Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T19:21:43.223Z Has data issue: false hasContentIssue false
  • English
  • Français

A Syntactic Operator for Forgetting that Satisfies Strong Persistence

Published online by Cambridge University Press:  20 September 2019

MATTI BERTHOLD ,
RICARDO GONÇALVES Open the ORCID record for RICARDO GONÇALVES [Opens in a new window] ,
MATTHIAS KNORR Open the ORCID record for MATTHIAS KNORR [Opens in a new window]  and
JOÃO LEITE
MATTI BERTHOLD
Affiliation:
Technische Universität Dresden and Universität Leipzig, Germany
RICARDO GONÇALVES
Affiliation:
NOVA LINCS, Departamento de Informática, Universidade Nova de Lisboa, Portugal
MATTHIAS KNORR
Affiliation:
NOVA LINCS, Departamento de Informática, Universidade Nova de Lisboa, Portugal
JOÃO LEITE
Affiliation:
NOVA LINCS, Departamento de Informática, Universidade Nova de Lisboa, Portugal
Get access Rights & Permissions [Opens in a new window]

Abstract

Whereas the operation of forgetting has recently seen a considerable amount of attention in the context of Answer Set Programming (ASP), most of it has focused on theoretical aspects, leaving the practical issues largely untouched. Recent studies include results about what sets of properties operators should satisfy, as well as the abstract characterization of several operators and their theoretical limits. However, no concrete operators have been investigated.

In this paper, we address this issue by presenting the first concrete operator that satisfies strong persistence – a property that seems to best capture the essence of forgetting in the context of ASP – whenever this is possible, and many other important properties. The operator is syntactic, limiting the computation of the forgetting result to manipulating the rules in which the atoms to be forgotten occur, naturally yielding a forgetting result that is close to the original program.

Keywords

Answer Set ProgrammingForgettingStrong PersistenceSyntactic Operator
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. 1038 - 1055
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

Alferes, J. J., Knorr, M., and Wang, K. 2013. Forgetting under the well-founded semantics. In Procs. of LPNMR. LNCS, vol. 8148. Springer, 36–41.Google Scholar
Berthold, M., Gonçalves, R., Knorr, M., and Leite, J. 2019. A syntactic operator for forgetting that satisfies strong persistence. CoRR abs/1907.12501.Google Scholar
Brass, S. and Dix, J. 1999. Semantics of (disjunctive) logic programs based on partial evaluation. J. Log. Program. 40, 1, 1–46.Google Scholar
Cabalar, P. and Ferraris, P. 2007. Propositional theories are strongly equivalent to logic programs. TPLP 7, 6, 745–759.Google Scholar
Cabalar, P., Pearce, D., and Valverde, A. 2007. Minimal logic programs. In Procs. of ICLP. Springer.Google Scholar
Delgrande, J. P. and Wang, K. 2015. A syntax-independent approach to forgetting in disjunctive logic programs. In Procs. of AAAI. AAAI Press, 1482–1488.Google Scholar
Eiter, T. and Kern-Isberner, G. 2019. A brief survey on forgetting from a knowledge representation and reasoning perspective. KI - Künstliche Intelligenz 33, 1, 9–33.Google Scholar
Eiter, T. and Wang, K. 2008. Semantic forgetting in answer set programming. Artif. Intell. 172, 14, 1644–1672.10.1016/j.artint.2008.05.002CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Comput. 9, 3-4, 365–385.Google Scholar
Gonçalves, R., Janhunen, T., Knorr, M., Leite, J., and Woltran, S. 2019. Forgetting in modular answer set programming. In Procs. of AAAI. AAAI Press.Google Scholar
Gonçalves, R., Knorr, M., and Leite, J. 2016a. The ultimate guide to forgetting in answer set programming. In Procs. of KR. AAAI Press, 135–144.Google Scholar
Gonçalves, R., Knorr, M., and Leite, J. 2016b. You can’t always forget what you want: on the limits of forgetting in answer set programming. In Procs. of ECAI. IOS Press, 957–965.Google Scholar
Gonçalves, R., Knorr, M., and Leite, J. 2017. Iterative variable elimination in ASP. In Procs. of EPIA. LNCS, vol. 10423. Springer, 643–656.Google Scholar
Gonçalves, R., Knorr, M., Leite, J., and Woltran, S. 2017. When you must forget: Beyond strong persistence when forgetting in answer set programming. TPLP 17, 5-6, 837–854.Google Scholar
Inoue, K. and Sakama, C. 1998. Negation as failure in the head. J. Log. Program. 35, 1, 39–78.Google Scholar
Inoue, K. and Sakama, C. 2004. Equivalence of logic programs under updates. In Procs. of JELIA. Springer.Google Scholar
Knorr, M. and Alferes, J. J. 2014. Preserving strong equivalence while forgetting. In Procs. of JELIA. LNCS, vol. 8761. Springer, 412–425.Google Scholar
Kontchakov, R., Wolter, F., and Zakharyaschev, M. 2010. Logic-based ontology comparison and module extraction, with an application to dl-lite. Artif. Intell. 174, 15, 1093–1141.Google Scholar
Lang, J., Liberatore, P., and Marquis, P. 2003. Propositional independence: Formula-variable independence and forgetting. J. Artif. Intell. Res. (JAIR) 18, 391–443.Google Scholar
Lang, J. and Marquis, P. 2010. Reasoning under inconsistency: A forgetting-based approach. Artif. Intell. 174, 12-13, 799–823.Google Scholar
Leite, J. 2017. A bird’s-eye view of forgetting in answer-set programming. In Procs. of LPNMR. LNCS, vol. 10377. Springer, 10–22.Google Scholar
Lifschitz, V., Pearce, D., and Valverde, A. 2001. Strongly equivalent logic programs. ACM Trans. Comput. Log. 2, 4, 526–541.Google Scholar
Lin, F. and Reiter, R. 1997. How to progress a database. Artif. Intell. 92, 1-2, 131–167.Google Scholar
Liu, Y. and Wen, X. 2011. On the progression of knowledge in the situation calculus. In Procs. of IJCAI. IJCAI/AAAI, 976–982.Google Scholar
Rajaratnam, D., Levesque, H. J., Pagnucco, M., and Thielscher, M. 2014. Forgetting in action. In Procs. of KR. AAAI Press.Google Scholar
Slota, M. and Leite, J. 2011. Back and forth between rules and se-models. In Procs. of LPNMR. Springer.Google Scholar
Wang, Y., Wang, K., and Zhang, M. 2013. Forgetting for answer set programs revisited. In Procs. of IJCAI. IJCAI/AAAI, 1162–1168.Google Scholar
Wang, Y., Zhang, Y., Zhou, Y., and Zhang, M. 2014. Knowledge forgetting in answer set programming. J. Artif. Intell. Res. (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. Ann. Math. Artif. Intell. 58, 1-2, 117–151.10.1007/s10472-010-9187-9CrossRefGoogle Scholar
Zhang, Y. and Foo, N. Y. 2006. Solving logic program conflict through strong and weak forgettings. Artif. Intell. 170, 8-9, 739–778.CrossRefGoogle Scholar
Zhang, Y. and Zhou, Y. 2009. Knowledge forgetting: Properties and applications. Artif. Intell. 173, 16-17, 1525–1537.CrossRefGoogle Scholar