Contradictions in Multiverse

A translation of Priest’s paraconsistent logic daC into many-sorted logic is presented. Besides, following the project of (Manzano, 1996), the representation theorem, the main theorem and the calculi equivalence are proved. So, it is demonstrated that the formulated translation preserves the set of valid formulas, the consequence relation, and the derivation relation of daC. Furthermore, the compactness and Löwenheim-Skolem theorems are proved for this logic. Alternative proofs for the soundness and completeness theorems for daC based on the translation are also presented.