Skip to main content
SpringerLink
Log in

Structural completeness in propositional logics of dependence

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a class of substitutions under which the logics are closed. We obtain an analogous result with respect to stable substitutions, for the negative variants of some well-known intermediate logics, which are intermediate theories that are closely related to inquisitive logic.

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. Burgess, J.P.: A remark on henkin sentences and their contraries. Notre Dame J. Form. Log. 44(3), 185–188 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford University Press, New York (1997)

    MATH  Google Scholar 

  3. Ciardelli, I.: Dependency as question entailment. In: Abramsky, S., Kontinen, J., Väänänen, J. (eds.) Dependence Logic: Theory and Application, Progress in Computer Science and Applied Logic, pp. 129–181. Birkhauser (2016)

  4. Ciardelli, I., Roelofsen, F.: Inquisitive logic. J. Philos. Logic 40(1), 55–94 (2011)

    Article  MathSciNet  Google Scholar 

  5. Ebbing, J., Hella, L., Meier, A., Müller, J.S., Virtema, J., Vollmer, H.: Extended modal dependence logic. 20th International Workshop. WoLLIC 2013, Proceedings, Lecture Notes in Computer Science, vol. 8071, pp. 126–137. Springer, Berlin (2013)

  6. Ghilardi, S.: Unification in intuitionistic logic. J. Symb. Logic 64, 859–880 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hella, L., Luosto, K., Sano, K., Virtema, J.: The Expressive Power of Modal Dependence Logic. In: Advances in Modal Logic 10, Invited and Contributed Papers from the Tenth Conference on Advances in Modal Logic, College Publications, London, 294–312 (2014)

  8. Henkin, L.: Some remarks on infinitely long formulas. Infinitistic Methods. In: Proceedings Symposium Foundations of Mathematics, pp. 167–183. Pergamon, Warsaw (1961)

  9. Hintikka, J.: The Principles of Mathematics Revisited. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  10. Hintikka, J., Sandu, G.: Informational independence as a semantical phenomenon. In: Fenstad, R.H.J.E., Frolov, I.T. (eds.) Logic, Methodology and Philosophy of Science, pp. 571–589. Elsevier, Amsterdam (1989)

    Google Scholar 

  11. Hodges, W.: Compositional semantics for a language of imperfect information. Log. J. IGPL 5, 539–563 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hodges, W.: Some strange quantifiers. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds.) Structures in Logic and Computer Science: A Selection of Essays in Honor of A. Ehrenfeucht, Lecture Notes in Computer Science, vol. 1261, pp. 51–65. Springer, London (1997)

    Chapter  Google Scholar 

  13. Iemhoff, R.: On the admissible rules of intuitionistic propositional logic. J. Symb. Log. 66, 281–294 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Iemhoff, R.: Consequence relations and admissible rules. Tech. Rep. 314, Department of Philosophy. Utrecht University, Utrecht (2013)

  15. Jeřábek, E.: Admissible rules of modal logics. J. Log. Comput. 15, 411–431 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kontinen, J., Väänänen, J.: A remark on negation in dependence logic. Notre Dame J. Form. Log. 52(1), 55–65 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kuusisto, A.: A double team semantics for generalized quantifiers logic. J. Logic Lang. Inform. 24(2), 149–191 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lohmann, P., Vollmer, H.: Complexity results for modal dependence logic. Stud. Logica. 101(2), 343–366 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Metcalfe, G.: Admissible rules: From characterizations to applications. In: Proceedings of WoLLIC 2012, LNCS, vol. 7456, pp. 56–69. Springer (2012)

  20. Miglioli, P., Moscato, U., Ornaghi, M., Quazza, S., Usberti, G.: Some results on intermediate constructive logics. Notre Dame J. Form. Log. 30(4), 543–562 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  21. Rozière, P.: Regles admissibles en calcul propositionnel intuitionniste. Ph.D. thesis, Université Paris VII (1992)

  22. Rybakov, V.: Admissibility of Logical Inference Rules. Elsevier, Amsterdam (1997)

    MATH  Google Scholar 

  23. Sano, K., Virtema, J.: Axiomatizing Propositional Dependence Logics Proceedings of the 24th EACSL Annual Conference on Computer Science Logic, 292–307 (2015)

  24. Väänänen, J.: Dependence Logic: A New Approach to Independence Friendly Logic. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  25. Wojtylak, P.: On a problem of H. Friedman and its solution by T. Prucnal. Rep. Math. Log. 38, 69–86 (2004)

  26. Yang, F.: On extensions and variants of dependence logic. Ph.D. thesis, University of Helsinki (2014)

  27. Yang, F., Väänänen, J.: Propositional logics of dependence. Ann. Pure Appl. Log. 167(7), 557–589 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy and Religious Studies, Utrecht University, Janskerkhof 13, Utrecht, 3512 BL, The Netherlands

    Rosalie Iemhoff & Fan Yang

Authors
  1. Rosalie Iemhoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fan Yang.

Additional information

Support by the Netherlands Organisation for Scientific Research under Grant 639.032.918 is gratefully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Iemhoff, R., Yang, F. Structural completeness in propositional logics of dependence. Arch. Math. Logic 55, 955–975 (2016). https://doi.org/10.1007/s00153-016-0505-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-016-0505-8

Keywords

Mathematics Subject Classification

Search

Navigation