An Elementary Proof of the Characterization Theorem for Conjunctive Multiple-Conclusion Consequence Relations

We give a characterization theorem for multiple-conclusion consequence relations with the conjunctive reading of conclusions. As in the case of disjunctive multiple-conclusion consequence relations, we define consequence relations in terms of sets of two-set partitions of formulae. We see that a binary relation between sets of formulae is a conjunctive multiple-conclusion consequence relation if it is closed under the properties of inclusion, transitivity and reducibility. To prove this result we use only the definition and some basic properties of conjunctive multiple-conclusion consequence relations.