Skip to main content

Pruning Search Space for Weighted First Order Horn Clause Satisfiability

  • Conference paper
Inductive Logic Programming (ILP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6489))

Included in the following conference series:

  • 801 Accesses

Abstract

Many SRL models pose logical inference as weighted satisfiability solving. Performing logical inference after completely grounding clauses with all possible constants is computationally expensive and approaches such as LazySAT [8] utilize the sparseness of the domain to deal with this. Here, we investigate the efficiency of restricting the Knowledge Base (Σ) to the set of first order horn clauses. We propose an algorithm that prunes the search space for satisfiability in horn clauses and prove that the optimal solution is guaranteed to exist in the pruned space. The approach finds a model, if it exists, in polynomial time; otherwise it finds an interpretation that is most likely given the weights. We provide experimental evidence that our approach reduces the size of search space substantially.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Selman, B., Levesque, H., Mitchell, D.: A New Method for Solving Hard Satisfiability Problems. In: AAAI 1992, San Jose, CA, pp. 440–446 (1992)

    Google Scholar 

  2. Selman, B., Kautz, H., Cohen, B.: Local Search Strategies for Satisfiability Testing. In: Second DIMACS Implementation Challenge on Cliques, Coloring and Satisfiability (1993)

    Google Scholar 

  3. Hogger, C.J.: Essentials of logic programming. Oxford University Press, New York (1990)

    MATH  Google Scholar 

  4. Heras, F., Larrosa, J., Oliveras, A.: MINIMAXSAT: an efficient weighted max-SAT solver. Journal of Artificial Intelligence Research 31(1), 1–32 (2008)

    MathSciNet  MATH  Google Scholar 

  5. Kisynski, J., Poole, D.: Lifted aggregation in directed first-order probabilistic models. In: Proceedings of the 21st International Joint Conference on Artifical Intelligence, California, USA, pp. 1922–1929 (2009)

    Google Scholar 

  6. Davis, M., Putnam, H., Logemann, G., Loveland, D.W.: A Machine Program for Theorem Proving. Communications of the ACM 5(7), 394–397 (1962)

    Article  MATH  Google Scholar 

  7. Singla, P., Domingos, P.: Discriminative training of Markov Logic Networks. In: AAAI 2005, pp. 868–873 (2005)

    Google Scholar 

  8. Singla, P., Domingos, P.: Memory-Efficient Inference in Relational Domains. In: Proceedings of the Twenty-First National Conference on Artificial Intelligence, pp. 488–493. AAAI Press, Boston (2006)

    Google Scholar 

  9. Alsinet, T., Many, F., Planes, J.: An efficient solver for weighted Max-SAT. Journal of Global Optimization, 61–73 (2008)

    Google Scholar 

  10. Shavlik, J., Natarajan, S.: Speeding up inference in Markov logic networks by preprocessing to reduce the size of the resulting grounded network. In: Proceedings of the 21st International JCAI (2009)

    Google Scholar 

  11. Fern, A.: A Penalty-Logic Simple-Transition Model for Structured Sequences. In: Computational Intelligence, pp. 302–334 (2009)

    Google Scholar 

  12. Mihalkova, L., Richardson, M.: Speeding up inference in statistical relational learning by clustering similar query literals. In: De Raedt, L. (ed.) ILP 2009. LNCS, vol. 5989, pp. 110–122. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. http://alchemy.cs.washington.edu/

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nair, N., Govindan, A., Jayaraman, C., Kiran, T.V.S., Ramakrishnan, G. (2011). Pruning Search Space for Weighted First Order Horn Clause Satisfiability. In: Frasconi, P., Lisi, F.A. (eds) Inductive Logic Programming. ILP 2010. Lecture Notes in Computer Science(), vol 6489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21295-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21295-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21294-9

  • Online ISBN: 978-3-642-21295-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics