Skip to main content
SpringerLink
Log in

Hierarchies in Inclusion Logic with Lax Semantics

  • Conference paper
Logic and Its Applications (ICLA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8923))

Included in the following conference series:

Abstract

We study the expressive power of fragments of inclusion logic under the so-called lax team semantics. The fragments are defined either by restricting the number of universal quantifiers or the arity of inclusion atoms in formulae. In case of universal quantifiers, the corresponding hierarchy collapses at the first level. Arity hierarchy is shown to be strict by relating the question to the study of arity hierarchies in fixed-point logics.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Galliani, P.: Inclusion and exclusion dependencies in team semantics: On some logics of imperfect information. Annals of Pure and Applied Logic 163(1), 68 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  2. Väänänen, J.: Dependence Logic. Cambridge University Press (2007)

    Google Scholar 

  3. Hodges, W.: Compositional Semantics for a Language of Imperfect Information. Journal of the Interest Group in Pure and Applied Logics 5(4), 539–563 (1997)

    MATH  MathSciNet  Google Scholar 

  4. Galliani, P., Hannula, M., Kontinen, J.: Hierarchies in independence logic. In: Rocca, S.R.D. (ed.) Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), vol. 23, pp. 263–280. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl (2013)

    Google Scholar 

  5. Galliani, P., Hella, L.: Inclusion Logic and Fixed Point Logic. In: Rocca, S.R.D. (ed.) Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), vol. 23, pp. 281–295. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl (2013)

    Google Scholar 

  6. Abramsky, S., Väänänen, J.: From IF to BI. Synthese 167, 207–230 (2009), doi:10.1007/s11229-008-9415-6

    Article  MATH  MathSciNet  Google Scholar 

  7. Yang, F.: Expressing Second-order Sentences in Intuitionistic Dependence Logic. Studia Logica 101(2), 323–342 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  8. Grädel, E.: Model-checking games for logics of imperfect information. Theor. Comput. Sci. 493, 2–14 (2013)

    Article  MATH  Google Scholar 

  9. Kontinen, J.: Coherence and computational complexity of quantifier-free dependence logic formulas. In: Kontinen, J., Väänänen, J. (eds.) Proceedings of Dependence and Independence in Logic. ESSLLI, pp. 58–77 (2010)

    Google Scholar 

  10. Durand, A., Kontinen, J.: Hierarchies in dependence logic. ACM Transactions on Computational Logic (TOCL) 13(4), 31 (2012)

    Article  MathSciNet  Google Scholar 

  11. Galliani, P., Väänänen, J.A.: On dependence logic. In: Baltag, A., Smets, S. (eds.) Johan van Benthem on Logical and Informational Dynamics, pp. 101–119. Springer (2014)

    Google Scholar 

  12. Ajtai, M.: \(\Sigma^1_1\)-formulae on finite structures. Ann. Pure Appl. Logic 4(1), 1–48 (1983)

    Article  MathSciNet  Google Scholar 

  13. Grohe, M.: Arity hierarchies. Ann. Pure Appl. Logic 82(2), 103–163 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hannula, M., Kontinen, J.: Hierarchies in independence and inclusion logic with strict semantics. Journal of Logic and Computation (2014), doi: 10.1093/logcom/exu057

    Google Scholar 

  15. Grädel, E., Väänänen, J.: Dependence and independence. Studia Logica 101(2), 399–410 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Hrushovski, E.: Extending partial isomorphisms of graphs. Combinatorica 12(4), 411–416 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  17. Fraïssé, R.: Sur une nouvelle classification des systmes de relations. Comptes Rendus 230, 1022–1024 (1950)

    MATH  Google Scholar 

  18. Ehrenfeucht, A.: An application of games to the completeness problem for formalized theories. Fundamenta Mathematicae 49, 129–141 (1961)

    MATH  MathSciNet  Google Scholar 

  19. Imhof, H.: Computational aspects of arity hierarchies. In: van Dalen, D., Bezem, M. (eds.) CSL 1996. LNCS, vol. 1258, pp. 211–225. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

    Miika Hannula

Authors
  1. Miika Hannula
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Mohua Banerjee

  2. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Powai, 400076, Mumbai, India

    Shankara Narayanan Krishna

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hannula, M. (2015). Hierarchies in Inclusion Logic with Lax Semantics. In: Banerjee, M., Krishna, S.N. (eds) Logic and Its Applications. ICLA 2015. Lecture Notes in Computer Science, vol 8923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45824-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-45824-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-45823-5

  • Online ISBN: 978-3-662-45824-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation