Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T17:07:36.407Z Has data issue: false hasContentIssue false
  • English
  • Français

Enhancing Magic Sets with an Application to Ontological Reasoning

Published online by Cambridge University Press:  20 September 2019

MARIO ALVIANO Open the ORCID record for MARIO ALVIANO [Opens in a new window] ,
NICOLA LEONE ,
PIERFRANCESCO VELTRI  and
JESSICA ZANGARI Open the ORCID record for JESSICA ZANGARI [Opens in a new window]
MARIO ALVIANO
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, Italy (e-mails: alviano@mat.unical.it, leone@mat.unical.it, veltri@mat.unical.it, zangari@mat.unical.it)
NICOLA LEONE
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, Italy (e-mails: alviano@mat.unical.it, leone@mat.unical.it, veltri@mat.unical.it, zangari@mat.unical.it)
PIERFRANCESCO VELTRI
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, Italy (e-mails: alviano@mat.unical.it, leone@mat.unical.it, veltri@mat.unical.it, zangari@mat.unical.it)
JESSICA ZANGARI
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, Italy (e-mails: alviano@mat.unical.it, leone@mat.unical.it, veltri@mat.unical.it, zangari@mat.unical.it)
Get access Rights & Permissions [Opens in a new window]

Abstract

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down program evaluation. This paper enhances the magic set technique by preventing the creation of (new) recursive definitions in the rewritten program. It turns out that the new version of magic sets is closed for Datalog programs with stratified negation and aggregations, which is very convenient to obtain efficient computation of the stable model of the rewritten program. Moreover, the rewritten program is further optimized by the elimination of subsumed rules and by the efficient handling of the cases where binding propagation is lost. The research was stimulated by a challenge on the exploitation of Datalog/dlv for efficient reasoning on large ontologies. All proposed techniques have been hence implemented in the dlv system, and tested for ontological reasoning, confirming their effectiveness.

Keywords

Datalogquery answeringmagic setsnonmonotonic reasoningaggregations.
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. 654 - 670
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

