Completeness of Subtrilattice Logic

Abstract

In this study, a new trilattice logic called subtrilattice logic (STL) is introduced in the form of a monosequent calculus, which is based on a restricted sequent that contains exactly one formula in both the antecedent and the succedent. Further, the completeness (with respect to the lattice-valued semantics), cut-elimination, decidability, and Craig interpolation theorems for STL are proved using an embedding-based technique.