Skip to main content

Quasi-Realization

  • Conference paper
  • First Online:
Book cover Logic, Language, and Computation (TbiLLC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10148))

Included in the following conference series:

Abstract

Justification logics connect with modal logics via Realization Theorems. The first such theorem was proved constructively by Artemov, [1]. It showed how to translate an S4 sequent proof, as a whole, into an LP proof. We present a different algorithmic Realization proof for LP/S4, proceeding step by step instead of working on the entire proof, and dividing the argument into two natural parts, one specific to LP/S4, the other widely applicable to justification/modal pairs. This structure makes an implementation easier, and we provide a link to one in Prolog.

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 EPUB and 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

References

  1. Artemov, S.N.: Explicit provability and constructive semantics. Bull. Symbolic Logic 7(1), 1–36 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Artemov, S.N.: The logic of justification. Rev. Symbolic Logic 1(4), 477–513 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Artemov, S.N., Yavorskaya (Sidon), T.: First-order logic of proofs. Technical report TR-2011005, City University of New York, May 2011

    Google Scholar 

  4. Feferman, S., Dawson Jr., J.W., Kleene, S.C., Moore, G.H., Solovay, R.M., van Heijenoort, J., Goldfarb, W.D., Parsons, C., Sieg, W. (eds.) Kurt Gödel Collected Works, vol. 5. Oxford (1986–2003)

    Google Scholar 

  5. Fitting, M.C.: Prolog code for S4 realization. See Realization Implemented. http://melvinfitting.org/bookspapers/techreports.html

  6. Fitting, M.C.: The logic of proofs, semantically. Ann. Pure Appl. Logic 132, 1–25 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fitting, M.C.: Realizations and LP. Ann. Pure Appl. Logic 161(3), 368–387 (2009). doi:10.1016/j.apal.2009.07.010

    Article  MathSciNet  MATH  Google Scholar 

  8. Fitting, M.C.: Reasoning with justifications. In: Makinson, D., Malinowski, J., Wansing, H. (eds.) Towards Mathematical Philosophy, Chap. 6. Trends in Logic, vol. 28, pp. 107–123. Springer, Dordrecht (2009)

    Chapter  Google Scholar 

  9. Fitting, M.C.: Possible world semantics for first order LP. Technical report TR-2011010, CUNY Ph.D. Program in Computer Science, September 2011

    Google Scholar 

  10. Fitting, M.C.: Realization implemented. Technical report TR-2013005, CUNY Ph.D. Program in Computer Science, May 2013

    Google Scholar 

  11. Fitting, M.C.: Realization using the model existence theorem. J. Logic Comput. 26, 213–234 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Fitting, M.C.: Modal logics, justification logics, and realization. Ann. Pure Appl. Logic 167, 615–648 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gödel, K.: Eine Interpretation des intuistionistischen Aussagenkalkuls. Ergebnisse eines mathematischen Kolloquiums 4, 39–40 (1933). Translated as An interpretation of the intuitionistic propositional calculus in [4] I, 296–301

    MATH  Google Scholar 

  14. Goetschi, R., Kuznets, R.: Realization for justification logics via nested sequents: modularity through embedding. Ann. Pure Appl. Logic 163(9), 1271–1298 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Smullyan, R.M.: A unifying principle in quantification theory. Proc. Natl. Acad. Sci. 49(6), 828–832 (1963)

    Article  MATH  Google Scholar 

  16. Smullyan, R.M., Logic, F.-O.: First-Order Logic. Springer, Heidelberg (1968). (Revised Edition, Dover Press, New York)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Melvin Fitting .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer-Verlag GmbH Germany

About this paper

Cite this paper

Fitting, M. (2017). Quasi-Realization. In: Hansen, H., Murray, S., Sadrzadeh, M., Zeevat, H. (eds) Logic, Language, and Computation. TbiLLC 2015. Lecture Notes in Computer Science(), vol 10148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54332-0_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-54332-0_17

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-54331-3

  • Online ISBN: 978-3-662-54332-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics