Skip to main content
SpringerLink
Log in

Proof Theory for Distributed Knowledge

  • Conference paper
Computational Logic in Multi-Agent Systems (CLIMA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5056))

Included in the following conference series:

Abstract

The proof theory of multi-agent epistemic logic extended with operators for distributed knowledge is studied. A proposition A is distributed knowledge within a group G if A follows from the totality of what the individual members of G know. There are known axiomatizations for epistemic logics with the distributed knowledge operator, but apparently no cut-free proof system for such logics has yet been presented. A Gentzen-style contraction-free sequent calculus system for propositional epistemic logic with operators for distributed knowledge is given, and a cut-elimination theorem for the system is proved. Examples of reasoning about distributed knowledge that use the calculus are given.

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. Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell University Press (1962)

    Google Scholar 

  2. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  3. Meyer, J.J.C., van der Hoek, W.: Epistemic Logic for AI and Computer Science. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  4. Ghidini, C., Serafini, L.: A context-based logic for distributed knowledge representation and reasoning. In: Bouquet, P., Serafini, L., Brézillon, P., Benercetti, M., Castellani, F. (eds.) CONTEXT 1999. LNCS (LNAI), vol. 1688, pp. 159–172. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  5. Artemov, S.N.: Research problems, http://web.cs.gc.cuny.edu/~sartemov/research_problems.html

  6. Negri, S., von Plato, J.: Structural Proof Theory. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  7. Negri, S.: Proof analysis in modal logic. Journal of Philosophical Logic 34, 507–544 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Baral, C., Kraus, S., Minker, J.: Combining multiple knowledge bases. IEEE Transactions on Knowledge and Data Engineering 3, 208–220 (1991)

    Article  Google Scholar 

  9. Cholvy, L., Garion, C.: Answering queries addressed to several databases according to a majority merging. Journal of Intelligent Information Systems 22, 175–201 (2004)

    Article  MATH  Google Scholar 

  10. Cholvy, L.: A modal logic for reasoning with contradictory beliefs which takes into account the number and the reliability of the sources. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 390–401. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. van der Hoek, W., Meyer, J.J.: A complete epistemic logic for multiple agents. In: Bacharach, M., Gérard-Varet, L.A., Mongin, P., Shin, H. (eds.) Epistemic Logic and the Theory of Games and Decisions, pp. 35–68. Kluwer Academic Publishers, Dordrecht (1997)

    Chapter  Google Scholar 

  12. van der Hoek, W., van Linder, B., Meyer, J.J.: Group knowledge is not always distributed (neither is it always implicit). Mathematical Social Sciences 38, 215–240 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Roelofsen, F.: Distributed knowledge. Journal of Applied Non-Classical Logics 17(2), 255–273 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Halpern, J.Y., Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence 54, 319–379 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  15. Fagin, R., Halpern, J.Y., Vardi, M.Y.: What can machines know? On the properties of knowledge in distributed systems. Journal of the ACM 39, 328–376 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  16. Russell, S.J., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Pearson Education International, London (2003)

    MATH  Google Scholar 

  17. Negri, S., von Plato, J.: Cut elimination in the presence of axioms. The Bulletin of Symbolic Logic 4, 418–435 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, University of Helsinki, P.O. Box 9, (Siltavuorenpenger 20 A), FIN-00014, Finland

    Raul Hakli & Sara Negri

Authors
  1. Raul Hakli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sara Negri
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computing, Imperial College London, London, UK

    Fariba Sadri

  2. National Institute of Informatics, Sokendai, Japan

    Ken Satoh

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hakli, R., Negri, S. (2008). Proof Theory for Distributed Knowledge. In: Sadri, F., Satoh, K. (eds) Computational Logic in Multi-Agent Systems. CLIMA 2007. Lecture Notes in Computer Science(), vol 5056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88833-8_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88833-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88832-1

  • Online ISBN: 978-3-540-88833-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation