Disjunctive and Conjunctive Multiple-Conclusion Consequence Relations

Abstract

Two different kinds of multiple-conclusion consequence relations taken from Shoesmith and Smiley (Multiple-conclusion logic, Cambridge University Press, Cambridge, 1978) and Galatos and Tsinakis (J Symb Logic 74:780–810, 2009) or Nowak (Bull Sect Logic 46:219–232, 2017), called here disjunctive and conjunctive, respectively, defined on a formal language, are considered. They are transferred into a bounded lattice and a complete lattice, respectively. The properties of such abstract consequence relations are presented.

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Acknowledgements

I am very indebted to both anonymous referees for their useful hints changing essentially the first version of the text.

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Correspondence to Marek Nowak.

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Presented by Andrzej Indrzejczak

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Nowak, M. Disjunctive and Conjunctive Multiple-Conclusion Consequence Relations. Stud Logica 108, 1125–1143 (2020). https://doi.org/10.1007/s11225-019-09889-8

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Keywords

  • Closure operation
  • Closure system
  • Multiple-conclusion consequence relation
  • Galois connection