Adrian, W. T., Alviano, M., Calimeri, F., Cuteri, B., Dodaro, C., Faber, W., Fuscà, D., Leone, N., Manna, M., Perri, S., Ricca, F., Veltri, P., and Zangari, J. 2018. The ASP system DLV: advancements and applications. KI 32, 2-3, 177–179.Google Scholar
Alviano, M., Amendola, G., Dodaro, C., Leone, N., Maratea, M., and Ricca, F. 2019. Evaluation of disjunctive programs in WASP. In M. Balduccini, Y. Lierler, and S. Woltran (Eds.), Logic Programming and Nonmonotonic Reasoning - 15th International Conference, LPNMR 2019, Philadelphia, PA, USA, June 3-7, 2019, Proceedings, Volume 11481 of Lecture Notes in Computer Science, pp. 241–255. Springer.Google Scholar
Alviano, M., Calimeri, F., Dodaro, C., Fuscà, D., Leone, N., Perri, S., Ricca, F., Veltri, P., and Zangari, J. 2017. The ASP system DLV2. In M. Balduccini and T. Janhunen (Eds.), Logic Programming and Nonmonotonic Reasoning - 14th International Conference, LPNMR 2017, Espoo, Finland, July 3-6, 2017, Proceedings, Volume 10377 of Lecture Notes in Computer Science, pp. 215–221. Springer.Google Scholar
Alviano, M. and Dodaro, C. 2016. Anytime answer set optimization via unsatisfiable core shrinking. Theory and Practice of Logic Programming 16, 5-6, 533–551.CrossRefGoogle Scholar
Alviano, M. and Dodaro, C. 2017. Unsatisfiable core shrinking for anytime answer set optimization. In C. Sierra (Ed.), Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017, pp. 4781–4785. ijcai.org.Google Scholar
Alviano, M., Dodaro, C., Järvisalo, M., Maratea, M., and Previti, A. 2018. Cautious reasoning in ASP via minimal models and unsatisfiable cores. Theory and Practice of Logic Programming 18, 3-4, 319–336.CrossRefGoogle Scholar
Alviano, M., Dodaro, C., and Maratea, M. 2018. Shared aggregate sets in answer set programming. Theory and Practice of Logic Programming 18, 3-4, 301–318.Google Scholar
Alviano, M., Dodaro, C., and Ricca, F. 2014. Anytime computation of cautious consequences in answer set programming. Theory and Practice of Logic Programming 14, 4-5, 755–770.CrossRefGoogle Scholar
Alviano, M. and Faber, W. 2011. Dynamic magic sets and super-coherent answer set programs. AI Commun. 24, 2, 125–145.Google Scholar
Alviano, M. and Faber, W. 2018. Aggregates in answer set programming. KI 32, 2-3, 119–124.Google Scholar
Alviano, M., Faber, W., and Gebser, M. 2015. Rewriting recursive aggregates in answer set programming: back to monotonicity. Theory and Practice of Logic Programming 15, 4-5, 559–573.Google Scholar
Alviano, M., Faber, W., and Gebser, M. 2016. From non-convex aggregates to monotone aggregates in ASP. In S. Kambhampati (Ed.), Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI 2016, New York, NY, USA, 9-15 July 2016, pp. 4100–4194. IJCAI/AAAI Press.Google Scholar
Alviano, M., Faber, W., Greco, G., and Leone, N. 2012. Magic sets for disjunctive datalog programs. Artif. Intell. 187, 156–192.Google Scholar
Alviano, M., Faber, W., and Woltran, S. 2014. Complexity of super-coherence problems in ASP. Theory and Practice of Logic Programming 14, 3, 339–361.CrossRefGoogle Scholar
Alviano, M., Greco, G., and Leone, N. 2011. Dynamic magic sets for programs with monotone recursive aggregates. In J. P. Delgrande and W. Faber (Eds.), Logic Programming and Nonmonotonic Reasoning - 11th International Conference, LPNMR 2011, Vancouver, Canada, May 16-19, 2011. Proceedings, Volume 6645 of Lecture Notes in Computer Science, pp. 148–160. Springer.Google Scholar
Balbin, I., Port, G. S., Ramamohanarao, K., and Meenakshi, K. 1991. Efficient bottom-up computation of queries on stratified databases. J. Log. Program. 11, 3&4, 295–344.Google Scholar
Bancilhon, F., Maier, D., Sagiv, Y., and Ullman, J. D. 1986. Magic sets and other strange ways to implement logic programs. In A. Silberschatz (Ed.), Proceedings of the Fifth ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, March 24-26, 1986, Cambridge, Massachusetts, USA, pp. 1–15. ACM.Google Scholar
Bartholomew, M., Lee, J., and Meng, Y. 2011. First-order semantics of aggregates in answer set programming via modified circumscription. In Logical Formalizations of Commonsense Reasoning, Papers from the 2011 AAAI Spring Symposium, Technical Report SS-11-06, Stanford, California, USA, March 21-23, 2011. AAAI.Google Scholar
Beeri, C. and Ramakrishnan, R. 1991. On the power of magic. J. Log. Program. 10, 3&4, 255–299.Google Scholar
Behrend, A. 2003. Soft stratification for magic set based query evaluation in deductive databases. In F. Neven, C. Beeri, and T. Milo (Eds.), Proceedings of the Twenty-Second ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, June 9-12, 2003, San Diego, CA, USA, pp. 102–110. ACM.Google Scholar
Codish, M. and Demoen, B. 1995. Analyzing logic programs using “PROP”-ositional logic programs and a magic wand. J. Log. Program. 25, 3, 249–274.Google Scholar
Dodaro, C., Alviano, M., Faber, W., Leone, N., Ricca, F., and Sirianni, M. 2011. The birth of a WASP: preliminary report on a new ASP solver. In F. Fioravanti (Ed.), Proceedings of the 26th Italian Conference on Computational Logic, Pescara, Italy, August 31 - September 2, 2011, Volume 810 of CEUR Workshop Proceedings, pp. 99–113. CEUR-WS.org.Google Scholar
