Presented at the 12th International Conference on Business Process Management (BPM 2014), 7-11 September 2014, Eindhoven, The Netherlands. Abstract: Process discovery is the task of generating models from event logs. Mining processes that operate in an environment of high variability is an ongoing research challenge because various algorithms tend to produce spaghetti-like models. This is particularly the case when procedural models are generated. A promising direction to tackle this challenge is the usage of declarative process modelling languages like Declare, which summarise complex behaviour in a compact set of behavioural constraints. However, Declare constraints with branching are expensive to be calculated.In addition, it is often the case that hundreds of branching Declare constraints are valid for the same log, thus making, again, the discovery results unreadable. In this paper, we address these problems from a theoretical angle. More specifically, we define the class of Target- Branched Declare constraints and investigate the formal properties it exhibits. Furthermore, we present a technique for the efficient discovery of compact Target-Branched Declare models. We discuss the merits of our work through an evaluation based on a prototypical implementation using both artificial and real-world event logs.

1. Discovering
Target-Branched Declare Constraints
Claudio Di Ciccio, Fabrizio Maria Maggi, and Jan Mendling
12th International Conference on Business Process Management
Eindhoven, The Netherlands
claudio.di.ciccio@wu.ac.at

2. Outline
 Process Mining,
Control-Flow Discovery
Imperative vs declarative
process modelling
Declare and
Target-Branched Declare
Target-Branched Declare
templates’ properties
Mining Target-Branched
Declare constraints
Experimental evaluation
Conclusions
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3. Outline
 Process Mining,
Control-Flow Discovery
 Imperative vs declarative
process modelling
Declare and
Target-Branched Declare
Target-Branched Declare
templates’ properties
Mining Target-Branched
Declare constraints
Experimental evaluation
Conclusions
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4. Outline
 Process Mining and
Control-Flow Discovery
 Imperative vs declarative
process modelling
 Declare and
Target-Branched Declare
Target-Branched Declare
templates’ properties
Mining Target-Branched
Declare constraints
Experimental evaluation
Conclusions
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5. Outline
 Process Mining and
Control-Flow Discovery
 Imperative vs declarative
process modelling
 Declare and
Target-Branched Declare
 TBDeclare templates’
properties
Mining Target-Branched
Declare constraints
Experimental evaluation
Conclusions
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6. Outline
 Process Mining and
Control-Flow Discovery
 Imperative vs declarative
process modelling
 Declare and
Target-Branched Declare
 TBDeclare templates’
properties
 Mining (and pruning)
TBDeclare constraints
Experimental evaluation
Conclusions
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7. Outline
 Process Mining and
Control-Flow Discovery
 Imperative vs declarative
process modelling
 Declare and
Target-Branched Declare
 TBDeclare templates’
properties
 Mining (and pruning)
TBDeclare constraints
 Experimental evaluation
Conclusions
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8. Outline
 Process Mining and
Control-Flow Discovery
 Imperative vs declarative
process modelling
 Declare and
Target-Branched Declare
 TBDeclare templates’
properties
 Mining (and pruning)
TBDeclare constraints
 Experimental evaluation
 Conclusion
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9. The event log
Process model
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10. The event log
Process instance Event log
Trace
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11. The event log
Event
Task
Process instance Event log
Trace
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12. The event log
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Event

13. The event log
SEITE 13
Event

14. The event log
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Event

15. The event log
Process instance Event log
Trace
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16. The event log
SEITE 16
Event

17. The event log
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Event

18. The event log
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Event

19. The event log
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Event

20. Control-flow discovery
?
Objective: understanding the
temporal structure that best
describes the process behind
the event log
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21. Mining flexible processes

22. Workflow Nets
as process models

23. Flexibility vs comprehensibility
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24. Declarative modelling of
processes
 Usage of constraints
 “Open model”
 Declare
 state-of-the-art language
If A is performed,
B must be performed,
no matter if before or afterwards
(responded existence)
Whenever B is performed,
C must be performed afterwards
and B can not be repeated
until C is done
(alternate response)
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25. Declare:
Relation Constraint Templates
RespondedExistence(A, B)
If A occurs in the process instance, then B occurs as well
CAC ✗ CAACB ✓
BCAC ✓ BCC ✓
Response(A, B)
If A occurs in the process instance, then B occurs after A
BCAAC ✗ CAACB ✓
CAC ✗ BCC ✓
AlternateResponse(A, B)
Each time A occurs in the process instance, then B occurs
afterwards, before A recurs
BCAAC ✗ CAACB ✗ CACB ✓
CABCA ✗ BCC ✓ CACBBAB ✓
ChainResponse(A, B)
Each time A occurs in the process instance, then B occurs
immediately afterwards
BCAAC ✗ BCAABC ✗ BCABABC ✓
Activation Target

