Disjunctive and Conjunctive Multiple-Conclusion Consequence Relations

  • Marek NowakEmail author


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.


Closure operation Closure system Multiple-conclusion consequence relation Galois connection 


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


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of LogicUniversity of LodzLodzPoland

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