Eiter, T., Ortiz, M., Simkus, M., Tran, T., and Xiao, G. 2012. Query rewriting for horn-shiq plus rules. In J. Hoffmann and B. Selman (Eds.), Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, July 22-26, 2012, Toronto, Ontario, Canada. AAAI Press.Google Scholar
Faber, W., Pfeifer, G., and Leone, N. 2011. Semantics and complexity of recursive aggregates in answer set programming. Artif. Intell. 175, 1, 278–298.Google Scholar
Ferraris, P. 2011. Logic programs with propositional connectives and aggregates. ACM Trans. Comput. Log. 12, 4, 25.Google Scholar
Furfaro, F., Greco, S., Ganguly, S., and Zaniolo, C. 2002. Pushing extrema aggregates to optimize logic queries. Inf. Syst. 27, 5, 321–343.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., and Schaub, T. 2009. On the implementation of weight constraint rules in conflict-driven ASP solvers. In P. M. Hill and D. S. Warren (Eds.), Logic Programming, 25th International Conference, ICLP 2009, Pasadena, CA, USA, July 14-17, 2009. Proceedings, Volume 5649 of Lecture Notes in Computer Science, pp. 250–264. Springer.Google Scholar
Gelder, A. V. 1989. Negation as failure using tight derivations for general logic programs. J. Log. Program. 6, 1&2, 109–133.Google Scholar
Gelder, A. V., Ross, K. A., and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. J. ACM 38, 3, 620–650.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Comput. 9, 3/4, 365–386.Google Scholar
Gelfond, M. and Zhang, Y. 2014. Vicious circle principle and logic programs with aggregates. Theory and Practice of Logic Programming 14, 4-5, 587–601.Google Scholar
Greco, G., Greco, S., Trubitsyna, I., and Zumpano, E. 2005. Optimization of bound disjunctive queries with constraints. Theory and Practice of Logic Programming 5, 6, 713–745.CrossRefGoogle Scholar
Greco, S. 2003. Binding propagation techniques for the optimization of bound disjunctive queries. IEEE Trans. Knowl. Data Eng. 15, 2, 368–385.Google Scholar
Kemp, D. B., Srivastava, D., and Stuckey, P. J. 1995. Bottom-up evaluation and query optimization of well-founded models. Theor. Comput. Sci. 146, 1&2, 145–184.Google Scholar
Kerisit, J. and Pugin, J. 1988. Efficient query answering on stratified databases. In FGCS, pp. 719–726.Google Scholar
Leone, N., Allocca, C., Alviano, M., Calimeri, F., Civili, C., Costabile, R., Cuteri, B., Fiorentino, A., Fuscà, D., Germano, S., Laboccetta, G., Manna, M., Perri, S., Reale, K., Ricca, F., Veltri, P., and Zangari, J. 2019. Large scale DLV: preliminary results. In A. Casagrande and E. G. Omodeo (Eds.), Proceedings of the 34th Italian Conference on Computational Logic, Trieste, Italy, June 19-21, 2019., Volume 2396 of CEUR Workshop Proceedings. CEUR-WS.org.Google Scholar
Leone, N., Allocca, C., Alviano, M., Calimeri, F., Civili, C., Costabile, R., Fiorentino, A., Fuscà, D., Germano, S., Laboccetta, G., Cuteri, B., Manna, M., Perri, S., Reale, K., Ricca, F., Veltri, P., and Zangari, J. 2019. Enhancing DLV for large-scale reasoning. In M. Balduccini, Y. Lierler, and S. Woltran (Eds.), Logic Programming and Nonmonotonic Reasoning - 15th International Conference, LPNMR 2019, Philadelphia, PA, USA, June 3-7, 2019, Proceedings, Volume 11481 of Lecture Notes in Computer Science, pp. 312–325. Springer.Google Scholar
Liu, L., Pontelli, E., Son, T. C., and Truszczynski, M. 2010. Logic programs with abstract constraint atoms: The role of computations. Artif. Intell. 174, 3-4, 295–315.CrossRefGoogle Scholar
Mumick, I. S., Pirahesh, H., and Ramakrishnan, R. 1990. The magic of duplicates and aggregates. In D. McLeod, R. Sacks-Davis, and H. Schek (Eds.), 16th International Conference on Very Large Data Bases, August 13-16, 1990, Brisbane, Queensland, Australia, Proceedings., pp. 264–277. Morgan Kaufmann.Google Scholar
Pelov, N., Denecker, M., and Bruynooghe, M. 2007. Well-founded and stable semantics of logic programs with aggregates. Theory and Practice of Logic Programming 7, 3, 301–353.Google Scholar
Przymusinski, T. C. 1989. On the declarative and procedural semantics of logic programs. J. Autom. Reasoning 5, 2, 167–205.Google Scholar
Ross, K. A. 1994. Modular stratification and magic sets for datalog programs with negation. J. ACM 41, 6, 1216–1266.CrossRefGoogle Scholar
Simons, P., Niemelä, I., and Soininen, T. 2002. Extending and implementing the stable model semantics. Artif. Intell. 138, 1-2, 181–234.Google Scholar
Stuckey, P. J. and Sudarshan, S. 1994. Compiling query constraints. In V. Vianu (Ed.), Proceedings of the Thirteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, May 24-26, 1994, Minneapolis, Minnesota, USA, pp. 56–67. ACM Press.Google Scholar
Whaley, J., Avots, D., Carbin, M., and Lam, M. S. 2005. Using datalog with binary decision diagrams for program analysis. In K. Yi (Ed.), Programming Languages and Systems, Third Asian Symposium, APLAS 2005, Tsukuba, Japan, November 2-5, 2005, Proceedings, Volume 3780 of Lecture Notes in Computer Science, pp. 97–118. Springer.Google Scholar