Skip to main content

Information, Awareness and Substructural Logics

  • Conference paper
Logic, Language, Information, and Computation (WoLLIC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8071))

Abstract

The paper outlines a generalisation of the awareness-based epistemic semantics by Fagin and Halpern. Awareness is construed as a relation between agents and pieces of information instead of formulas. The main motive for introducing the generalisation is that it shows substructural logics to be a natural component of information-based epistemic logic: substructural logics can be seen as describing the logical behaviour of pieces of information. Substructural epistemic logics are introduced and some of their properties are discussed. In addition, extensions of substructural epistemic logics invoking group-epistemic and dynamic modalities are sketched.

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

Access this chapter

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 49.99
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. Adriaans, P., van Benthem, J. (eds.): Philosophy of Information. Elsevier, Amsterdam (2008)

    Google Scholar 

  2. Alchourron, C., Gärdenfors, P., Makinson, D.: On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. J. Symbolic Logic 50, 510–530 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  3. Artemov, S.: Operational Modal Logic. Technical report, Cornell University (1995)

    Google Scholar 

  4. Artemov, S.: Explicit Provability and Constructive Semantics. B. Symb. Log. 7, 1–36 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Artemov, S.: The Logic of Justification. Rev. Symb. Log. 1, 477–513 (2008)

    Article  MATH  Google Scholar 

  6. Artemov, S.: Why Do We Need Justification Logic? In: van Benthem, J., Gupta, A., Pacuit, E. (eds.) Games, Norms and Reasons: Logic at the Crossroads, pp. 23–38. Springer, Dordrecht (2011)

    Chapter  Google Scholar 

  7. Baltag, A., Moss, L., Sołecki, S.: The Logic of Common Knowledge, Public Announcements, and Private Suspicions. In: Gilboa, I. (ed.) Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK 1998), pp. 43–56. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  8. Baltag, A., Moss, L.: Logics for Epistemic Programs. Synthese 139, 165–224 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Baltag, A., Renne, B., Smets, S.: The Logic of Justified Belief Change, Soft Evidence and Defeasible Knowledge. In: Ong, L., de Queiroz, R. (eds.) WoLLIC 2012. LNCS, vol. 7456, pp. 168–190. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  10. van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (2011)

    Book  MATH  Google Scholar 

  11. van Benthem, J., Pacuit, E.: Dynamic Logics of Evidence-Based Beliefs. Studia Logica 99, 61–92 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bílková, M., Majer, O., Peliš, M., Restall, G.: Relevant Agents. In: Beklemishev, L., Goranko, V., Shehtman, V. (eds.) Advances in Modal Logic, vol. 8, pp. 22–38. College Publications, London (2010)

    Google Scholar 

  13. Bucheli, S., Kuznets, R., Renne, B., Sack, J., Studer, T.: Justified Belief Change. In: Arrazola, X., Ponte, M. (eds.) Proceedings of the Second ILCLI International Workshop on Logic and Philosophy of Knowledge, Communication and Action (LogKCA 2010). The University of the Basque Country Press, San Sebastian (2010)

    Google Scholar 

  14. Bucheli, S., Kuznets, R., Studer, T.: Realizing public announcements by justifications. To appear in J. Comput. Syst. Sci.

    Google Scholar 

  15. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer, Dordrecht (2008)

    MATH  Google Scholar 

  16. Dretske, F.: Knowledge and the Flow of Information. MIT Press, Cambridge (1981)

    Google Scholar 

  17. Fagin, R., Halpern, J.: Belief, Awareness, and Limited Reasoning. Artif. Intell. 34, 39–76 (1988)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  19. Fitting, M.: Logic of Proofs, Semantically. Ann. Pure Appl. Logic 132, 1–25 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. Fitting, M.: Reasoning with Justifications. In: Makinson, D., Malinowski, J., Wansing, H. (eds.) Towards Mathematical Philosophy: Papers from the Studia Logica Conference Trends in Logic IV, pp. 107–123. Springer, Dordrecht (2009)

    Google Scholar 

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

    Google Scholar 

  22. Hintikka, J.: Impossible Possible Worlds Vindicated. J. Philos. Logic 4, 475–484 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  23. Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)

    MATH  Google Scholar 

  24. Kripke, S.: Semantical Analysis of Intuitionistic Logic. In: Crossley, J., Dummett, M.A.E. (eds.) Formal Systems and Recursive Functions, pp. 92–130. North-Holland Publishing Company, Amsterdam (1965)

    Chapter  Google Scholar 

  25. Kuznets, R., Studer, T.: Update as Evidence: Belief Expansion. In: Artemov, S., Nerode, A. (eds.) LFCS 2013. LNCS, vol. 7734, pp. 266–279. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  26. Mares, E.: Relevant Logic. A Philosophical Interpretation. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  27. Renne, B.: Public Communication in Justification Logic. J. Logic Comput. 21, 1005–1034 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Restall, G.: Information Flow and Relevant Logics. In: Seligman, J., Westerstøahl, D. (eds.) Logic, Language, and Computation, vol. 1, pp. 463–467. CSLI Publications, Stanford (1995)

    Google Scholar 

  29. Restall, G.: An Introduction to Substructural Logics. Routledge, London (2000)

    Google Scholar 

  30. Sequoiah-Grayson, S.: Epistemic Closure and Commutative, Nonassociative Residuated Structures. Synthese 190, 113–128 (2013)

    Article  Google Scholar 

  31. Shannon, C.E.: A Mathematical Theory of Communication. AT&T Tech. J. 27, 379–423, 623–656 (1948)

    Google Scholar 

  32. Schröder-Heister, P., Došen, K.: Substructural Logics. Oxford University Press, Oxford (1993)

    Google Scholar 

  33. Urquhart, A.: Semantics for Relevant Logics. J. Symbolic Logic 37, 159–169 (1972)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sedlár, I. (2013). Information, Awareness and Substructural Logics. In: Libkin, L., Kohlenbach, U., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2013. Lecture Notes in Computer Science, vol 8071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39992-3_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39992-3_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39991-6

  • Online ISBN: 978-3-642-39992-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics