A Purely Logical Account of Sequentiality in Proof Search

  • Paola Bruscoli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2401)

Abstract

A strict correspondence between the proof-search space of a logical formal system and computations in a simple process algebra is established. Sequential composition in the process algebra corresponds to a logical relation in the formal system in this sense our approach is purely logical, no axioms or encodings are involved. The process algebra is a minimal restriction of CCS to parallel and sequential composition; the logical system is a minimal extension of multiplicative linear logic. This way we get the first purely logical account of sequentiality in proof search. Since we restrict attention to a small but meaningful fragment, which is then of very broad interest, our techniques should become a common basis for several possible extensions. In particular, we argue about this work being the first step in a two-step research for capturing most of CCS in a purely logical fashion.

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References

  1. [1]
    Samson Abramsky and Radha Jagadeesan. Games and full completeness for multiplicative linear logic. Journal of Symbolic Logic, 59(2):543–574, June 1994.Google Scholar
  2. [2]
    Jean-Marc Andreoli and Remo Pareschi. Linear Objects: Logical processes with built-in inheritance. New Generation Computing, 9:445–473, 1991.CrossRefGoogle Scholar
  3. [3]
    Gerhard Gentzen. Investigations into logical deduction. In M. E. Szabo, editor, The Collected Papers of Gerhard Gentzen, pages 68–131. North-Holland, Amsterdam, 1969.Google Scholar
  4. [4]
    Jean-Yves Girard. Linear logic. Theoretical Computer Science, 50:1–102, 1987.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Alessio Guglielmi. Concurrency and plan generation in a logic programming language with a sequential operator. In P. Van Hentenryck, editor, Logic Programming, 11th International Conference, S. Margherita Ligure, Italy, pages 240–254. The MIT Press, 1994.Google Scholar
  6. [6]
    Alessio Guglielmi. Sequentiality by linear implication and universal quantification. In Jörg Desel, editor, Structures in Concurrency Theory, Workshops in Computing, pages 160–174. Springer-Verlag, 1995.Google Scholar
  7. [7]
    Alessio Guglielmi. A system of interaction and order. Technical Report WV-01-01, Dresden University of Technology, 2001. On the web at: http://www.ki.inf.tu-dresden.de/~guglielm/Research/Gug/Gug.pdf.
  8. [8]
    Alessio Guglielmi and Lutz Straßburger. Non-commutativity and MELL in the calculus of structures. In L. Fribourg, editor, CSL 2001, volume 2142 of Lecture Notes in Computer Science, pages 54–68. Springer-Verlag, 2001. On the web at: http://www.ki.inf.tu-dresden.de/~guglielm/Research/GugStra/GugStra.pdf.Google Scholar
  9. [9]
    Alessio Guglielmi and Lutz Straßburger. A non-commutative extension of MELL in the calculus of structures. Technical Report WV-02-03, Dresden University of Technology, 2002. On the web at: http://www.ki.inf.tu-dresden.de/~guglielm/Research/NEL/NELbig.pdf, submitted.
  10. [10]
    Joshua S. Hodas and Dale Miller. Logic programming in a fragment of intuitionistic linear logic. Information and Computation, 110(2):327–365, May 1994.Google Scholar
  11. [11]
    Dale Miller. The π-calculus as a theory in linear logic: Preliminary results. In E. Lamma and P. Mello, editors, 1992 Workshop on Extensions to Logic Programming, volume 660 of Lecture Notes in Computer Science, pages 242–265. Springer-Verlag, 1993.Google Scholar
  12. [12]
    Dale Miller. Forum: A multiple-conclusion specification logic. Theoretical Computer Science, 165:201–232, 1996.MATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    Dale Miller, Gopalan Nadathur, Frank Pfenning, and Andre Scedrov. Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic, 51:125–157, 1991.CrossRefMathSciNetMATHGoogle Scholar
  14. [14]
    Robin Milner. Communication and Concurrency. International Series in Computer Science. Prentice Hall, 1989.Google Scholar
  15. [15]
    Lutz Straßburger. A local system for linear logic. Technical Report WV-02-01, Dresden University of Technology, 2002. On the web at: http://www.ki.inf.tu-dresden.de/~lutz/lls.pdf.
  16. [16]
    Alwen Fernanto Tiu. Properties of a logical system in the calculus of structures. Technical Report WV-01-06, Dresden University of Technology, 2001. On the web at: http://www.cse.psu.edu/~tiu/thesisc.pdf.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Paola Bruscoli
    • 1
  1. 1.Fakultät InformatikTechnische Universität DresdenDresdenGermany

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