This document discusses approaches to handling deletions in ontology stream reasoning. It presents three main approaches: global DRed using a truth maintenance system, local DRed using left-hand side contexts, and a counting approach with no re-derivation. The document evaluates these approaches on benchmark ontologies and finds that combining elements of the global and local approaches helps reduce over-deletion and re-derivation costs. It concludes by discussing directions for future work such as combining addition and deletion streams and handling inconsistencies.

1. The Maze of Deletion in
Ontology Stream Reasoning
Keynote speech at ISWC2016 Workshop on Stream Reasoning
(SR2016)
Kobe, Japan, 18 Oct, 2016
Jeff Z. Pan
Department of Computing Science
University of Aberdeen, UK

2. Ontology Stream Reasoning
• An ontology stream can be viewed as a sequence
(O1, t1), ..., (On, tn), where
• Oi is a snapshot ontology at time point ti
• Oi+1 Oi is addition (Add)
• Oi Oi+1 is deletion (Del)
• Currently, existing approaches focus on classfication /
materialisation of tractable languages, such as OWL 2 EL
• Forward Chaining Completion FCC(L, S, R)=R*(L U S), where
• L is the list of axioms to be processed
• S is the list of processed axioms
• R is a completion rule set

3. Ontology Incremental Reasoning
• A simplified setting, where deletion (Del) is an empty set
• Difference between naïve reasoning and incremental
reasoning
• naïve reasoning: FCC(O U Add, Ø, R)
• incremental reasoning: FCC(Add, FCC(O, Ø, R), R)
• where FCC(O, Ø, R), or simply R*(O), can be reused
• Among DL researchers, stream reasoning sometimes
also called incremental reasoning

4. DRed: Delete and Re-derivation
[Gupta and Mumick,1995]
• Over-deletion (OD):
• over-estimates the consequences of the original
deletion (Del)
• deletes all these potential consequences
• Re-derivation: re-derives the over-deleted
consequences
• incremental reasoning (see the previous slide)

5. What are the variants of Dred and how
well do they perform?

6. OD in Global Dred (TMS) [Ren and Pan 2011]
• Truth Maintenance System
§ A loopless directed graph
§ Nodes: axioms / entailments
§ Edges: derivation relations
among axioms / entailments
§ All entailments are reachable
from their justifications
§ OD is calculated based on
derivation relations

7. Re-D in Global Dred (TMS) [Ren and Pan 2011]
• Re-derivation:
• FCC(R*(O)OD, Ø, R)
• Limitations:
1. Need to maintain
derivation relations
2. All axioms in R*(O)OD will
be reprocessed, even
irrelevant to re-derivation

8. OD in Local Re-derivation [Kazakov and Klinov, 2013]
• This approach uses the notion of LHS context
• DEL contains the entailments that can be directly or
indirectly deriver from premises in Del
• Broken refers to all axioms sharing the relevant LHS
contexts
• OD = Broken (O Del)

9. Re-D in Local Re-derivation [Kazakov and Klinov, 2013]
• Re-derivation
• Closure needs to be re-computed for all the Broken
relevant contexts
• Limitations
• Almost always over-deletes more axioms than
necessary
• If most contexts are affected, it is similar to redo the
reasoning all over again

10. 10
No Re-derivation (Counting Approach) :
• OD: if alpha is in Del, N(alpha) will decrease 1, so are all
axioms derived from alpha
• Require all justifications for all entailments in the closure, which
is expensive even for EL.
• Good candidate for approximate reasoning
No Re-derivation [Ubani et al, 2013]

11. Can we do better?

12. Backward Chaining Re-derivation
[Ren et al. 2016]
12
alpha1
alpha2
beta1
alpha3
alpha4
beta2
• One approach is full backward chairing re-derivation
• starting from the entailments that are attempted
to be re-derived (OD)
• Limitation: the testing of the same axiom may
be invoked multiple times
• Motik et al. has related work in OWL 2 RL

13. Backward Chaining Re-derivation
[Ren et al. 2016]
13
alpha1
alpha2
beta1
alpha3
alpha4
beta2
• It is enough to use backward chaining
• to check if all premises are in R*(O), and
• produce L’=R(R*(O) OD) (R*(O) OD)
• Then use forward chaining
• to compute FCC(L’, R*(O)OD), R)

14. Experimental Setup
• Experimental Ontologies: LUBM, UOBM (10
Universities, divided into 200 ABoxes)*
• 64-bit Ubuntu 14.04 with 3.20GHz CPU and 10G
RAM allocated to JVM
• We experimented with update ratios of 2%, 4%,
10% and 20%
Compared Approaches:
• TMS-based DRed
• Local DRed
• TMS-based DRed (replacing re-derivation)
• Local DRed (replacing re-derivation)
* We are redoing some experiments on the SNOMED CT
ontology, due to some technical issues in our previous
experiment
14

15. Experiment with Count of Processed Axioms
15

16. Experiment with Time Consumption
16

17. Discussions and Outlook
• Discussions
• Three approaches for DRed
• Evaluations suggest that the combined approaches
help on OD and Re-D
• Outlook
• More evaluations with application ontologies (such
as those in smart cities) for local DRed
• Possible ways to combine different DRed
approaches
• Combine Add/Del streams with the window operator
• Inconsistency handling
17

18. Further presentation / reading
• Smart Planet session at ISWC (2pm, Wed)
• Predicting Energy Consumption of Ontology Reasoning
over Mobile Devices (Isa Guclu, Yuan-Fang Li, Jeff Z.
Pan and Martin J. Kollingbaum)
• Books on Knowledge Graph
• Jeff Z. Pan, Guido Vetere, Jose Manuel Gomez Perez
and Honghan Wu (Eds.). Exploiting Linked Data and
Knowledge Graphs for Large Organisations. Springer.
2016.
• Jeff Z. Pan, Diego Calvanese, Thomas Eiter, Ian
Horrocks, Michael Kifer, Fangzhen Lin and Yuting Zhao
(Eds.). Logical Foundations of Knowledge Graph
Construction and Querying Answering. Springer. 2016
18

19. References
• [Gupta and Mumick,1995] Gupta, A., and Mumick, I. S. 1995. Maintenance of
Materialized Views: Problems, Techniques, and Applications. IEEE Data
Engineering Bulletin 18(2):3–18.
• [Ren and Pan,2011] Yuan Ren and Jeff Z. Pan. Optimising Ontology Stream
Reasoning with Truth Maintenance System. In CIKM 2011. 831-836.
• [Kazakov and Klinov,2013] Kazakov, Y., and Klinov, P. 2013. Incremental
reasoning in owl el without bookkeeping. In ISWC 2013 . Springer. 232–247.
• [Ubani et al, 2013] Urbani, J.; Margara, A.; Jacobs, C.; van Harmelen, F.; and Bal,
H.. Dynamite: Parallel materialization of dynamic RDF data. In ISWC 2013 .
Springer. 657–672.
• Boris Motik, Yavor Nenov, Robert Piro, Ian Horrocks. Combining Rewriting and
Incremental Materialisation Maintenance for Datalog Programs with Equality. In
AAAI2015.
• [Ren et al. 2016] Yuan Ren, Jeff Z. Pan, Isa Guclu, Martin Kollingbaum. A
Combined approach to Incremental Reasoning for EL Ontologies. In RR2016,
167-183.
19

20. The Maze of Deletion in
Ontology Stream Reasoning
Acknowledgement:
Ren Yuan, Isa Guclu and Martin J. Kollingbaum
Thank you
… questions?