Skip to main content
SpringerLink
Log in

Truth, Partial Logic and Infinitary Proof Systems

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an \(\omega \)-rule.

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. Blamey, S., Partial logic. In D. Gabbay and F. Guenthner, (eds.), Handbook of Philosophical Logic, vol. 5, Kluwer, 2 edn., 2002, pp. 261–353.

  2. Buchholz, W., Skript: Logik I, 2001.

  3. Burgess, J. P., The truth is never simple. The Journal of Symbolic Logic 51:663–681, 1986.

  4. Buss, S. R., (ed.). Handbook of Proof Theory. Elsevier Science Publisher, Amsterdam, 1998.

  5. Cantini, A., Notes on formal theories of truth. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 35:97–130, 1989.

    Article  Google Scholar 

  6. Cantini, A., A theory of formal truth arithmetically equivalent to ID\(_1\). The Journal of Symbolic Logic 55:244–259, 1990.

    Article  Google Scholar 

  7. Field, H., Saving Truth from Paradox. Oxford University Press, Oxford 2008.

  8. Fischer, M., V. Halbach, J. Kriener, and J. Stern. Axiomatizing semantic theories of truth? Review of Symbolic Logic 8:257–278, 2015.

    Article  Google Scholar 

  9. Fischer, M., L. Horsten, and C. Nicolai. Iterated reflection over full disquotational truth. To appear in Journal of Logic and Computation, 2017. doi:10.1093/logcom/exx023.

  10. Halbach, V., Axiomatic Theories of Truth. Cambridge University Press, Cambridge, UK, revised edition, 2014.

  11. Halbach, V., and Horsten, L., Axiomatizing Kripke’s theory of truth. The Journal of Symbolic Logic 71:677–712, 2006.

    Article  Google Scholar 

  12. Halbach, V., and C. Nicolai. On the costs of nonclassical logic. Journal of Philosophical Logic, 2017. doi:10.1007/s10992-017-9424-3.

  13. Kripke, S., Outline of a theory of truth. The Journal of Philosophy 72:690–716, 1975.

    Article  Google Scholar 

  14. Meadows, T., Infinitary tableau for semantic truth. Review of Symbolic Logic 8(2):207–235, 2015.

    Article  Google Scholar 

  15. Priest, G., In Contradiction. Oxford University Press, Oxford, 2 edition, 2006.

  16. Reinhardt, W. N., Some remarks on extending and interpreting theories with a partial predicate for truth. The Journal of Philosophical Logic 15:219–251, 1986.

  17. Welch, P., Games for truth. Bulletin of Symbolic Logic 15(4): 410-427, 2009

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ludwig-Maximilians-Universität, München, Germany

    Martin Fischer & Norbert Gratzl

Authors
  1. Martin Fischer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Norbert Gratzl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin Fischer.

Additional information

Presented by Heinrich Wansing

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fischer, M., Gratzl, N. Truth, Partial Logic and Infinitary Proof Systems. Stud Logica 106, 515–540 (2018). https://doi.org/10.1007/s11225-017-9751-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-017-9751-y

Keywords

Search

Navigation