# Best-effort inductive logic programming via fine-grained cost-based hypothesis generation

- 148 Downloads

**Part of the following topical collections:**

## Abstract

We describe the Inspire system which participated in the first competition on inductive logic programming (ILP). Inspire is based on answer set programming (ASP). The distinguishing feature of Inspire is an ASP encoding for hypothesis space generation: given a set of facts representing the mode bias, and a set of cost configuration parameters, each answer set of this encoding represents a single rule that is considered for finding a hypothesis that entails the given examples. Compared with state-of-the-art methods that use the length of the rule body as a metric for rule complexity, our approach permits a much more fine-grained specification of the shape of hypothesis candidate rules. The Inspire system iteratively increases the rule cost limit and thereby increases the search space until it finds a suitable hypothesis. The system searches for a hypothesis that entails a single example at a time, utilizing an ASP encoding derived from the encoding used in XHAIL. We perform experiments with the development and test set of the ILP competition. For comparison we also adapted the ILASP system to process competition instances. Experimental results show that the cost parameters for the hypothesis search space are an important factor for finding hypotheses to competition instances within tight resource bounds.

## Keywords

Inductive logic programming Answer set programming Hypothesis generation Rule complexity Best-effort## Notes

### Acknowledgements

This work has been supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under Grant Agreement 114E777, by the Austrian Science Fund (FWF) under Grant Agreement P27730, and by the Austrian Research Promotion Agency (FFG) under Grant Agreement 861263.

