisation of the Gabbay–de Jongh logics by means of refutation systems employing ideas from admissibility.

Keyphrases: admissible rules, gabbay de jongh logics, intermediate logic, refutation systems

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 82-84.

Links:	https://easychair.org/publications/paper/wM8
	https://doi.org/10.29007/1mcd

BibTeX entry

@inproceedings{TACL2013:Syntactic_Characterization_Gabbay_de,
  author    = {Jeroen Goudsmit},
  title     = {A Syntactic Characterization of the Gabbay-de Jongh Logics},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/wM8},
  doi       = {10.29007/1mcd},
  pages     = {82-84},
  year      = {2014}}

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