skip to main content
10.1145/2370776.2370786acmotherconferencesArticle/Chapter ViewAbstractPublication PagesppdpConference Proceedingsconference-collections
research-article

Modeling datalog fact assertion and retraction in linear logic

Published: 19 September 2012 Publication History

Abstract

Practical algorithms have been proposed to efficiently recompute the logical consequences of a Datalog program after a new fact has been asserted or retracted. This is essential in a dynamic setting where facts are frequently added and removed. Yet while assertion is logically well understood as incremental inference, the monotonic nature of first-order logic is ill-suited to model retraction. As such, the traditional logical interpretation of Datalog offers at most an abstract specification of Datalog systems, but has tenuous relations to the algorithms that perform efficient assertions and retractions in practical implementations. This paper proposes a logical interpretation of Datalog based on linear logic. It not only captures the meaning of Datalog updates, but also provides an operational model that underlies the dynamic changes of the set of inferable facts, all within the confines of logic. We prove the correctness of this interpretation with respect to its traditional counterpart.

References

[1]
M. P. Ashley-Rollman, P. Lee, S. C. Goldstein, P. Pillai, and J. D. Campbell. A language for large ensembles of independently executing nodes. In Proc. of ICLP'09, volume 5649/2009, pages 265--280. Springer-Verlag, 2009.
[2]
I. Balbin and K. Ramamohanarao. A generalization of the differential approach to recursive query evaluation. J. Log. Program., 4(3):259--262, 1987.
[3]
F. Bancilhon, D. Maier, Y. Sagiv, and J. D. Ullman. Magic sets and other strange ways to implement logic programs (extended abstract). In Proc. of PODS'86, pages 1--15. ACM, 1986.
[4]
S. Ceri, G. Gottlob, and L. Tanca. What you always wanted to know about datalog (and never dared to ask). IEEE Trans. on Knowl. and Data Eng., 1(1):146--166, March 1989.
[5]
I. Cervesato. NEXCEL, a Deductive Spreadsheet. The Knowledge Engineering Review, 22:221--236, 2007.
[6]
I. Cervesato and A. Scedrov. Relating state-based and process-based concurrency through linear logic. Inf. Comput., 207(10):1044--1077, 2009.
[7]
F. Cruz, M. P. Ashley-Rollman, S. C. Goldstein, Ricardo Rocha, and F. Pfenning. Bottom-up logic programming for multicores. In Vitor Santos Costa, editor, Proc. of DAMP 2012 - Short Papers. ACM Digital Library, January 2012.
[8]
H. Gallaire, J. Minker, and J. M. Nicolas. Logic and databases: A deductive approach. ACM Comput. Surv., 16(2):153--185, June 1984.
[9]
J. Y. Girard. Linear logic. Theor. Comput. Sci., 50:1--102, 1987.
[10]
S. Grumbach and F. Wang. Netlog, a rule-based language for distributed programming. In Proc. of PADL'10, volume 5937/2010, pages 88--103. Springer-Verlag, 2010.
[11]
A. Gupta, I. S. Mumick, and V. S. Subrahmanian. Maintaining views incrementally. In Proc. of SIGMOD'93, pages 157--166. ACM, 1993.
[12]
E. S. L. Lam and I. Cervesato. Modeling datalog assertion and retraction in linear logic (full-version). Technical Report Carnegie Mellon University-CSQTR-113/Carnegie Mellon University-CS-12--126, Carnegie Mellon University, Jun 2012.
[13]
Ninghui Li and John C. Mitchell. Datalog with constraints: A foundation for trust-management languages. In Proc. of PADL'03, volume 2562/2003, pages 58--73. Springer-Verlag, 2003.
[14]
B. T. Loo, T. Condie, M. Garofalakis, D. E. Gay, J. M. Hellerstein, P. Maniatis, R. Ramakrishnan, T. Roscoe, and I. Stoica. Declarative networking: language, execution and optimization. In Proc. of SIGMOD '06, pages 97--108. ACM, 2006.
[15]
D. Miller, G. Nadathur, F. Pfenning, and A. Scedrov. Uniform proofs as a foundation for logic programming. Proc. of APAL'91, 51:125--157, 1991.
[16]
V. Nigam, L. Jia, B. T. Loo, and A. Scedrov. Maintaining distributed logic programs incrementally. In Proc. of PPDP'11, pages 125--136. ACM, 2011.
[17]
V. Nigam and D.Miller. Algorithmic specifications in linear logic with subexponentials. In Proc. of PPDP'09, pages 129--140. ACM, 2009.
[18]
F. Pfenning. Structural cut elimination. In Proc. of LICS'95, pages 156--166. IEEE Press, 1995.
[19]
L. Vieille. Recursive axioms in deductive databases: The query/subquery approach. In Expert Database Conf., pages 253--267. Benjamin Cummings, 1986.

Cited By

View all

Index Terms

  1. Modeling datalog fact assertion and retraction in linear logic

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Other conferences
    PPDP '12: Proceedings of the 14th symposium on Principles and practice of declarative programming
    September 2012
    226 pages
    ISBN:9781450315227
    DOI:10.1145/2370776
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    Sponsors

    • Kuleuven Belgium: Kuleuven Belgium

    In-Cooperation

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 19 September 2012

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. assertion
    2. datalog
    3. linear logic
    4. retraction

    Qualifiers

    • Research-article

    Conference

    PPDP'12
    Sponsor:
    • Kuleuven Belgium

    Acceptance Rates

    Overall Acceptance Rate 230 of 486 submissions, 47%

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)1
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 14 Feb 2025

    Other Metrics

    Citations

    Cited By

    View all

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Figures

    Tables

    Media

    Share

    Share

    Share this Publication link

    Share on social media