26. Declare:
Relation Constraint Templates
RespondedExistence(B, A)
If B occurs in the process instance, then A occurs as well
CAC ✓ CAACB ✓
BCAC ✓ BCC ✗
Precedence(A, B)
B occurs in the process instance only if preceded by A
BCAAC ✗ CAACB ✓
CAC ✓ BCC ✓
AlternatePrecedence(A, B)
Each time B occurs in the process instance, it is preceded by A
and no other B can recur in between
BCAAC ✗ CAACB ✓ CACB ✓
CABCA ✓ BCC ✗ CACBAB ✓
ChainPrecedence(A, B)
Each time B occurs in the process instance, then B occurs
immediately beforehand
BCAAC ✗ BCAABC ✗ CABABCA ✓
Target Activation

27. Constraints mining
?
Objective: understanding the
constraints that best define
the allowed behaviour of the
process behind the event log
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28. Constraints mining
An example
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A A B C A B C A C B C D
A C C A B B C B C A C B B D
C C C C C A A B C A A B A A B
A B B B D
C B A B D
A B B D
A A A C A C B D
A B C D
C A B A A C C B B D
B C C D
C A A C C C A A B C B C C B D

29. The role of Support
A A B C A B C A C B C D
A C C A B B C B C A C B B D
C C C C C A A B C A A B A A B
A B B B D
C B A B D
A B B D
A A A C A C B D
A B C D
C A B A A C C B B D
B C C D
C A A C C C A A B C B C C B D
 Support for
 Response(A, B)
 1.0
 Precedence(A, B)
 0.926 (25/27)
 Pruning on the basis of a
support threshold
 E.g., 0.95
 A threshold equal to 1.0
for a constraint means
“always valid in the log”
Activation
Target
Target
Activation
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30. Target-Branched Declare
Response(A, {B,C})
If A occurs in the trace,
then B or C occur
afterwards
AADB  BCAAC 
CABD  CAABC 
BCAA BCBDCC 
Precedence({A,C}, B)
If B occurs in the trace,
then A or C occur
beforehand
AADB  BCAAC
CABD  CCCBC 
BCAA BCBDCC
Target
Target
Target
Activation
Activation
Target
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31. The expressive power of
TBDeclare
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B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E

32. The expressive power of
TBDeclare
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B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E

33. The expressive power of
TBDeclare
B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E
 Support for
 Response(A, B)
 0.640 (16/25)
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34. B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E
The expressive power of
TBDeclare
 Support for
 Response(A, B)
 0.640 (16/25)
 Response(A, C)
 0.600 (15/25)
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35. B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E
The expressive power of
TBDeclare
 Support for
 Response(A, B)
 0.640 (16/25)
 Response(A, C)
 0.600 (15/25)
 RespondedExistence(A, B)
 0.720 (18/25)
 RespondedExistence(A, C)
 0.600 (15/25)
 Precedence(A, B)
 0.714 (10/14)
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 …

36. The expressive power of
TBDeclare
 Support for
 Response(A, B)
 0.640 (16/25)
 Response(A, C)
 0.600 (15/25)
 No non-branched
constraint is valid in the
whole log
(no Support eq. to 1)
 No Response constraint has
Support higher than 0.75
B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E
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37. The expressive power of
TBDeclare
B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E
SEITE 37 Threshold 0.75

38. Objective
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+ Expressive Power
+ Conciseness

39. The expressive power of
TBDeclare
Support for
 Response(A, {B, C})
 1.0
B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E
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40. TBDeclare properties:
subsumption hierarchy
Increasing
support
(≥)
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41. TBDeclare properties:
set-dominance
Increasing
support
(≥)
1
2
3
4
Branching factor
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3087 possible constraints
⇒
10 activities, br.factor 3

42. Amount of constraints
B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E
Support for
 Response(A, {B, C}),
 Response(A, {B, C, E}),
 Response(A, {B, C, D}),
 Response(A, {B, C, D, E}),
 RespondedExistence(A, {B, C}),
 RespondedExistence(A, {B, C, E}),
 RespondedExistence(A, {B, C, D}),
 RespondedExistence(A, {B, C, D, E}):
 1.0
Redundant!
Constraints
set-
dominance-
based
pruning
Constraints
subsumpt’n-
based
pruning
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Redundant!

