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Interpolation in 16-Valued Trilattice Logics |
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| Authors: | Reinhard Muskens Stefan Wintein |
| Affiliation: | 1.Tilburg Center for Logic, Ethics and Philosophy of Science (TiLPS),Tilburg University,Tilburg,The Netherlands;2.Faculty of Philosophy,Erasmus University Rotterdam,Rotterdam,The Netherlands |
| 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 Open image in new window Open image in new window Open image in new window ({SIXTEEN}_3); and Open image in new window Open image in new window Open image in new window Open image in new window (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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