Interpolation in 16-Valued Trilattice Logics

摘要

In a recent paper we have defined an analytic tableau calculus for a functionally complete extension of Shramko and Wansing's logic based on the trilattice . This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic-such as the relations , , and that each correspond to a lattice order in ; and , the intersection of and . It turns out that our method of characterising these semantic relations-as intersections of auxiliary relations that can be captured with the help of a single calculus-lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that , when restricted to , the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano.