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Machine Checking Proof Theory: An Application of Logic to Logic

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Logic and Its Applications (ICLA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5378))

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Abstract

Modern proof-assistants are now mature enough to formalise many aspects of mathematics. I outline some work we have done using the proof-assistant Isabelle to machine-check aspects of proof theory in general, and specifically the proof theory of provability logic GL.

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References

  1. Dawson, J.E., Goré, R.: Formalised Cut Admissibility for Display Logic. In: Carreño, V.A., Muñoz, C.A., Tahar, S. (eds.) TPHOLs 2002. LNCS, vol. 2410, pp. 131–147. Springer, Heidelberg (2002)

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  2. Goré, R., Ramanayake, R.: Valentini’s Cut Elimination for Provability Logic Resolved. In: Advances in Modal Logic, vol. 7, pp. 67–86. College Publications, London (2008)

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  3. Leivant, D.: On the Proof Theory of the Modal Logic for Arithmetic Provability. Journal of Symbolic Logic 46, 531–538 (1981)

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  4. Mints, G.: Cut elimination for provability logic. Collegium Logicum (2005)

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  5. Moen, A.: The proposed algorithms for eliminating cuts in the provability calculus GLS do not terminate. In: NWPT 2001, Norwegian Computing Center, December 10 (2001), http://publ.nr.no/3411

  6. Negri, S.: Proof Analysis in Modal Logic. Journal of Philosophical Logic 34, 507–544 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Solovay, R.M.: Provability Interpretations of Modal Logic. Israel Journal of Mathematics 25, 287–304 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  8. Valentini, S.: The Modal Logic of Provability: Cut-elimination. Journal of Philosophical Logic 12, 471–476 (1983)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Sciences Laboratory, The Australian National University, Canberra

    Rajeev Goré

Authors
  1. Rajeev Goré
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Editor information

Editors and Affiliations

  1. Institute of Mathematical Sciences, CIT Campus, 600113, Chennai, India

    R. Ramanujam

  2. National Institute of Advanced Studies, Indian Institute of Science Campus, 560012, Bangalore, India

    Sundar Sarukkai

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© 2008 Springer-Verlag Berlin Heidelberg

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Goré, R. (2008). Machine Checking Proof Theory: An Application of Logic to Logic. In: Ramanujam, R., Sarukkai, S. (eds) Logic and Its Applications. ICLA 2009. Lecture Notes in Computer Science(), vol 5378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92701-3_2

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  • DOI: https://doi.org/10.1007/978-3-540-92701-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92700-6

  • Online ISBN: 978-3-540-92701-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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