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Rethinking Defeasible Reasoning: A Scalable Approach

Published online by Cambridge University Press:  24 February 2020

MICHAEL J. MAHER ,
ILIAS TACHMAZIDIS Open the ORCID record for ILIAS TACHMAZIDIS [Opens in a new window] ,
GRIGORIS ANTONIOU ,
STEPHEN WADE  and
LONG CHENG
MICHAEL J. MAHER
Affiliation:
Reasoning Research Institute, Australia (e-mail: [email protected])
ILIAS TACHMAZIDIS
Affiliation:
University of Huddersfield, UK (e-mails: [email protected], [email protected], [email protected])
GRIGORIS ANTONIOU
Affiliation:
University of Huddersfield, UK (e-mails: [email protected], [email protected], [email protected])
STEPHEN WADE
Affiliation:
University of Huddersfield, UK (e-mails: [email protected], [email protected], [email protected])
LONG CHENG
Affiliation:
Dublin City University, Ireland (e-mail: [email protected])
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Abstract

Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks, and social media. Analytics in terms of defeasible reasoning – for example, for decision making – could provide richer knowledge of the underlying domain. Traditionally, defeasible reasoning has focused on complex knowledge structures over small to medium amounts of data, but recent research efforts have attempted to parallelize the reasoning process over theories with large numbers of facts. Such work has shown that traditional defeasible logics come with overheads that limit scalability. In this work, we design a new logic for defeasible reasoning, thus ensuring scalability by design. We establish several properties of the logic, including its relation to existing defeasible logics. Our experimental results indicate that our approach is indeed scalable and defeasible reasoning can be applied to billions of facts.

Keywords

defeasible reasoningparallel peasoningscalability
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 4 , July 2020 , pp. 552 - 586
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Copyright
© Cambridge University Press 2020

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Footnotes

*

We thank the referees for their comments, which helped improve this paper.

