Journal of Philosophical Logic

, Volume 44, Issue 5, pp 473–487

Analytic Tableaux for all of SIXTEEN3

Article

DOI: 10.1007/s10992-014-9337-3

Cite this article as:
Muskens, R. & Wintein, S. J Philos Logic (2015) 44: 473. doi:10.1007/s10992-014-9337-3
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Abstract

In this paper we give an analytic tableau calculus PL16 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.

Keywords

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

Copyright information

© 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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