Journal of Philosophical Logic

, Volume 44, Issue 5, pp 473–487 | Cite as

Analytic Tableaux for all of SIXTEEN 3

  • Reinhard MuskensEmail author
  • Stefan Wintein


In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t , ⊧ f , ⊧ i , and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment relations will in general require developing four tableaux, while proving that they are in the ⊧ relation may require six.


Trilattice SIXTEEN3 Tableau calculi Functional completeness Truth entailment Falsity entailment Information entailment 



We would like to thank the referee for encouraging words and helpful comments. Stefan Wintein wants to thank the Netherlands Organisation for Scientific Research (NWO) for funding the project The Structure of Reality and the Reality of Structure (project leader: F. A. Muller), in which he is employed. Reinhard Muskens gratefully acknowledges NWO’s funding of his project 360-80-050, Towards Logics that Model Natural Reasoning.


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Tilburg Center for Logic, Ethics, and Philosophy of Science (TiLPS)Tilburg UniversityTilburgNetherlands
  2. 2.Faculty of PhilosophyErasmus University RotterdamRotterdamNetherlands

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