Skip to main content
SpringerLink
Log in

Concurrent logic programming as uniform linear proofs

  • Conference paper
  • First Online:
Algebraic and Logic Programming (ALP 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 850))

Included in the following conference series:

Abstract

We describe \(\mathcal{L}\mathcal{C}\), a formalism based on the proof theory of linear logic, whose aim is to specify concurrent computations and whose language restriction (as compared to other linear logic language) provides a simpler operational model that can lead to a more practical language core. The \(\mathcal{L}\mathcal{C}\) fragment is proveded to be an abstract logic programming language, that is any sequent can be derived by uniform proofs. The resulting class of computations can be viewed in terms of multiset rewriting and is reminiscent of the computations arising in the Chemical Abstract Machine and in the Gamma model.

The fragment makes it possible to give a logic foundation to existing extensions of Horn clause logic, such as Generalized Clauses, whose declarative semantics was based on an ad hoc construction.

Programs and goals in \(\mathcal{L}\mathcal{C}\) can declaratively be characterized by a suitable instance of the phase semantics of linear logic. A canonical phase model is associated to every \(\mathcal{L}\mathcal{C}\) program. Such a model gives a full characterization of the program computations and can be obtained through a fixpoint construction.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Abramsky. Computational interpretations of linear logic. Theoretical Computer Science, 111(1 & 2):3–59, 1993.

    Google Scholar 

  2. J. M. Andreoli. Logic programming with focusing proofs in linear logic. Journal of Logic and Computation, 2(3):297–347, 1992.

    Google Scholar 

  3. J. M. Andreoli and R. Pareschi. Linear Objects: logical processes with built-in inheritance. In D. H. D. Warren and P. Szeredi, editors, Proc. Seventh Int'l Conf. on Logic Programming, pages 495–590. The MIT Press, Cambridge, Mass., 1990.

    Google Scholar 

  4. J. M. Andreoli and R. Pareschi. Communication as fair distribution of knowledge. In Proc. of OOPSLA '91, pages 212–229, 1991.

    Google Scholar 

  5. K. R. Apt. Introduction to Logic Programming. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B: Formal Models and Semantics, pages 495–574. Elsevier, Amsterdam and The MIT Press, Cambridge, 1990.

    Google Scholar 

  6. J-P. Banâtre and D. Le Metayer. The gamma model and its discipline of programming. Science of Computer Programming, 15(1):55–77, 1990.

    Google Scholar 

  7. G. Berry and G. Boudol. The chemical abstract machine. In Proc. Seventeenth Annual ACM Symp. on Principles of Programming Languages, pages 81–94, 1990.

    Google Scholar 

  8. A. Brogi. And-parallelism without shared variables. In D. H. D. Warren and P. Szeredi, editors, Proc. Seventh Int'l Conf. on Logic Programming, pages 306–319. The MIT Press, Cambridge, Mass., 1990.

    Google Scholar 

  9. K. L. Clark and S. Gregory. PARLOG: parallel programming in logic. ACM Transactions on Programming Languages and Systems, 8:1–49, 1986.

    Google Scholar 

  10. F. S. de Boer, J. N. Kok, C. Palamidessi, and J. J. M. M. Rutten. Semantic models for concurrent logic languages. Theoretical Computer Science, 86:3–33, 1991.

    Google Scholar 

  11. M. Falaschi, G. Levi, and C. Palamidessi. A Synchronization Logic: Axiomatics and Formal Semantics of Generalized Horn Clauses. Information and Control, 60(1):36–69, 1984.

    Google Scholar 

  12. D. Gelernter. Generative Communication in Linda. ACM Transactions on Programming Languages and Systems, 7(1):80–113, 1985.

    Google Scholar 

  13. J.Y. Girard. Linear logic. Theoretical Computer Science, 50:1–102, 1987.

    Google Scholar 

  14. A. Guglielmi and G.Levi. Chemical logic programming? In D. Saccà, editor, Proc. Eight Italian Conference on Logic Programming, pages 39–51, 1993.

    Google Scholar 

  15. J. S. Hodas and D. Miller. Logic programming in a fragment of intuitionistic linear logic. In Proc. Sixth IEEE Symp. on Logic In Computer Science, pages 32–42, 1991.

    Google Scholar 

  16. R. Pareschi J. M. Andreoli, T. Castagnetti. Abstract Interpretation of Linear Logic Programming. In D. Miller, editor, Proc. 1993 Int'l Symposium on Logic Programming, pages 295–314. The MIT Press, Cambridge, Mass., 1993.

    Google Scholar 

  17. N. Kobayashi and A. Yonezawa. Acl-a concurrent linear logic programming paradigm. In Proc. of the 1993 International Symposium on Logic Programming, pages 279–294, Vancouver, 1993.

    Google Scholar 

  18. N. Kobayashi and A. Yonezawa. Asynchronous communication model based on linear logic. Technical report, Department of Information Science, University of Tokyo, July 1992.

    Google Scholar 

  19. Y. Lafont. The linear abstract machine. Theoretical Computer Science, 59:157–180, 1988.

    Google Scholar 

  20. Y. Lafont. Interaction nets. In Proc. Fifth IEEE Symp. on Logic In Computer Science, pages 95–108, 1990.

    Google Scholar 

  21. G. Levi and F. Sirovich. A problem reduction model for non-independent subproblems. In Proc. Fourth International Joint Conference on Artificial Intelligence, pages 340–344, 1975.

    Google Scholar 

  22. G. Levi and F. Sirovich. Generalized and-or graphs. Artificial Intelligence, 7:243–259, 1976.

    Google Scholar 

  23. D. Miller. The π-calculas as a theory in linear logic: Preliminary result. In E. Lamma and P. Mello, editors, Proc. of Third International Workshop on Extensions of Logic Programming, volume 660 of Lecture Notes in Computer Science, pages 242–264. Springer-Verlag, Berlin, 1992.

    Google Scholar 

  24. D. Miller, F. Pfenning, G. Nadathur, and A. Scedrov. Uniform proofs as a foundation for Logic Programming. Annals of Pure and Applied Logic, 51:125–157, 1991.

    Google Scholar 

  25. L. Monteiro. An extension to horn clause logic allowing the definition of concurrent processes. In G. Goos and J. Hartmanis, editors, Proc. of International Colloquium on Formalization of Programming Concepts, volume 107 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1981.

    Google Scholar 

  26. L. Monteiro. A proposal for distributed programming in logic. In J. A. Campbell, editor, Implementations of Prolog, pages 329–340. Ellis-Horwood, 1984.

    Google Scholar 

  27. E. Y. Shapiro. The family of concurrent logic programming languages. ACM Computing Surveys, 21(3):412–510, 1989.

    Google Scholar 

  28. K. Ueda. Guarded Horn Clauses. In E.Y. Shapiro, editor, Concurrent Prolog: Collected Papers, volume 1, pages 140–156. The MIT Press, Cambridge, Mass., 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Corso Italia, 40, 56125, Pisa, Italy

    Paolo Volpe

Authors
  1. Paolo Volpe
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Giorgio Levi Mario Rodríguez-Artalejo

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag

About this paper

Cite this paper

Volpe, P. (1994). Concurrent logic programming as uniform linear proofs. In: Levi, G., Rodríguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1994. Lecture Notes in Computer Science, vol 850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58431-5_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-58431-5_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58431-5

  • Online ISBN: 978-3-540-48791-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation