Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T21:53:07.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Reasoning on Multirelational Contextual Hierarchies via Answer Set Programming with Algebraic Measures

Published online by Cambridge University Press:  05 November 2021

LORIS BOZZATO Open the ORCID record for LORIS BOZZATO [Opens in a new window] ,
THOMAS EITER Open the ORCID record for THOMAS EITER [Opens in a new window]  and
RAFAEL KIESEL Open the ORCID record for RAFAEL KIESEL [Opens in a new window]
LORIS BOZZATO
Affiliation:
Fondazione Bruno Kessler, Via Sommarive 18, 38123 Trento, Italy (e-mail: [email protected])
THOMAS EITER
Affiliation:
Technische Universit¨at Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria (e-mails: [email protected], [email protected])
RAFAEL KIESEL
Affiliation:
Technische Universit¨at Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria (e-mails: [email protected], [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Dealing with context-dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework, which is rooted in description logics but links on the reasoning side strongly to logic programs and Answer Set Programming (ASP) in particular. The CKR framework caters for reasoning with defeasible axioms and exceptions in contexts, which was extended to knowledge inheritance across contexts in a coverage (specificity) hierarchy. However, the approach supports only this single type of contextual relation and the reasoning procedures work only for restricted hierarchies, due to nontrivial issues with model preference under exceptions. In this paper, we overcome these limitations and present a generalization of CKR hierarchies to multiple contextual relations, along with their interpretation of defeasible axioms and preference. To support reasoning, we use ASP with algebraic measures, which is a recent extension of ASP with weighted formulas over semirings that allows one to associate quantities with interpretations depending on the truth values of propositional atoms. Notably, we show that for a relevant fragment of CKR hierarchies with multiple contextual relations, query answering can be realized with the popular asprin framework. The algebraic measures approach is more powerful and enables, for example, reasoning with epistemic queries over CKRs, which opens interesting perspectives for the use of quantitative ASP extensions in other applications.

Keywords

defeasible knowledgedescription logicsASPalgebraic measuresjustifiable exceptions
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Issue 5: 37th International Conference on Logic Programming Special Issue I , September 2021 , pp. 593 - 609
Check for updates
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re- use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

Baader, F., Calvanese, D., McGuinness, D., Nardi, D. and Patel-Schneider, P., Eds. 2003. The Description Logic Handbook. Cambridge University Press.Google Scholar
Bistarelli, S., Montanari, U., Rossi, F., Schiex, T., Verfaillie, G. and Fargier, H. 1999. Semiring-based csps and valued csps: Frameworks, properties, and comparison. Constraints 4, 199–240.Google Scholar
Bonatti, P. A., Faella, M., Petrova, I. and Sauro, L. 2015. A new semantics for overriding in description logics. Artificial Intelligence 222, 1–48.Google Scholar
Bozzato, L., Eiter, T. and Serafini, L. 2018a. Enhancing context knowledge repositories with justifiable exceptions. Artificial Intelligence 257, 72–126.CrossRefGoogle Scholar
Bozzato, L., Eiter, T. and Serafini, L. 2019. Justifiable exceptions in general contextual hierarchies. In Proc. Context 2019, G. Bella and P. Bouquet, Eds. LNCS, vol. 11939. Springer, 26–39.Google Scholar
Bozzato, L. and Serafini, L. 2013. Materialization calculus for contexts in the semantic web. In DL2013. CEUR-WP, vol. 1014. CEUR-WS.org, 552–572.Google Scholar
Bozzato, L., Serafini, L. and Eiter, T. 2018b. Reasoning with justifiable exceptions in contextual hierarchies. In Proceedings of KR 2018. AAAI Press, 329–338.Google Scholar
Brewka, G., Delgrande, J. P., Romero, J. and Schaub, T. 2015. asprin: Customizing answer set preferences without a headache. In Proceedings of AAAI 2015. AAAI Press, 1467–1474.Google Scholar
Britz, K., Casini, G., Meyer, T., Moodley, K., Sattler, U. and Varzinczak, I. 2021. Principles of KLM-style defeasible description logics. ACM Transactions on Computational Logic 22, 1, 1:1–1:46.Google Scholar
Buccafurri, F., Faber, W. and Leone, N. 1999. Disjunctive logic programs with inheritance. In Proceedings of ICLP 1999, D. D. Schreye, Ed. MIT Press, 79–93.Google Scholar
Calvanese, D., Kharlamov, E., Nutt, W. and Thorne, C. 2008. Aggregate queries over ontologies. In Proceedings of ONISW 2008. ACM Press, 97–104.Google Scholar
de Bruijn, J., Eiter, T. and Tompits, H. 2008. Embedding approaches to combining rules and ontologies into autoepistemic logic. In KR 2008. AAAI Press, 485–495.Google Scholar
Droste, M. and Gastin, P. 2005. Weighted automata and weighted logics. In Proceedings of ICALP 2005. LNCS, vol. 3580. Springer, 513–525.Google Scholar
Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R. and Tompits, H. 2008. Combining answer set programming with description logics for the semantic web. Artificial Intelligence 172, 1495–1539.CrossRefGoogle Scholar
Eiter, T. and Kiesel, R. 2020. Weighted LARS for quantitative stream reasoning. In Proceedings of ECAI 2020. Frontiers in Artificial Intelligence and Applications, vol. 325. IOS Press, 729–736.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385.CrossRefGoogle Scholar
Gil, O. F. 2014. On the nonmonotonic description logic. CoRR abs/1404.6566.Google Scholar
Giordano, L. and Dupré, D. T. 2020. An ASP approach for reasoning in a concept-aware multipreferential lightweight DL. Theory and Practice of Logic Programming 20, 5, 751–766.CrossRefGoogle Scholar
Giordano, L., Gliozzi, V., Olivetti, N. and Pozzato, G. L. 2011. Reasoning about typicality in low complexity DLs: The logics and. In Proceedings of IJCAI 2011. AAAI Press, 894–899.Google Scholar
Giunchiglia, F. and Serafini, L. 1994. Multilanguage hierarchical logics, or: How we can do without modal logics. Artificial Intelligence 65, 1, 29–70.CrossRefGoogle Scholar
Green, T. J., Karvounarakis, G. and Tannen, V. 2007. Provenance semirings. In Proceedings of PODS 2007. ACM, 31–40.Google Scholar
Horrocks, I., Kutz, O. and Sattler, U. 2006. The even more irresistible. In Proceedings KR 2006. AAAI Press, 57–67.Google Scholar
Kimmig, A., Van den Broeck, G. and De Raedt, L. 2011. An algebraic prolog for reasoning about possible worlds. In Proc. AAAI 2011. AAAI Press, 209–214.Google Scholar
Klarman, S. 2013. Reasoning with contexts in description logics. Ph.D. thesis, VU Amsterdam.Google Scholar
Krötzsch, M. 2010. Efficient inferencing for OWL EL. In Proceedings of JELIA 2010. Springer, 234–246.Google Scholar
McCarthy, J. 1993. Notes on formalizing context. In Proceedings of IJCAI 1993. Morgan Kaufmann, 555–562.Google Scholar
Pensel, M. and Turhan, A. 2018. Reasoning in the defeasible description logic - computing standard inferences under rational and relevant semantics. International Journal of Approximate Reasoning 103, 28–70.CrossRefGoogle Scholar
Serafini, L. and Homola, M. 2012. Contextualized knowledge repositories for the semantic web. Journal of Web Semantics 12, 64–87.CrossRefGoogle Scholar
Straccia, U., Lopes, N., Lukácsy, G. and Polleres, A. 2010. A general framework for representing and reasoning with annotated semantic web data. In Proceedings of AAAI 2010. AAAI Press, 1437–1442.Google Scholar
Supplementary material: PDF

Bozzato et al. supplementary material

Online Appendix

Download Bozzato et al. supplementary material(PDF)
PDF 259.5 KB