iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://unpaywall.org/10.1007/978-3-662-48561-3_21
Algebraic Semantics for Dynamic Dynamic Logic | SpringerLink
Skip to main content
Springer Nature Link
Log in

Algebraic Semantics for Dynamic Dynamic Logic

  • Conference paper
  • First Online:
Logic, Rationality, and Interaction (LORI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9394))

Included in the following conference series:

  • 1051 Accesses

Abstract

Dynamic dynamic logic (DDL) is a generalisation of propositional dynamic logic PDL and dynamic epistemic logic. In this paper, we develop algebraic semantics for DDL without the constant program. We introduce inductive and continuous modal Kleene algebras for PDL and show the validity of reduction axioms in algebraic models and hence the algebraic completeness of DDL.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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.

Similar content being viewed by others

References

  1. Danecki, R.: Nondeterministic propositional dynamic logic with intersection is decidable. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 34–53. Springer, Heidelberg (1985)

    Chapter  Google Scholar 

  2. Enderton, H.B.: Computability Theory: An Introduction to Recursion Theory. Elsevier (2011)

    Google Scholar 

  3. Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. Journal of Computer and System Sciences 18(2), 194–211 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  4. Harel, D.: Dynamic logic. In: Handbook of Philosophical Logic, vol. II, pp. 496–604. D. Reidel Publishers (1984)

    Google Scholar 

  5. Kozen, D.: A representation theorem for models of *-free pdl. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 351–362. Springer, Heidelberg (1980)

    Chapter  Google Scholar 

  6. Kozen, D.: On induction vs.*-continuity. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 167–176. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  7. Kozen, D.: Kleene algebra with tests. ACM Transactions on Programming Languages and Systems 19(3), 427–443 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kurz, A., Palmigiano, A.: Epistemic updates on algebras. Logical Methods in Computer Science 9(4:17), 1–28 (2013)

    MathSciNet  MATH  Google Scholar 

  9. Lutz, C., Walther, D.: PDL with Negation of Atomic Programs. Journal of Applied Non-Classical Logic 15(2), 189–214 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lutz, C.: PDL with intersection and converse is decidable. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 413–427. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Ma, M., Sano, K.: How to update neighborhood models. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI. LNCS, vol. 8196, pp. 204–217. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  12. Ma, M., Palmigiano, A., Sadrzadeh, M.: Algebraic semantics and model completeness for intuitionistic public announcement logic. Annals of Pure and Applied Logic 165(4), 963–995 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pratt, V.: Dynamic algebras: examples, constructions, applications. Studia Logica 50(3-4), 571–605 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  14. Resende, P.: Lectures on étale groupoids, inverse semigroups and quantales (2006), http://www.math.ist.utl.pt/~pmr/poci55958/gncg51gamap-version2.pdf

  15. Segerberg, K.: A completeness theorem in the modal logic of programs. Banach Center Publications 9(1), 31–46 (1982)

    MathSciNet  MATH  Google Scholar 

  16. Girard, P., Seligman, J., Liu, F.: General dynamic dynamic logic. In: Ghilardi, S., Bolander, T., Moss, L. (eds.) Advances in Modal Logic, vol. 9, pp. 239–260. Colledge Publications (2012)

    Google Scholar 

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

    Google Scholar 

  18. Plaza, L.: Logics of public communications. Synthese 158(2), 165–179 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Vakarelov, D.: Filtration theorem for dynamic algebras with tests and inverse operator. In: Salwicki, A. (ed.) Logic of Programs 1980. LNCS, vol. 148, pp. 314–324. Springer, Heidelberg (1983)

    Chapter  Google Scholar 

  20. van Benthem, J., Pacuit, E.: Dynamic logics of evidence-based beliefs. Studia Logica 99(1), 61–92 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. van Ditmarsch, H., van der Hoek, W., Kooi, B.P.: Dynamic epistemic logic. Springer Science & Business Media (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Logic and Intelligence, Southwest University, Chongqing, China

    Minghui Ma & Jeremy Seligman

  2. Department of Philosophy, University of Auckland, Aukland, New Zealand

    Jeremy Seligman

Authors
  1. Minghui Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeremy Seligman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Minghui Ma .

Editor information

Editors and Affiliations

  1. Dept of Comp Sci, Univ of Liverpool, Liverpool, United Kingdom

    Wiebe van der Hoek

  2. Department of Philosophy, Group in Logic & the Methodology of Sci. University of California, Berkeley, California, USA

    Wesley H. Holliday

  3. Institute of Philosophy of Mind and Cognition, National Yang-Ming University, Taipei, Taiwan

    Wen-fang Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ma, M., Seligman, J. (2015). Algebraic Semantics for Dynamic Dynamic Logic. In: van der Hoek, W., Holliday, W., Wang, Wf. (eds) Logic, Rationality, and Interaction. LORI 2015. Lecture Notes in Computer Science(), vol 9394. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48561-3_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-48561-3_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48560-6

  • Online ISBN: 978-3-662-48561-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation