Disjunctive and Conjunctive Multiple-Conclusion Consequence Relations.

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. [ABSTRACT FROM AUTHOR]