ensuring model consistency in declarative process discovery

Ensuring Model Consistency in Declarative Process DiscoveryClaudio Di Ciccio, Fabrizio Maria Maggi, Marco Montali and Jan Mendling

13th International Conference on Business Process ManagementInnsbruck, Austria

claudio.di.ciccio@wu.ac.at

Foreword

Event logsProcess discovery

Declarative process discovery

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The event log

Process model

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The event log

Process instance Event log

Trace

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The event log

EventTask

Process instance Event log

Trace

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The event log

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Event

The event log

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Event

The event log

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Event

The event log

Process instance Event log

Trace

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The event log

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Event

The event log

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Event

The event log

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Event

The event log

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Event

Process discovery

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Process discovery

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?

Mining flexible processes

Declarative process discovery

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?

Objective: understanding the constraints that best define the allowed behaviour of the process behind the event log

Declarative modelling ofprocesses

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 repeateduntil C is done

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Declare:existence templates

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Existence(n, A)Activity A occurs at least n times in the process instanceBCAAC ✓ BCAAAC ✓ BCAC ✗ (for n = 2)

Absence(A)Activity A does not occur in the process instanceBCC ✓ BCAC ✗

Absence(n+1, A)Activity A occurs at most n+1 times in the process instanceBCAAC ✗ BCAC ✓ BCC ✓ (for n = 2)

Exactly(n, A)Activity A occurs exactly n times in the process instanceBCAAC ✗ BCAAAC ✗ BCAC ✗ (for n = 2)

Init(A)Activity A is the first to occur in each process instanceBCAAC ✗ ACAAAC ✓ BCC ✗

Absence(2, A) AtMostOne(A)

Existence(1, A) Participation(A)

Subsumption hierarchy ofrelation Declare templates

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Declare: Forward-unidirectionalrelation constraint templates

RespondedExistence(A, B)If A occurs in the process instance, then B occurs as wellCAC ✗ CAACB ✓BCAC ✓ BCC ✓

Response(A, B)If A occurs in the process instance, then B occurs after ABCAAC ✗ CAACB ✓CAC ✗ BCC ✓

AlternateResponse(A, B)Each time A occurs in the process instance, then B occurs afterwards, before A recursBCAAC ✗ CAACB ✗ CACB ✓CABCA ✗ BCC ✓ CACBBAB ✓

ChainResponse(A, B)Each time A occurs in the process instance, then B occurs immediately afterwardsBCAAC ✗ BCAABC ✗ BCABABC ✓

Activation Target

Declare: Backward-unidirectionalrelation constraint templates

RespondedExistence(B, A)If B occurs in the process instance, then A occurs as wellCAC ✓ CAACB ✓BCAC ✓ BCC ✗

Precedence(A, B)B occurs in the process instance only if preceded by ABCAAC ✗ 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 betweenBCAAC ✗ CAACB ✓ CACB ✓CABCA ✓ BCC ✗ CACBAB ✓

ChainPrecedence(A, B)Each time B occurs in the process instance, then B occurs immediately beforehandBCAAC ✗ BCAABC ✗ CABABCA ✓

Target Activation

Declare:Coupling relation templates

CoExistence(A, B)If B occurs in the process instance, then A occurs, and viceversaCAC ✗ CAACB ✓BCAC ✓ BCC ✗

Succession(A, B)A occurs if and only if it is followed by B in the process instanceBCAAC ✗ CAACB ✓CAC ✗ BCC ✗

AlternateSuccession(A, B)A and B occur in the process instance if and only if the latter follows the former, and they alternate each other in the traceBCAAC ✗ CAACB ✗ CACB ✓CABCA ✗ BCC ✗ CACBAB ✓

ChainSuccession(A, B)A and B occur in the process instance if and only if the latter immediately follows the formerBCAAC ✗ BCAABC ✗ CABABC ✓

Target Activation

Activation Target

Declare:negative relation constraints

NotCoExistence(A, B)A and B never occur together in the process instanceCAC ✓ CAACB ✗BCAC ✗ BCC ✓

NotSuccession(A, B)A can never occur before B in the process instanceBCAAC ✓ CAACB ✗CAC ✓ BCC ✓

