Disjunctive Multiple-Conclusion Consequence Relations

Marek Nowak

doi:10.18778/0138-0680.48.4.05

Authors

Marek Nowak Department of Logic and Methodology of Science, University of Lodz, Poland

DOI:

https://doi.org/10.18778/0138-0680.48.4.05

Keywords:

multiple-conclusion consequence relation, closure operation, Galois connection

Abstract

The concept of multiple-conclusion consequence relation from [8] and [7] is considered. The closure operation C assigning to any binary relation r (dened on the power set of a set of all formulas of a given language) the least multiple-conclusion consequence relation containing r, is dened on the grounds of a natural Galois connection. It is shown that the very closure C is an isomorphism from the power set algebra of a simple binary relation to the Boolean algebra of all multiple-conclusion consequence relations.

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