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On the monotonicity of (LDL) logic programs with set

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Abstract

LDL is one of the recently proposed logical query languages, which incorporate set, for data and knowledge base systems. Since LDL programs can simulate negation, they are not monotonic in general. On the other hand, there are monotonic LDL programs. This paper addresses the natural question of “When are the generally nonmonotonic LDL programs monotonic?” and investigates related topics such as useful applications for monotonicity. We discuss four kinds of monotonicity, and examine two of them in depth. The first of the two, called “ω-monotonicity”, is shown to be undecidable even when limited to single-stratum programs. The second, called “uniform monotonicity”, is shown to implyω-monotonicity. We characterize the uniform monotonicity of a program (i) by a relationship between its Bancilhon-Khoshafian semantics and its LDL semantics, and (ii) with a useful property called subset completion independence. Characterization (ii) implies that uniformly monotonie programs can be evaluated more efficiently by discarding dominated facts. Finally, we provide some necessary and/or sufficient, syntactic conditions for uniform monotonicity. The conditions pinpoint (a) enumerated set terms, (b) negations of membership and inclusion, and (c) sharing of set terms as the main source for nonuniform monotonicity.

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References

  1. S. Abiteboul and S. Grumbach, COL: A language for complex objects based on recursive rules, in:Proc. Int. Workshop on Theory and Applications of Nested Relations and Complex Objects (1987).

  2. S. Abiteboul and S. Grumbach, COL: A logic-based language for complex objects, in:Advances in Database Technology — EDBT '88, Lecture Notes in Computer Science (Springer, 1988).

  3. F. Bancilhon and S. Khoshafian, A calculus for complex objects, J. Comput. Syst. Sci. 38(1989)326–340.

    Google Scholar 

  4. C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli and S. Tsur, Sets and negation in a logic database language (LDL1), in:Proc. PODS (1987) pp. 21–37.

  5. G. Dong and S. Ginsburg, On decomposing chain datalog programs into P (left-)linear sequences of chain rules, Technical report, Melbourne University (1991).

  6. M.A. Harrison,Introduction to Formal Language Theory (Addison-Wesley, Reading, MA, 1978)

    Google Scholar 

  7. R. Hull and J. Su, Untyped sets, inventions, and computable queries, a preliminary version of the paper appeared in:Proc. 1989 ACM Symp. on Principles of Database Systems, pp. 347–359; Technical Report, University of Southern California (1989).

  8. G.M. Kuper, Logic programming with sets, in:Proc. PODS (1987) pp. 11–20; complete version, ref. [10].

  9. G.M. Kuper, On the expressive power of logic programming languages with sets, in:Proc. PODS (1988) pp. 10–14.

  10. G.M. Kuper, Logic programming with sets, J. Comput. Syst. Sci. 41(1990)44–64; extended abstract, ref. [8].

    Google Scholar 

  11. J.W. Lloyd,Foundations of Logic Programming, 2nd ed. (Springer, 1987).

  12. S. Naqvi and S. Tsur,A Logical Language for Data and Knowledge Bases (Computer Science Press, New York, 1989).

    Google Scholar 

  13. O. Shmueli, S. Tsur and C. Zaniolo, Rewriting of rules containing set terms in a logic data language (LDL), in:Proc. PODS (1988).

  14. J.D. Ullman and A. Van Gelder, Parallel complexity of logical query programs, Algorithmica 3(1988)5–42.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Computer Science Department, The University of Melbourne, 3052, Parkville, Vic, Australia

    G. Dong

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  1. G. Dong
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Additional information

Supported in part by the NSF under grant CCR-86-18907. Part of the work was done while the author was at Flinders University. An extended abstract of this paper appeared in Proc. 3rd Int. Symp. on Mathematical Fundamentals of Database and Knowledge Base Systems, Germany (1991), LNCS 495, pp. 201–215.

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Dong, G. On the monotonicity of (LDL) logic programs with set. Ann Math Artif Intell 7, 107–127 (1993). https://doi.org/10.1007/BF01556352

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  • DOI: https://doi.org/10.1007/BF01556352

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