## References

- Alviano, M., Dodaro, C., Marques-Silva, J., & Ricca, F. (2015). Optimum stable model search: Algorithms and implementation.
*Journal of Logic and Computation*, article number exv061.Google Scholar - Andres, B., Kaufmann, B., Matheis, O., & Schaub, T. (2012). Unsatisfiability-based optimization in clasp. In
*International conference on logic programming (ICLP), technical communications*(pp. 212–221).Google Scholar - Ansótegui, C., Bonet, M. L., & Levy, J. (2013). SAT-based MaxSAT algorithms.
*Artificial Intelligence*,*196*, 77–105.MathSciNetCrossRefzbMATHGoogle Scholar - Apt, K. R., Blair, H. A., & Walker, A. (1988). Towards a theory of declarative knowledge. In J. Minker (Ed.),
*Foundations of deductive databases and logic programming*(pp. 89–148). Morgan Kaufmann.Google Scholar - Athakravi, D., Alrajeh, D., Broda, K., Russo, A., & Satoh, K. (2015). Inductive learning using constraint-driven bias. In J. Davis & J. Ramon (Eds.),
*Inductive logic programming*(pp. 16–32). Cham: Springer.CrossRefGoogle Scholar - Athakravi, D., Corapi, D., Broda, K., & Russo, A. (2014). Learning through hypothesis refinement using answer set programming. In G. Zaverucha, V. Santos Costa, & A. Paes (Eds.),
*Inductive logic programming*(pp. 31–46). Berlin: Springer.Google Scholar - Baral, C. (2004).
*Knowledge representation, reasoning, and declarative problem solving*. Cambridge: Cambridge University Press.zbMATHGoogle Scholar - Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet allocation.
*Journal of Machine Learning*,*3*, 993–1022.zbMATHGoogle Scholar - Brewka, G., Eiter, T., & Truszczynski, M. (2011). Answer set programming at a glance.
*Communications of the ACM*,*54*(12), 92–103.CrossRefGoogle Scholar - Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., et al. (2012).
*ASP-Core-2 input language format*. Tech. rep., ASP Standardization Working Group.Google Scholar - Clocksin, W. F., & Mellish, C. S. (2003).
*Programming in PROLOG*. Berlin: Springer.CrossRefzbMATHGoogle Scholar - Corapi, D., Russo, A., De Vos, M., Padget, J., & Satoh, K. (2011). Normative design using inductive learning.
*Theory and Practice of Logic Programming*,*11*(4–5), 783–799.MathSciNetCrossRefzbMATHGoogle Scholar - Corapi, D., Russo, A., & Lupu, E. (2010). Inductive logic programming as abductive search. In: International conference on logic programming (ICLP), technical communications, (pp. 54–63).Google Scholar
- Corapi, D., Russo, A., & Lupu, E. (2012). Inductive logic programming in answer set programming. In S. H. Muggleton, A. Tamaddoni-Nezhad, & F. A. Lisi (Eds.),
*Inductive logic programming*(pp. 91–97). Berlin: Springer.CrossRefGoogle Scholar - Craven, M. (2001). Relational learning with statistical predicate invention.
*Machine Learning*,*43*, 97–119.CrossRefzbMATHGoogle Scholar - Dietterich, T. G., Domingos, P., Getoor, L., Muggleton, S., & Tadepalli, P. (2008). Structured machine learning: The next ten years.
*Machine Learning*,*73*(1), 3–23.CrossRefGoogle Scholar - Faber, W., Pfeifer, G., & Leone, N. (2011). Semantics and complexity of recursive aggregates in answer set programming.
*Artificial Intelligence*,*175*(1), 278–298.MathSciNetCrossRefzbMATHGoogle Scholar - Flach, P. A. (1993). Predicate invention in inductive data engineering. In
*European conference on machine learning (EMCL)*(pp. 83–94).Google Scholar - Gebser, M., Kaminski, R., Kaufmann, B., & Schaub, T. (2012a).
*Answer set solving in practice*. Morgan Claypool.Google Scholar - Gebser, M., Kaminski, R., König, A., & Schaub, T. (2011). Advances in gringo series 3. In
*International conference on logic programming and non-monotonic reasoning (LPNMR)*(pp. 345–351).Google Scholar - Gebser, M., Kaufmann, B., & Schaub, T. (2012b). Conflict-driven answer set solving: From theory to practice.
*Artificial Intelligence*,*187–188*, 52–89.MathSciNetCrossRefzbMATHGoogle Scholar - Gelfond, M., & Kahl, Y. (2014).
*Knowledge representation, reasoning, and the design of intelligent agents: The answer-set programming approach*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Gelfond, M., & Lifschitz, V. (1988). The stable model semantics for logic programming. In
*International conference and symposium on logic programming (ICLP/SLP)*(pp. 1070–1080).Google Scholar - Gulwani, S., Hernández-Orallo, J., Kitzelmann, E., Muggleton, S. H., Schmid, U., & Zorn, B. (2015). Inductive programming meets the real world.
*Communications of the ACM*,*58*(11), 90–99.CrossRefGoogle Scholar - Kakas, A. C., Kowalski, R. A., & Toni, F. (1992). Abductive logic programming.
*Journal of Logic and Computation*,*2*(6), 719–770.MathSciNetCrossRefzbMATHGoogle Scholar - Katzouris, N., Artikis, A., & Paliouras, G. (2015). Incremental learning of event definitions with inductive logic programming.
*Machine Learning*,*100*(2–3), 555–585.MathSciNetCrossRefzbMATHGoogle Scholar - Kazmi, M., Schüller, P., & Saygn, Y. (2017). Improving scalability of inductive logic programming via pruning and best-effort optimisation.
*Expert Systems with Applications*,*87*, 291–303.CrossRefGoogle Scholar - Law, M., Russo, A., & Broda, K. (2014). Inductive learning of answer set programs. In
*European conference on logics in artificial intelligence (JELIA)*(pp. 311–325).Google Scholar - Law, M., Russo, A., & Broda, K. (2015). Learning weak constraints in answer set programming.
*Theory and Practice of Logic Programming*,*15*(4–5), 511–525.MathSciNetCrossRefzbMATHGoogle Scholar - Law, M., Russo, A., & Broda, K. (2016a). Iterative learning of answer set programs from context dependent examples.
*Theory and Practice of Logic Programming*,*16*(5–6), 834–848.MathSciNetCrossRefzbMATHGoogle Scholar - Law, M., Russo, A., & Broda, K. (2017).
*Inductive learning of answer set programs v3.1.0 user manual*. Tech. rep., Imperial College of Science, Technology and Medicine, Department of Computing.Google Scholar - Law, M., Russo, A., Cussens, J., & Broda, K. (2016b).
*The 2016 competition on inductive logic programming*. Retrieved March 29, 2017, http://ilp16.doc.ic.ac.uk/competition. - LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning.
*Nature*,*521*(7553), 436–444.CrossRefGoogle Scholar - Lifschitz, V. (2008). What is answer set programming? In
*AAAI conference on artificial intelligence*(pp. 1594–1597).Google Scholar - Mitra, A., & Baral, C. (2016). Addressing a question answering challenge by combining statistical methods with inductive rule learning and reasoning. In D. Schuurmans & M. P. Wellman (Eds.),
*Association for the advancement of artificial intelligence*(pp. 2779–2785). AAAI Press.Google Scholar - Muggleton, S. (1987). Duce, an oracle-based approach to constructive induction. In
*International joint conference on artificial intelligence (IJCAI)*(pp. 287–292).Google Scholar - Muggleton, S. (1995). Inverse entailment and Progol.
*New generation computing*,*13*(3–4), 245–286.CrossRefGoogle Scholar - Muggleton, S., & Buntine, W. (1992). Machine invention of first-order predicates by inverting resolution. In
*Proceedings of the fifth international conference on machine learning*(pp. 339–352).Google Scholar - Muggleton, S., & De Raedt, L. (1994). Inductive logic programming: Theory and methods.
*The Journal of Logic Programming*,*19*, 629–679.MathSciNetCrossRefzbMATHGoogle Scholar - Muggleton, S., De Raedt, L., Poole, D., Bratko, I., Flach, P., Inoue, K., et al. (2012). ILP turns 20: Biography and future challenges.
*Machine Learning*,*86*(1), 3–23.MathSciNetCrossRefzbMATHGoogle Scholar - Muggleton, S. H., Lin, D., Pahlavi, N., & Tamaddoni-Nezhad, A. (2014). Meta-interpretive learning: Application to grammatical inference.
*Machine Learning*,*94*(1), 25–49.MathSciNetCrossRefzbMATHGoogle Scholar - Muggleton, S. H., Lin, D., & Tamaddoni-Nezhad, A. (2015). Meta-interpretive learning of higher-order dyadic datalog: Predicate invention revisited.
*Machine Learning*,*100*(1), 49–73.MathSciNetCrossRefzbMATHGoogle Scholar - Otero, R. P. (2001). Induction of stable models. In
*Conference on inductive logic programming*(pp. 193–205).Google Scholar - Ray, O. (2009). Nonmonotonic abductive inductive learning.
*Journal of Applied Logic*,*7*, 329–340.MathSciNetCrossRefzbMATHGoogle Scholar - Sakama, C., & Inoue, K. (2009). Brave induction: A logical framework for learning from incomplete information.
*Machine Learning*,*76*, 3–35.CrossRefGoogle Scholar