Skip to main content
SpringerLink
Log in

Some paraconsistent sentential calculi

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

In [8] Jaśkowski defined by means of an appropriate interpretation a paraconsistent calculusD 2 . In [9] J. Kotas showed thatD 2 is equivalent to the calculusM(S5) whose theses are exactly all formulasa such thatMa is a thesis ofS5. The papers [11], [7], [3], and [4] showed that interesting paraconsistent calculi could be obtained using modal systems other thanS5 and modalities other thanM. This paper generalises the above work. LetA be an arbitrary modality (i.e. string ofM's,L's and negation signs). Then theA-extension of a set of formulasX is {α¦Aα ε X}}. Various properties ofA-extensions of normal modal systems are examined, including a problem of their axiomatizability

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. J. Błaszczuk,Remarks on M n -counterparts of some normal calculi,Bulletin of the Section of Logic, Polish Academy of Sciences, Vol. 6, No. 2 (1977), pp. 82–86.

    Google Scholar 

  2. J. J. Błaszczuk,Weakest normal modal calculi with respect to M n -counterparts,Bulletin of the Section of Logic, Polish Academy of Sciences, Vol.7, No. 3 (1978), pp. 102–106.

    Google Scholar 

  3. J. J. Błaszczuk, W. Dziobiak,An axiomatization of M n -counterparts for some modal logics,Reports on Mathematical Logic, Vol. 6 (1976), pp. 3–6.

    Google Scholar 

  4. J. J. Błaszczuk, W. Dziobiak,Modal logics connected with systems S4 n of Sobociński,Studia Logica, Vol. XXXVI, No. 3 (1977), pp. 151–164.

    Google Scholar 

  5. M. J. Cresswell, G. E. Hughes,An Introduction to Modal Logics, Methuen and Co. Ltd., London 1968.

    Google Scholar 

  6. W. Dziobiak,Semantics of Kripke's style for some modal systems.Bulletin of the Section of Logic, Polish Academy of Sciences, Vol. 5, No. 2 (1976), pp. 63–67.

    Google Scholar 

  7. T. Furmanowski,Remarks on discussive propositional calculus,Studia Logica, Vol. XXXIV, No. 1 (1975), pp. 39–43.

    Google Scholar 

  8. S. Jaśkowski,Rachunek zdań dla systemów dedukcyjnych sprzecznych,Studia Societatis Scientiarum Torunensis, Vol. 1 (1948), 57–77. (An English translation of this paper appeared inStudia Logica, Vol. XXIV (1969), pp. 143–157.)

    Google Scholar 

  9. J. Kotas,The axiomatization of S. Jaśkowski's discussive system,Studia Logica, Vol. XXXIII, No. 2 (1974), pp. 195–200.

    Google Scholar 

  10. J. Kotas. N. C. A. da Costa,On some modal logical systems defined in connection to Jaśkowski's problem, inNon-Classical Logics, Model Theory and Computability (Eds. A. I. Arruda, N. C. A. da Costa and R. Chuaqui), North-Holland, 1977, pp. 57–73.

  11. J. Perzanowski,On M-fragments and L-fragments of normal modal propositional logics,Reports on Mathematical Logic, Vol. 5 (1975), pp. 63–72.

    Google Scholar 

  12. K. Segerberg,An Essay in Classical Modal Logic, Uppsala 1971.

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Nicholas Copernicus University, Poland

    Jerzy J. Błaszczuk

Authors
  1. Jerzy J. Błaszczuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Błaszczuk, J.J. Some paraconsistent sentential calculi. Stud Logica 43, 51–61 (1984). https://doi.org/10.1007/BF00935739

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00935739

Keywords

Search

Navigation