Embedding-Based Methods for Trilattice Logic

Shramko-Wansing´s trilattice logics are sixteen-valued logics based on the algebraic structures of trilattices that can suitably represent generalized truth values. In this paper, an alternative new proof of the cut-elimination and completeness theorems for such a trilattice logic is obtained using two embedding theorems. Moreover, the Craig interpolation and Maksimova separation theorems for this logic are proved using the same embedding theorems. The results on Craig interpolation and Maksimova separation are new results of this paper.