References

Antoniou, G., Batsakis, S., Mutharaju, R., Pan, J. Z., Qi, G., Tachmazidis, I., Urbani, J. and Zhou, Z. 2018. A survey of large-scale reasoning on the web of data. The Knowledge Engineering Review 33, e21.Google Scholar
Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 1999. On the modelling and analysis of regulations. In Proceedings of the Australasian Conference on Information Systems, 20–29.Google Scholar
Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 2000. A flexible framework for defeasible logics. In AAAI/IAAI. AAAI Press/The MIT Press, 405–410.Google Scholar
Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 2001. Representation results for defeasible logic. ACM Transactions on Computational Logic 2, 2, 255–287.CrossRefGoogle Scholar
Armbrust, M., Xin, R. S., Lian, C., Huai, Y., Liu, D., Bradley, J. K., Meng, X., Kaftan, T., Franklin, M. J., Ghodsi, A. and Zaharia, M. 2015. Spark sql: Relational data processing in spark. In Proceedings of the 2015 ACM SIGMOD Conference. ACM, 1383–1394.Google Scholar
Billington, D., Antoniou, G., Governatori, G. and Maher, M. J. 2010. An inclusion theorem for defeasible logics. ACM Transactions on Computational Logic 12, 1, 6.Google Scholar
Cheng, L., Van Dongen, B. and Van Der Aalst, W. 2019. Scalable discovery of hybrid process models in a cloud computing environment. IEEE Trans. Services Computing.CrossRefGoogle Scholar
Condie, T., Das, A., Interlandi, M., Shkapsky, A., Yang, M. and Zaniolo, C. 2018. Scaling-up reasoning and advanced analytics on BigData. TPLP 18, 5–6, 806–845.Google Scholar
Cook, S. and Nguyen, P. 2010. Logical Foundations of Proof Complexity. Cambridge University Press.CrossRefGoogle 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
Dowling, W. F. and Gallier, J. H. 1984. Linear-time algorithms for testing the satisfiability of propositional Horn formulae. The Journal of Logic Programming 1, 3, 267–284.CrossRefGoogle Scholar
Gelder, A. V., Ross, K. A. and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. Journal of ACM 38, 3, 620–650.Google Scholar
Goodman, E. L., Jimenez, E., Mizell, D., Al-Saffar, S., Adolf, B. and Haglin, D. J. 2011. High-Performance Computing Applied to Semantic Databases. In ESWC (2), 31–45.Google Scholar
Governatori, G. and Maher, M. J. 2017. Annotated defeasible logic. TPLP 17, 5-6, 819–836.Google Scholar
Governatori, G., Milosevic, Z. and Sadiq, S. W. 2006. Compliance checking between business processes and business contracts. In Tenth IEEE International Enterprise Distributed Object Computing Conference (EDOC 2006), 221–232.Google Scholar
Governatori, G., Olivieri, F., Rotolo, A. and Scannapieco, S. 2013. Computing strong and weak permissions in defeasible logic. Journal of Philosophical Logic 42, 6, 799–829.CrossRefGoogle Scholar
Governatori, G. and Pham, D. H. 2009. DR-CONTRACT: An architecture for e-contracts in defeasible logic. IJBPIM 4, 3, 187–199.CrossRefGoogle Scholar
Governatori, G. and Rotolo, A. 2008. BIO logical agents: Norms, beliefs, intentions in defeasible logic. Autonomous Agents and Multi-Agent Systems 17, 1, 36–69.CrossRefGoogle Scholar
Grosof, B. N., Labrou, Y. and Chan, H. Y. 1999. A declarative approach to business rules in contracts: courteous logic programs in XML. In Proceedings of the First ACM Conference on Electronic Commerce (EC-99), Denver, CO, USA, November 3–5, 1999, 68–77.Google Scholar
Hashmi, M., Governatori, G., Lam, H. and Wynn, M. T. 2018. Are we done with business process compliance: state of the art and challenges ahead. Knowledge and Information Systems 57, 1, 79–133.CrossRefGoogle Scholar
Heino, N. and Pan, J. Z. 2012. RDFS reasoning on massively parallel hardware. In The Semantic Web - ISWC 2012 – 11th International Semantic Web Conference, Boston, MA, USA, November 11–15, 2012, Proceedings, Part I, Cudré-Mauroux, P., Heflin, J., Sirin, E., Tudorache, T., Euzenat, J., Hauswirth, M., Parreira, J. X., Hendler, J., Schreiber, G., Bernstein, A., and Blomqvist, E., Eds. LNCS, vol. 7649. Springer, 133–148.Google Scholar
Islam, M. B. and Governatori, G. 2018. RuleRS: A rule-based architecture for decision support systems. Artificial Intelligence and Law 26, 4, 315–344.CrossRefGoogle Scholar
Kim, J. and Park, Y. 2015. Scalable owl-horst ontology reasoning using SPARK. In 2015 International Conference on Big Data and Smart Computing, BIGCOMP 2015, Jeju, South Korea, February 9–11, 2015, 79–86.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 Logic Programming and Nonmonotonic Reasoning – 15th International Conference, LPNMR 2019, Philadelphia, PA, USA, June 3–7, 2019, Proceedings, Balduccini, M., Lierler, Y., and Woltran, S., Eds. LNCS, vol. 11481. Springer, 312–325.Google Scholar
