Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-25T12:21:04.852Z Has data issue: false hasContentIssue false
  • English
  • Français

When you must forget: Beyond strong persistence when forgetting in answer set programming*

Published online by Cambridge University Press:  30 August 2017

RICARDO GONÇALVES Open the ORCID record for RICARDO GONÇALVES [Opens in a new window] ,
MATTHIAS KNORR ,
JOÃO LEITE  and
STEFAN WOLTRAN
RICARDO GONÇALVES
Affiliation:
NOVA LINCS, Universidade Nova de Lisboa, Lisboa, Portugal (e-mails: rjrg@fct.unl.pt, mkn@fct.unl.pt, jleite@fct.unl.pt)
MATTHIAS KNORR
Affiliation:
NOVA LINCS, Universidade Nova de Lisboa, Lisboa, Portugal (e-mails: rjrg@fct.unl.pt, mkn@fct.unl.pt, jleite@fct.unl.pt)
JOÃO LEITE
Affiliation:
NOVA LINCS, Universidade Nova de Lisboa, Lisboa, Portugal (e-mails: rjrg@fct.unl.pt, mkn@fct.unl.pt, jleite@fct.unl.pt)
STEFAN WOLTRAN
Affiliation:
TU Wien, Wien, Austria (e-mail: woltran@dbai.tuwien.ac.at)
Get access Rights & Permissions [Opens in a new window]

Abstract

Among the myriad of desirable properties discussed in the context of forgetting in Answer Set Programming, strong persistence naturally captures its essence. Recently, it has been shown that it is not always possible to forget a set of atoms from a program while obeying this property, and a precise criterion regarding what can be forgotten has been presented, accompanied by a class of forgetting operators that return the correct result when forgetting is possible. However, it is an open question what to do when we have to forget a set of atoms, but cannot without violating this property. In this paper, we address this issue and investigate three natural alternatives to forget when forgetting without violating strong persistence is not possible, which turn out to correspond to the different possible relaxations of the characterization of strong persistence. Additionally, we discuss their preferable usage, shed light on the relation between forgetting and notions of relativized equivalence established earlier in the context of Answer Set Programming, and present a detailed study on their computational complexity.

Keywords

forgettingAnswer Set Programmingstrong equivalencerelativized equivalencecomputational complexity
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 17 , Special Issue 5-6: 33rd International Conference on Logic Programming , September 2017 , pp. 837 - 854
Copyright
Copyright © Cambridge University Press 2017 

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.)

Footnotes

*

R. Gonçalves, M. Knorr and J. Leite were partially supported by FCT strategic project NOVA LINCS (UID/CEC/04516/2013). R. Gonçalves was partially supported by FCT grant SFRH/BPD/100906/2014 and M. Knorr by FCT grant SFRH/BPD/86970/2012. S. Woltran was supported by the Austrian Science Fund (FWF): Y698, P25521.

