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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)
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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 

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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.

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