NotChainSuccession(A, B)A and B occur in the process instance if and only if the latter does not immediately follows the formerBCAAC ✓ BCAABC ✗ CBACBA ✓

Target Activation

Activation Target

Mining declarative processes:ingredients

“Submit draft”,“Write deliverable”,“Organise agenda”,…

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a,b,c,…

Activities Process alphabet

Mining declarative processes

RespondedExistence(a,b) ?RespondedExistence(a,c) ?…Response(a,b) ?Response(a,c) ?…

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• Support:fraction of cases fulfilling the constraint

• Confidence:support scaled by fraction of traces in which the activation occurs

• Interest factor:confidence scaled by fraction of traces in which the target occurs

Support Conf. I.F.

Threshold

Threshold

Threshold

Mining declarative processes

RespondedExistence(a,b) ?RespondedExistence(a,c) ?…Response(a,b) ?Response(a,c) ?…

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Support Conf. I.F.

Mining declarative processes

RespondedExistence(a,b) RespondedExistence(a,c) ?…Response(a,b) ?Response(a,c) …

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Support Conf. I.F.

Mining declarative processes

RespondedExistence(a,b) RespondedExistence(a,c) ?…Response(a,b) Response(a,c) …

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Support Conf. I.F.

Mining declarative processes

RespondedExistence(a,b) RespondedExistence(a,c) …Response(a,b) Response(a,c) …

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Support Conf. I.F.

Mining declarative processes

RespondedExistence(a,b)RespondedExistence(a,c) andResponse(a,b) Response(a,c)and…

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From constraints-based model to FSA

RespondedExistence(a,b)RespondedExistence(a,c) andResponse(a,b) Response(a,c)and…

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[^a]*((a.*b.*)|(b.*a.*))*[^a]* [^a]*(a.*c)*[^a]*

RegularExpression

DeterministicFiniteState

Automaton

To be kept in mind

RespondedExistence(a,b)RespondedExistence(a,c) andResponse(a,b) Response(a,c)and…

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[^a]*((a.*b.*)|(b.*a.*))*[^a]* [^a]*(a.*c)*[^a]*

RegularExpression

DeterministicFiniteState

Automaton

So far, so good

What is the problem?

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While mining a real-life log…

Support threshold: 0.85 Confidence threshold: 0.25 Interest factor threshold: 0.25

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While mining a real-life log…

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Submit

draft

Write

deliverableOrganise

agenda

Time to challenge the X

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Submit

draft

Write

deliverableOrganise

agenda

Time to challenge the X

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The result

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The problem

When support threshold is lower than 100%,constraints can be valid through most of the log, though being in conflict

Example: an event log consists of two traces:1. <a, b, a, b, a, b, c>2. <a, b, a, b, a, c>

Support threshold: 0.7• a is always the first

Init(a)• c is always the last

End(c)• In 6 cases over 8 (75%), a and c do not directly follow each

other NotChainSuccession(a,c)

• In 5 cases over 7 (71.143%), b and c do not directly follow each other

NotChainSuccession(b,c)

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The problem

When support threshold is lower than 100%,constraints can be valid through most of the log, though being in conflict

Example: an event log consists of two traces:1. <a, b, a, b, a, b, c>2. <a, b, a, b, a, c>

Support threshold: 0.7• a is always the first

Init(a)• c is always the last

End(c)• In 6 cases over 8 (75%), a and c do not directly follow each

other NotChainSuccession(a,c)

• In 5 cases over 7 (71.143%), a and b do not directly follow each other

NotChainSuccession(b,c)

Question: what can be done right before c? inconsistency!

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The problem

When support threshold is lower than 100%,constraints can be valid through most of the log, though being in conflict

How to trust a discovery algorithm that can return inconsistent models?

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Which

constraints

conflict?

How can we be

sure we found

all conflictin

g

constraints?

From whereshould westart?

Can we avoidto check the

same sets ofconstraints

more than once?

The solution

Cross-product of automata

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The solution

Rationale:1. How to find inconsistencies among constraints?

Use the automaton-based model for constraints Do cross-product automata recognise the empty

language?2. How to search the inconsistencies?