43. Amount of constraints
B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E
Support for
 Response(A, {B, C}),
 Response(A, {B, C, E}),
 Response(A, {B, C, D}),
 Response(A, {B, C, D, E}),
 RespondedExistence(A, {B, C}),
 RespondedExistence(A, {B, C, E}),
 RespondedExistence(A, {B, C, D}),
 RespondedExistence(A, {B, C, D, E}):
 1.0
Redundant!
Constraints
set-
dominance-
based
pruning
Constraints
subsumpt’n-
based
pruning
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Redundant!

44. TBDeclare results pruning:
hierarchy-based
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45. TBDeclare results pruning:
hierarchy-based
0.280
0.360
0.200
0.520
1.000
1.000
0.360
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46. TBDeclare results pruning:
hierarchy-based
0.280
0.520
1.000
1.000
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47. TBDeclare results pruning:
hierarchy-based
1.000
1.000
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48. TBDeclare results pruning:
hierarchy-based
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49. Redundant!
Amount of constraints
B A A B A B C D
A A D B B A A D C
B A D D A D D A B E
C A B C
D A D B D
A E A C
A A A D B
D A D D B D
A A A D C D
A D D D A C
A A B
E D E B C E E C B E
Support for
 Response(A, {B, C}),
 Response(A, {B, C, E}),
 Response(A, {B, C, D}),
 Response(A, {B, C, D, E}),
 RespondedExistence(A, {B, C}),
 RespondedExistence(A, {B, C, E}),
 RespondedExistence(A, {B, C, D}),
 RespondedExistence(A, {B, C, D, E}):
 1.0
Constraints
set-
dominance-
based
pruning
Constraints
subsumpt’n-
based
pruning
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Redundant!

50. TBDeclare properties:
set-dominance
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51. TBDeclare properties:
set-dominance
1.000 0.880 0.679 0.880 0.720 0.800
0.640 0.600 0.720 0.160
1.000 1.000 0.920 0.920
1.000
Increasing
support
(≥)
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<

52. TBDeclare properties:
set-dominance
1.000 0.880 0.679 0.880 0.720 0.800
0.640 0.600 0.720 0.160
1.000 1.000 0.920 0.920
1.000
<
Increasing
support
(≥)
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53. TBDeclare properties:
set-dominance
1.000
1.000 1.000
1.000
≥
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54. TBDeclare properties:
set-dominance
1.000
1.000 1.000
≥
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55. TBDeclare properties:
set-dominance
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56. TBDeclare properties:
set-dominance
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57. Evaluation:
synthetic and real-world logs
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Activities Trace
length
Traces
in log
Branching
factor
Support
threshold
8 4 - 25 10,000 3 1.00
 Generating process:
 ChainPrecedence ({A, B}, C),
 ChainPrecedence ({A, B, D}, C),
 AlternateResponse(A, {B, C}),
 Rspnd’Existence(A, {B, C , D , E}),
 Response(A, {B, C}),
 Precedence({A, B, C, D}, E)
Synthetic
logs
set-up

58. Evaluation:
synthetic and real-world logs
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Activities Trace
length
Traces
in log
Branching
factor
Support
threshold
8 4 - 25 10,000 3 1.00
 Generating process:
 ChainPrecedence ({A, B}, C),
 ChainPrecedence ({A, B, D}, C),
 AlternateResponse(A, {B, C}),
 Rspnd’Existence(A, {B, C , D , E}),
 Response(A, {B, C}),
 Precedence({A, B, C, D}, E)
 BPI Challenge 2012:
 262,200 events, 24 activities, 13,087 cases
Synthetic
logs
set-up

59. Evaluation:
constraints pruning
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BPI Challenge 2012
(0) 6,654,480 (1) 10,676 (2) 1446 (3) 12

60. Evaluation:
performance
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BPI Challenge 2012
(KB) 00:07.274 (Const’s) 25:51.678 (Total) 26:11.380

61. Conclusions
 What we saw:
 Properties of TBDeclare constraints
 Mining TBDeclare models
 Reducing the number of returned items
 Effectiveness and performance evaluation
 More in the paper:
 Algorithm for computing support
 Proof of set-dominance property for TBDeclare constraints
 Future work:
 Better performance for Alternate-* constraints
 Branched Declare mining
 Inclusion of data into the mining process
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62. Discovering
Target-Branched Declare Constraints
Claudio Di Ciccio, Fabrizio Maria Maggi, and Jan Mendling
12th International Conference on Business Process Management
Eindhoven, The Netherlands
claudio.di.ciccio@wu.ac.at