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A Method of Defining Paraconsistent Tableaus

  • Tomasz Jarmużek
  • Marcin Tkaczyk
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 152)

Abstract

The aim of this paper is to show how to simply define paraconsistent tableau systems by liberalization of construction of complete tableaus. The presented notions allow us to list all tableau inconsistencies that appear in a complete tableau. Then we can easily choose these inconsistencies that are effects of interactions between premises and a conclusion, simultaneously excluding other inconsistencies. A general technique we describe is presented here for the case of Propositional Logic, as the simplest one, but it can be easily extended to more complex cases. In other words, a kind of paraconsistent consequence relation is being studied here, and a simple tableau system is shown to exist that captures that consequence relation.

Keywords

Blind rule Paraconsistent consequence relation Paraconsistent tableaus t-inconsistency Tableau rules Tableaus 

Mathematics Subject Classification (2000)

Primary 99Z99 Secondary 00A00 

Notes

Acknowledgments

Many thanks to an anonymous reviewer for helpful comments and suggestions.

References

  1. 1.
    Priest, G.: An Introduction to Non-Classical Logic. Cambridge University Press, Cambridge (2001)Google Scholar
  2. 2.
    Jarmużek, T.: Formalizacja metod tablicowych dla logik zdań i logik nazw (Formalization of tableau methods for propositional logics and for logics of names). Wydawnictwo UMK, Toruń (2013)Google Scholar
  3. 3.
    Jarmużek, T.: Tableau Metatheorem for Modal Logics. In: Ciuni, R., Wansing, H., Willkommen, C. (eds.) Recent Trends in Philosophical Logic, pp. 105–123. Springer (2013)Google Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Departament of LogicNicolaus Copernicus University in ToruńToruńPoland
  2. 2.Departament of LogicThe John Paul II Catholic University of LublinLublinPoland

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