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On Modal Logics Defining Jaśkowski-Like Discussive Logics

  • Marek Nasieniewski
  • Andrzej Pietruszczak
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 152)

Abstract

The present paper concerns Jaśkowski-like discussive logics which arise by modification of Jaśkowski’s original translation of discussive conjunction. In each case, we indicate the smallest modal logic defining a given Jaśkowski-like discussive logic.

Keywords

Modal logic Jaśkowski logic \(\mathbf {D}_{\mathbf {2}}\) Jaśkowski-like discussive logics Minimal modal logics defining \(\mathbf {D}_{\mathbf {2}}\) Minimal modal logics defining Jaśkowski-like discussive logics Jaśkowski’s problem 

Mathematics Subject Classification (2000)

Primary 03B45 Secondary 03B53 

Notes

Acknowledgments

We would like to thank anonymous referee for her/his useful suggestions on a previous version of this paper.

References

  1. 1.
    Bull, R.A., Segerberg, K.: Basic modal logic. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. II, pp. 1–88. D. Reidel Publishing Company, Dordrecht (1984)Google Scholar
  2. 2.
    Chellas, B.F.: Modal Logic. An Introduction. Cambridge University Press, Cambridge (1980)CrossRefzbMATHGoogle Scholar
  3. 3.
    Ciuciura, J.: On the da Costa, Dubikajtis and Kotas’ system of the discursive logic, \({\mathbf{D}}_{\mathbf{2}}^{\varvec {*}}\). Logic Log. Philos. 14, 235–252 (2005)MathSciNetzbMATHGoogle Scholar
  4. 4.
    da Costa, N.C.A., Dubikajtis, L.: On Jaśkowski’s discussive logic. In: Arruda, A.I., da Costa, N.C.A., Chuaqui, R. (eds.) Non-Classical Logics, Model Theory and Computability, pp. 57–73. North-Holland Publishing, Amsterdam (1977)Google Scholar
  5. 5.
    Jaśkowski, S.: Rachunek zdań dla systemów dedukcyjnych sprzecznych. Studia Societatis Scientiarum Torunensis, Sect. A, I(5), pp. 57–77 (1948). The first English version: Propositional calculus for contradictory deductive systems. Studia Logica, vol. 24, pp. 143–157 (1969). The second English version: Logic and Logical Philosophy, vol. 7, pp. 35–56 (1999)Google Scholar
  6. 6.
    Jaśkowski, S.: O koniunkcji dyskusyjnej w rachunku zdań dla systemów dedukcyjnych sprzecznych. Studia Societatis Scientiarum Torunensis, Sect. A, vol. I, no. 8, pp. 171–172 (1949). The English version: On the discussive conjunction in the propositional calculus for inconsistent deductive systems. Logic and Logical Philosophy, vol. 7, pp. 57–59 (1999)Google Scholar
  7. 7.
    Kotas, J., da Costa, N.C.A.: On some modal logical systems defined in connexion with Jaśkowski’s problem. In: Arruda, A.I., da Costa, N.C.A., Chuaqui, R. (eds.) Non Classical Logics, Model Theory and Computability, pp. 57–73. North-Holland Publishing, Amsterdam (1977)Google Scholar
  8. 8.
    Nasieniewski, M., Pietruszczak, A.: A method of generating modal logics defining Jaśkowski’s discussive logic D\(_{2}\). Stud. Logica 97(1), 161–182 (2011)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Nasieniewski, M., Pietruszczak, A.: On the weakest modal logics defining Jaśkowski’s logic D\(_{2}\) and the D\(_{2}\)-consequence. Bull. Sect. Logic 41, 215–232 (2012)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Nasieniewski, M., Pietruszczak, A.: On modal logics defining Jaśkowski’s D2-consequence. In: Tanaka, K., Berto, F., Mares, E., Paoli, F. (eds.) Paraconsistency: Logic and Applications, chapter IX, Logic, Epistemology and the Unity of Science Series, vol. 26, pp. 141–160. Springer (2013)Google Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Department of LogicNicolaus Copernicus University in ToruńToruńPoland

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