Liu, C., Qi, G., Wang, H. and Yu, Y. 2011. Large Scale Fuzzy pD* Reasoning Using MapReduce. In 10th International Semantic Web Conference, Bonn, Germany, October 23–27. LNCS, vol. 7031. Springer, 405–420.Google Scholar
Maher, M. J. 2001. Propositional defeasible logic has linear complexity. TPLP 1, 6, 691–711.Google Scholar
Maher, M. J. 2012. Relative expressiveness of defeasible logics. TPLP 12, 4–5, 793–810.Google Scholar
Maher, M. J. 2013. Relative expressiveness of defeasible logics II. TPLP 13, 4–5, 579–592.Google Scholar
Maher, M. J., Antoniou, G. and Billington, D. 1998. A study of provability in defeasible logic. In Proc. 11th Australian Joint Conference on Artificial Intelligence. LNCS, vol. 1502. Springer, 215–226.Google Scholar
Martinez-Angeles, C. A., de Castro Dutra, I., Costa, V. S. and Buenabad-Chávez, J. 2013. A datalog engine for GPUs. In Declarative Programming and Knowledge Management - Declarative Programming Days, KDPD 2013, Unifying INAP, WFLP, and WLP, Kiel, Germany, September 11–13, 2013, Revised Selected Papers, Hanus, M. and Rocha, R., Eds. LNCS, vol. 8439. Springer, 152–168.Google Scholar
Mutharaju, R., Hitzler, P., Mateti, P. and Lécué, F. 2015. Distributed and scalable OWL EL reasoning. In The Semantic Web. Latest Advances and New Domains – 12th European Semantic Web Conference, ESWC 2015, Portoroz, Slovenia, May 31 – June 4, 2015. Proceedings, Gandon, F., Sabou, M., Sack, H., d’Amato, C., Cudré-Mauroux, P., and Zimmermann, A., Eds. LNCS, vol. 9088. Springer, 88–103.Google Scholar
Oren, E., Kotoulas, S., Anadiotis, G., Siebes, R., ten Teije, A. and van Harmelen, F. 2009. Marvin: Distributed reasoning over large-scale Semantic Web data. J. Web Sem. 7, 4, 305–316.CrossRefGoogle Scholar
Prakken, H. 1997. Logical Tools for Modelling Legal Argument: A Study of Defeasible Reasoning in Law. Kluwer Academic Publishers.CrossRefGoogle Scholar
Skylogiannis, T., Antoniou, G., Bassiliades, N., Governatori, G. and Bikakis, A. 2007. DR-NEGOTIATE – A system for automated agent negotiation with defeasible logic-based strategies. Data & Knowledge Engineering 63, 2, 362–380.CrossRefGoogle Scholar
Tachmazidis, I. 2015. Large-scale reasoning with nonmonotonic and imperfect knowledge through mass parallelization. Ph.D. thesis, University of Huddersfield, UK.Google Scholar
Tachmazidis, I. and Antoniou, G. 2013. Computing the stratified semantics of logic programs over big data through mass parallelization. In Theory, Practice, and Applications of Rules on the Web – 7th International Symposium, RuleML 2013, Seattle, WA, USA, July 11–13, 2013. Proceedings, Morgenstern, L., Stefaneas, P. S., Lévy, F., Wyner, A. Z., and Paschke, A., Eds. LNCS, vol. 8035. Springer, 188–202.Google Scholar
Tachmazidis, I., Antoniou, G. and Faber, W. 2014. Efficient computation of the well-founded semantics over big data. TPLP 14, 4–5, 445–459.Google Scholar
Tachmazidis, I., Antoniou, G., Flouris, G. and Kotoulas, S. 2012a. Towards parallel nonmonotonic reasoning with billions of facts. In Principles of Knowledge Representation and Reasoning: Proceedings of the Thirteenth International Conference, KR 2012, Rome, Italy, June 10–14, 2012, Brewka, G., Eiter, T., and McIlraith, S. A., Eds. AAAI Press.Google Scholar
Tachmazidis, I., Antoniou, G., Flouris, G., Kotoulas, S. and McCluskey, L. 2012b. Large-scale parallel stratified defeasible reasoning. In ECAI 2012 – 20th European Conference on Artificial Intelligence. Including Prestigious Applications of Artificial Intelligence (PAIS-2012) System Demonstrations Track, Montpellier, France, August 27–31, 2012, Raedt, L. D., Bessière, C., Dubois, D., Doherty, P., Frasconi, P., Heintz, F., and Lucas, P. J. F., Eds. Frontiers in Artificial Intelligence and Applications, vol. 242. IOS Press, 738–743.Google Scholar
Urbani, J., Kotoulas, S., Maassen, J., van Harmelen, F. and Bal, H. E. 2012. Webpie: A web-scale parallel inference engine using mapreduce. Journal of Web Semantics, 10, 59–75.CrossRefGoogle Scholar
Zhou, Z., Qi, G., Liu, C., Hitzler, P. and Mutharaju, R. 2013. Scale reasoning with fuzzy-EL+ ontologies based on MapReduce. In Proceedings of the IJCAI-2013 Workshop on Weighted Logics for Artificial Intelligence, WL4AI-2013, Beijing, China, August 2013, 87–93.Google Scholar