References

Alferes, J. J., Knorr, M. and Wang, K. 2013. Forgetting under the well-founded semantics. In Proc. of LPNMR, Cabalar, P. and Son, T. C., Eds. Lecture Notes in Computer Science, vol. 8148. Springer, 36–41.Google Scholar
Alferes, J. J., Leite, J. A., Pereira, L. M., Przymusinska, H. and Przymusinski, T. C. 2000. Dynamic updates of non-monotonic knowledge bases. The Journal of Logic Programming 45, 1–3, 43–70.Google Scholar
Bledsoe, W. W. and Hines, L. M. 1980. Variable elimination and chaining in a resolution-based prover for inequalities. In Proc. of CADE, Bibel, W. and Kowalski, R. A., Eds. Lecture Notes in Computer Science, vol. 87. Springer, 70–87.Google Scholar
Delgrande, J. P., Schaub, T., Tompits, H. and Woltran, S. 2013. A model-theoretic approach to belief change in answer set programming. ACM Transactions on Computational Logic 14, 2, 14.Google Scholar
Delgrande, J. P. and Wang, K. 2015. A syntax-independent approach to forgetting in disjunctive logic programs. In Proc. of AAAI, Bonet, B. and Koenig, S., Eds. AAAI Press, 1482–1488.Google Scholar
Eiter, T., Fink, M., Sabbatini, G. and Tompits, H. 2002. On properties of update sequences based on causal rejection. Theory and Practice of Logic Programming (TPLP) 2, 6, 721–777.Google Scholar
Eiter, T., Fink, M. and Woltran, S. 2007. Semantical characterizations and complexity of equivalences in answer set programming. ACM Transactions on Computational Logic 8, 3, 1–53.Google Scholar
Eiter, T. and Gottlob, G. 1995. On the computational cost of disjunctive logic programming: Propositional case. Annals of Mathematics and Artificial Intelligence 15, 3–4, 289–323.Google Scholar
Eiter, T. and Wang, K. 2008. Semantic forgetting in answer set programming. Artificial Intelligence 172, 14, 1644–1672.Google Scholar
European Parliament. 2016. General data protection regulation. Official Journal of the European Union L119/59, 1–88.Google Scholar
Gonçalves, R., Knorr, M. and Leite, J. 2016a. Forgetting in ASP: The forgotten properties. In Proc. of JELIA, Michael, L. and Kakas, A. C., Eds. Lecture Notes in Computer Science, vol. 10021. Springer, 543–550.Google Scholar
Gonçalves, R., Knorr, M. and Leite, J. 2016b. The ultimate guide to forgetting in answer set programming. In Proc. of KR, Baral, C., Delgrande, J. and Wolter, F., Eds. AAAI Press, 135–144.Google Scholar
Gonçalves, R., Knorr, M. and Leite, J. 2016c. You can't always forget what you want: On the limits of forgetting in answer set programming. In Proc. of ECAI, Fox, M. S. and Kaminka, G. A., Eds. IOS Press, 957–965.Google Scholar
Knorr, M. and Alferes, J. J. 2014. Preserving strong equivalence while forgetting. In Proc. of JELIA, Fermé, E. and Leite, J., Eds. Lecture Notes in Computer Science, vol. 8761. Springer, 412–425.Google Scholar
Konev, B., Ludwig, M., Walther, D. and Wolter, F. 2012. The logical difference for the lightweight description logic EL. Journal of Artificial Intelligence Research (JAIR) 44, 633–708.CrossRefGoogle Scholar
Konev, B., Lutz, C., Walther, D. and Wolter, F. 2013. Model-theoretic inseparability and modularity of description logic ontologies. Artificial Intelligence 203, 66–103.Google Scholar
Kontchakov, R., Wolter, F. and Zakharyaschev, M. 2010. Logic-based ontology comparison and module extraction, with an application to dl-lite. Artificial Intelligence 174, 15, 1093–1141.Google Scholar
Lang, J., Liberatore, P. and Marquis, P. 2003. Propositional independence: Formula-variable independence and forgetting. Journal of Artificial Intelligence Research (JAIR) 18, 391–443.Google Scholar
Lang, J. and Marquis, P. 2010. Reasoning under inconsistency: A forgetting-based approach. Artificial Intelligence 174, 12–13, 799–823.Google Scholar
Larrosa, J. 2000. Boosting search with variable elimination. In Proc. of CP, Dechter, R., Ed. Lecture Notes in Computer Science, vol. 1894. Springer, 291–305.Google Scholar
Larrosa, J., Morancho, E. and Niso, D. 2005. On the practical use of variable elimination in constraint optimization problems: ‘still-life’ as a case study. Journal of Artificial Intelligence Research (JAIR) 23, 421–440.Google Scholar
Leite, J. 2017. A bird's-eye view of forgetting in answer-set programming. In Proc. of LPNMR, Balduccini, M. and Janhunen, T., Eds. LNAI, vol. 10377. Springer, 10–22.Google Scholar
Lewis, C. I. 1918. A Survey of Symbolic Logic. University of California Press. Republished by Dover, 1960.Google Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 4, 526–541.Google Scholar
Lifschitz, V., Tang, L. R. and Turner, H. 1999. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25, 3–4, 369–389.Google Scholar
Lin, F. and Reiter, R. 1997. How to progress a database. Artificial Intelligence 92, 1–2, 131–167.CrossRefGoogle Scholar
Liu, Y. and Wen, X. 2011. On the progression of knowledge in the situation calculus. In Proc. of IJCAI, T. Walsh, Ed. IJCAI/AAAI, 976–982.Google Scholar
Middeldorp, A., Okui, S. and Ida, T. 1996. Lazy narrowing: Strong completeness and eager variable elimination. Theoretical Computer Science 167, 1&2, 95–130.Google Scholar
Moinard, Y. 2007. Forgetting literals with varying propositional symbols. Journal of Logic and Computation 17, 5, 955–982.CrossRefGoogle Scholar
Rajaratnam, D., Levesque, H. J., Pagnucco, M. and Thielscher, M. 2014. Forgetting in action. In Proc. of KR, Baral, C., Giacomo, G. D., and Eiter, T., Eds. AAAI Press, 498–507.Google Scholar
Sakama, C. and Inoue, K. 2003. An abductive framework for computing knowledge base updates. Theory and Practice of Logic Programming (TPLP) 3, 6, 671–713.Google Scholar
Slota, M. and Leite, J. 2012. Robust equivalence models for semantic updates of answer-set programs. In Proc. of KR, Brewka, G., Eiter, T., and McIlraith, S. A., Eds. AAAI Press, 158–168.Google Scholar
Slota, M. and Leite, J. 2014. The rise and fall of semantic rule updates based on se-models. Theory and Practice of Logic Programming 14, 6, 869–907.Google Scholar
Wang, Y., Wang, K. and Zhang, M. 2013. Forgetting for answer set programs revisited. In Proc. of IJCAI, Rossi, F., Ed. IJCAI/AAAI, 1163–1168.Google Scholar
Wang, Y., Zhang, Y., Zhou, Y. and Zhang, M. 2012. Forgetting in logic programs under strong equivalence. In Proc of KR, Brewka, G., Eiter, T., and McIlraith, S. A., Eds. AAAI Press, 643–647.Google Scholar
Wang, Y., Zhang, Y., Zhou, Y. and Zhang, M. 2014. Knowledge forgetting in answer set programming. Journal of Artificial Intelligence Research (JAIR) 50, 31–70.Google Scholar
Wang, Z., Wang, K., Topor, R. W. and Pan, J. Z. 2010. Forgetting for knowledge bases in DL-Lite. Annals of Mathematics and Artificial Intelligence 58, 1–2, 117–151.CrossRefGoogle Scholar
Weber, A. 1986. Updating propositional formulas. In Expert Database Conf., 487–500.Google Scholar
Wong, K.-S. 2009. Forgetting in logic programs. Ph.D. thesis, The University of New South Wales.Google Scholar
Zhang, Y. and Foo, N. Y. 2006. Solving logic program conflict through strong and weak forgettings. Artificial Intelligence 170, 8–9, 739–778.Google Scholar