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Conference on Computability in Europe

CiE 2006: Logical Approaches to Computational Barriers pp 65–74Cite as

Deep Inference and Its Normal Form of Derivations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3988))

Abstract

We see a notion of normal derivation for the calculus of structures, which is based on a factorisation of derivations and which is more general than the traditional notion of cut-free proof in this formalism.

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References

  1. Brünnler, K.: Atomic cut elimination for classical logic. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 86–97. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Brünnler, K.: Deep Inference and Symmetry in Classical Proofs. PhD thesis, Technische Universität Dresden (September 2003)

    Google Scholar 

  3. Brünnler, K.: Cut elimination inside a deep inference system for classical predicate logic. Studia Logica 82(1), 51–71 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brünnler, K., Lengrand, S.: On two forms of bureaucracy in derivations. In: Bruscoli, P., Lamarche, F., Stewart, C. (eds.) Structures and Deduction, Technische Universität Dresden, pp. 69–80 (2005)

    Google Scholar 

  5. Brünnler, K., Tiu, A.F.: A local system for classical logic. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS, vol. 2250, pp. 347–361. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Bruscoli, P., Guglielmi, A.: On the proof complexity of deep inference (in preparation, 2006)

    Google Scholar 

  7. Di Gianantonio, P.: Structures for multiplicative cyclic linear logic: Deepness vs cyclicity. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 130–144. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Fürmann, C., Pym, D.: Order-enriched categorical models of the classical sequent calculus (submitted, 2004)

    Google Scholar 

  9. Gentzen, G.: Investigations into logical deduction. In: Szabo, M.E. (ed.) The Collected Papers of Gerhard Gentzen, pp. 68–131. North-Holland Publishing Co., Amsterdam (1969)

    Google Scholar 

  10. Guglielmi, A.: The calculus of structures website, Available from: http://alessio.guglielmi.name/res/cos/index.html

  11. Guglielmi, A.: A system of interaction and structure. Technical Report WV-02-10, Technische Universität Dresden. ACM Transactions on Computational Logic (to appear, 2002)

    Google Scholar 

  12. Guglielmi, A.: The problem of bureaucracy and identity of proofs from the perspective of deep inference. In: Bruscoli, P., Lamarche, F., Stewart, C. (eds.) Structures and Deduction, Technische Universität Dresden, pp. 53–68 (2005)

    Google Scholar 

  13. Guglielmi, A., Straßburger, L.: Non-commutativity and MELL in the calculus of structures. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 54–68. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Guiraud, Y.: The three dimensions of proofs. Annals of pure and applied logic (to appear, 2005)

    Google Scholar 

  15. Hein, R., Stewart, C.: Purity through unravelling. In: Bruscoli, P., Lamarche, F., Stewart, C. (eds.) Structures and Deduction, Technische Universität Dresden, pp. 126–143 (2005)

    Google Scholar 

  16. Kahramanoğullari, O.: Reducing nondeterminism in the calculus of structures (manuscript, 2005)

    Google Scholar 

  17. Lamarche, F., Straßburger, L.: Naming proofs in classical propositional logic. In: Urzyczyn, P. (ed.) TLCA 2005. LNCS, vol. 3461, pp. 246–261. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. McKinley, R.: Categorical models of first-order classical proofs. The degree of Doctor of Philosophy of the University of Bath (submitted, 2005)

    Google Scholar 

  19. Pym, D.J.: The Semantics and Proof Theory of the Logic of Bunched Implications. Applied Logic Series, vol. 26. Kluwer Academic Publishers, Dordrecht (2002)

    MATH  Google Scholar 

  20. Schütte, K.: Schlussweisen-Kalküle der Prädikatenlogik. Mathematische Annalen 122, 47–65 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  21. Schütte, K.: Proof Theory. Springer, Heidelberg (1977)

    Book  MATH  Google Scholar 

  22. Stewart, C., Stouppa, P.: A systematic proof theory for several modal logics. In: Schmidt, R., Pratt-Hartmann, I., Reynolds, M., Wansing, H. (eds.) Advances in Modal Logic, vol. 5, pp. 309–333. King’s College Publications (2005)

    Google Scholar 

  23. Stouppa, P.: A deep inference system for the modal logic S5. Studia Logica (to appear, 2006)

    Google Scholar 

  24. Straßburger, L.: Linear Logic and Noncommutativity in the Calculus of Structures. Ph.D thesis, Technische Universität Dresden (2003)

    Google Scholar 

  25. Straßburger, L.: On the axiomatisation of boolean categories with and without medial (manuscript, 2005)

    Google Scholar 

  26. Tiu, A.F.: Properties of a Logical System in the Calculus of Structures. Master’s thesis, Technische Universität Dresden (2001)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für angewandte Mathematik und Informatik, Neubrückstr. 10, CH – 3012, Bern, Switzerland

    Kai Brünnler

Authors
  1. Kai Brünnler
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Swansea University, Singleton Park, SA2 8PP, Swansea, United Kingdom

    Arnold Beckmann

  2. Department of Computer Science, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK

    Ulrich Berger

  3. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, Amsterdam, TV, The Netherlands

    Benedikt Löwe

  4. School of Physical Sciences, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, United Kingdom

    John V. Tucker

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Brünnler, K. (2006). Deep Inference and Its Normal Form of Derivations. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_7

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  • DOI: https://doi.org/10.1007/11780342_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35466-6

  • Online ISBN: 978-3-540-35468-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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