Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T04:49:53.814Z Has data issue: false hasContentIssue false
  • English
  • Français

The Expressive Power of Higher-Order Datalog

Published online by Cambridge University Press:  20 September 2019

ANGELOS CHARALAMBIDIS Open the ORCID record for ANGELOS CHARALAMBIDIS [Opens in a new window] ,
CHRISTOS NOMIKOS  and
PANOS RONDOGIANNIS
ANGELOS CHARALAMBIDIS
Affiliation:
Institute of Informatics and Telecommunications, NCSR “Demokritos”, Greece (e-mail: [email protected])
CHRISTOS NOMIKOS
Affiliation:
Dept of Computer Science and Engineering, University of Ioannina, Greece (e-mail: [email protected])
PANOS RONDOGIANNIS
Affiliation:
Dept of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

A classical result in descriptive complexity theory states that Datalog expresses exactly the class of polynomially computable queries on ordered databases (Papadimitriou 1985; Grädel 1992; Vardi 1982; Immerman 1986; Leivant 1989). In this paper we extend this result to the case of higher-order Datalog. In particular, we demonstrate that on ordered databases, for all k ≥ 2, k-order Datalog captures (k − 1)-EXPTIME. This result suggests that higher-order extensions of Datalog possess superior expressive power and they are worthwhile of further investigation both in theory and in practice.

Keywords

DatalogHigher-Order Logic ProgrammingDescriptive Complexity Theory
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 19 , Special Issue 5-6: 35th International Conference on Logic Programming , September 2019 , pp. 925 - 940
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bezem, M. 1999. Extensionality of simply typed logic programs. In Logic Programming: The 1999 International Conference, Las Cruces, New Mexico, USA, November 29 - December 4, 1999, Schreye, D. D., Ed. MIT Press, 395–410.Google Scholar
Charalambidis, A., Handjopoulos, K., Rondogiannis, P., and Wadge, W. W. 2013. Extensional higher-order logic programming. ACM Trans. on Computational Logic 14, 3, 21.Google Scholar
Charalambidis, A., Rondogiannis, P., and Symeonidou, I. 2018. Approximation fixpoint theory and the well-founded semantics of higher-order logic programs. TPLP 18, 3-4, 421–437.Google Scholar
Charalambidis, A., Rondogiannis, P., and Troumpoukis, A. 2018. Higher-order logic programming: An expressive language for representing qualitative preferences. Science of Computer Programming 155, 173–197.Google Scholar
Chen, W., Kifer, M., and Warren, D. S. 1993. HILOG: A foundation for higher-order logic programming. Journal of Logic Programming 15, 3, 187–230.Google Scholar
Dantsin, E., Eiter, T., Gottlob, G., and Voronkov, A. 2001. Complexity and expressive power of logic programming. ACM Computing Surveys 33, 3, 374–425.CrossRefGoogle Scholar
Grädel, E. 1992. Capturing complexity classes by fragments of second-order logic. Theoretical Computer Science 101, 1, 35–57.Google Scholar
Immerman, N. 1986. Relational queries computable in polynomial time. Information and Control 68, 1-3, 86–104.Google Scholar
Jones, N. D. 2001. The expressive power of higher-order types or, life without CONS. Journal of Functional Programming 11, 1, 5–94.Google Scholar
Kountouriotis, V., Rondogiannis, P., and Wadge, W. W. 2005. Extensional higher-order datalog. In Short Paper Proceedings of the 12th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR). 1–5.Google Scholar
Leivant, D. 1989. Descriptive characterizations of computational complexity. Journal of Computer and System Science 39, 1, 51–83.Google Scholar
Lloyd, J. W. 1987. Foundations of Logic Programming. Springer Verlag.Google Scholar
Lovrenčić, A. and Čubrilo, M. 1999. Amalgamation of heterogeneous data sources using amalgamated annotated hilog. In 3rd international IEEE Conference on Intelligent Engineering Systems (INES’99).Google Scholar
Miller, D. and Nadathur, G. 1986. Higher-order logic programming. In Proceedings of the Third International Conference on Logic Programming (ICLP). 448–462.Google Scholar
Papadimitriou, C. H. 1985. A note on the expressive power of prolog. Bulletin of the EATCS 26, 21–22.Google Scholar
Vardi, M. Y. 1982. The complexity of relational query languages (extended abstract). In Proceedings of the 14th Annual ACM Symposium on Theory of Computing, May 5-7, 1982, San Francisco, California, USA. ACM, 137–146.Google Scholar
Wadge, W. W. 1991. Higher-order horn logic programming. In Logic Programming, Proceedings of the 1991 International Symposium, San Diego, California, USA, Oct. 28 - Nov 1, 1991. MIT Press, 289–303.Google Scholar
Yang, G., Kifer, M., and Zhao, C. 2003. Flora-2: A rule-based knowledge representation and inference infrastructure for the semantic web. In OTM Confederated International Conferences “On the Move to Meaningful Internet Systems”. Vol. 2888. Springer, 671–688.Google Scholar
Supplementary material: PDF

Charalambidis et al. supplementary material

Online Appendix

Download Charalambidis et al. supplementary material(PDF)
PDF 302 KB