Trilattice logic: an embedding-based approach

Paraconsistent many-valued logics are known to be useful for describing inconsistency-tolerant and uncertain reasoning more appropriately than logics that are non-paraconsistent and two-valued. Shramko-Wansing's trilattice logics are paraconsistent sixteen-valued logics based on the algebraic structures of trilattices that can suitably represent generalized truth values. In this article, an alternative new proof of the cut-elimination and completeness theorems for such a trilattice logic is obtained using two embedding theorems. The Craig interpolation and Maksimova separation theorems for this logic are also proved using the same embedding theorems. The results on Craig interpolation and Maksimova separation are new results of this article. Moreover, the above mentioned results are extended to a temporal extension of the trilattice logic. The results on the temporal extension are also new contribution of this article.