Abstract
In a recent paper we have defined an analytic tableau calculus \({{\mathbf {\mathsf{{PL}}}}}_{\mathbf {16}}\) for a functionally complete extension of Shramko and Wansing’s logic based on the trilattice \({SIXTEEN}_3\). 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 \({SIXTEEN}_3\); 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 \(\mathcal {L}_{tf}\), the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano.
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Presented by Heinrich Wansing
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Muskens, R., Wintein, S. Interpolation in 16-Valued Trilattice Logics. Stud Logica 106, 345–370 (2018). https://doi.org/10.1007/s11225-017-9742-z
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DOI: https://doi.org/10.1007/s11225-017-9742-z