Skip to main content
Log in

If-Logic and Truth-definition

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

In this paper we show that first-order languages extended with partially ordered connectives and partially ordered quantifiers define, under a certain interpretation, their own truth-predicate. The interpretation in question is in terms of games of imperfect information. This result is compared with those of Kripke and Feferman.

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

Access this article

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. Barwise, J.: Some applications of the Henkin quantifiers, Israel J. of Mathematics, 25 (1976), 47- 63.

    Google Scholar 

  2. Blass, A. and Gurevich, Y.: Henkin Quantifiers and Complete Problems, Annals of Pure and Applied Logic, 32 (1986), 1- 16.

    Google Scholar 

  3. Enderton, H. B.: Finite partially-ordered quantifiers, Z. Math. Logic Grundlag. Math. 16 (1970), 393- 397.

    Google Scholar 

  4. Hella, L. and Sandu, G.: Partially ordered connectives and finite graphs, in: M. Mostowski, M. Krynicki and L. V. Szczerba (eds), Quantifiers II, Kluwer Academic Publishers (1995), 79- 88.

  5. Henkin, L.: Some remarks on infinitely long formulas, in: Infinitistic Methods, Warsaw (1961), 167- 183.

  6. Hintikka, J. and Kulas, J.: The Game of Language, D. Reidel, Dordrecht (1983).

    Google Scholar 

  7. Hintikka, J.: Defining truth, the whole truth and nothing but the truth, Reports from the Department of philosophy of the University of Helsinki, 2 (1991).

  8. Hintikka, J. and Sandu, G.: Informational Independence as a Semantical Phenomenon, in: J. E. Fenstad et al. (eds), Logic Methodology and Philosophy of Science VIII, Elsevier Science Publishers, Amsterdam (1989), 571- 589.

    Google Scholar 

  9. Hodges, W.: Elementary Predicate Logic, in: F. Gabbay and F. Guenther (eds), Handbook of Philosophical Logic, I, D. Reidel, Dordrecht (1989).

    Google Scholar 

  10. Krynicki, M. and Lachlan, A.: On the semantics of the Henkin quantifier, J. Symbolic Logic 44 (1979), 184- 200.

    Google Scholar 

  11. Krynicki, M.: Hierarchies of Partially Ordered Connectives and Quantifiers, Mathematical Logic Quaterley 39 (1993), 287- 294.

    Google Scholar 

  12. Krynicki, M. and Mostowski, M.: Henkin Quantifiers, in: M. Mostowski and L. V. Szczerba (eds), Quantifiers II, Kluwer Academic Publishers (1995), 193- 262.

  13. Saarinen, E. (ed.): Game-theoretical Semantics, D. Reidel, Dordrecht (1979).

    Google Scholar 

  14. Sandu, G.: On the logic of informational independence and its applications, J. Philosophical Logic 22 (1993), 29- 60.

    Google Scholar 

  15. Sandu, G. and Väänänen, J.: Partially Ordered Connectives, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 38 (1992), 361- 372.

    Google Scholar 

  16. Walkoe, W.: Finite partially order quantification, J. Symbolic Logic 35 (1970), 535- 550.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sandu, G. If-Logic and Truth-definition. Journal of Philosophical Logic 27, 143–164 (1998). https://doi.org/10.1023/A:1017905122049

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1017905122049

Keywords

Navigation