Exploit:a) The product operation between automatab) The hierarchy of Declare templates

Guideline: Preserve the most meaningful constraints

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The algorithm /1

1. Divide the constraints having a support of 100% from the rest

Those that have a support of 100% cannot contradict each other

In other words, we consider them “safe”

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NotChainSuccession(a, c) 0.75 0.75 0.75 Response(a, b) 0.83 0.83 0.83 ChainSuccession(b, a) 0.72 0.72 0.72 ChainResponse(b, a) 0.80 0.80 0.80 ChainSuccession(a, b) 0.91 0.91 0.91 NotChainSuccession(b, c) 0.71 0.71 0.71 …

Init(a) 1.00 1.00 1.00 Participation(b) 1.00 1.00 1.00 AtMostOne(c) 1.00 1.00 1.00 End(c) 1.00 1.00 1.00 ChainPrecedence(a, b) 1.00 1.00 1.00 CoExistence(a, b) 1.00 1.00 1.00 …

The algorithm /2

2. Sort constraints having a support of less than 100% (“unsafe”) by:

i. Support (desc.)ii. Confidence (desc.)iii. Interest Factor (desc.)

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Init(a) 1.00 1.00 1.00 Participation(b) 1.00 1.00 1.00 AtMostOne(c) 1.00 1.00 1.00 End(c) 1.00 1.00 1.00 ChainPrecedence(a, b) 1.00 1.00 1.00 CoExistence(a, b) 1.00 1.00 1.00 …

ChainSuccession(a, b) 0.91 0.91 0.91 Response(a, b) 0.83 0.83 0.83 ChainResponse(b, a) 0.80 0.80 0.80 NotChainSuccession(a, c) 0.75 0.75 0.75 ChainSuccession(b, a) 0.72 0.72 0.72 NotChainSuccession(b, c) 0.71 0.71 0.71 …

sort

The algorithm /3

3. Create the automaton representing the safe constraints, as the product of the single constraints’ automata

Initialise the“product automaton”

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…

Init(a) Participation(b)

ChainPrecedence(a,b)

The algorithm /3

3. Create the automaton representing the safe constraints, as the product of the single constraints’ automata

Initialise the“product automaton”

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The algorithm /4

For every unsafe-constraint automaton, following the order of step 2:4. Intersect the product

automaton with the unsafe constraint

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NotChainSuccession(a,c)

The algorithm /4

4. (…cnt) If the result accepts only

an empty language: discard it if no constraint

is higher in the hierarchy relax the constraint

otherwise, and repeat step 4.

Else, include the unsafe-constraint in the list of returned constraints, and save the product automaton

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…

NotChainSuccession(b,c)

The algorithm /4

4. Return the process model made of:

safe constraints, and unsafe constraints not

leading to automata recognising empty languages

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The algorithm: recap

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Init(a)

Participation(b)AtMostOne(c)End(c) ChainPrecedence(a, b)…

ChainSuccession(a, b)Response(a, b)ChainResponse(b, a)NotChainSuccession(a, c) ChainSuccession(b, a)NotChainSuccession(b, c)…

sort

…

…

1

Event log

Declare constraints

Automata

Safe constraints

(support 100%)

Unsafe

constr

aints

Product

automaton

The algorithm: recap

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Init(a)

Participation(b)AtMostOne(c)End(c) ChainPrecedence(a, b)…

ChainSuccession(a, b)Response(a, b)ChainResponse(b, a)NotChainSuccession(a, c) ChainSuccession(b, a)NotChainSuccession(b, c)…

sort

…

…

1

2

Event log

Declare constraints

Automata

Safe constraints

Unsafe

constr

aints

Product

automaton

Conclusion

Which were the conflicting constraints in the log?What is more in the paper

Limitations and future work

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Which were the conflicting constraints in the log?

1. NotSuccession(send meeting, organize agenda)2. NotChainSuccession(send draft, send deliverable)3. Succession(send draft, submit report)

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Conclusions, limitations and future work

We have presented an algorithm that automatically finds inconsistencies in a mined Declare model (more in the paper)

The checks are purely based on operations over automata Optimisations exploit Declare semantics http://github.com/cdc08x/minerful

Limitations: The order in which the constraints are checked deeply affects the returned result Performances are heavily affected by the interplay of constraints

Future work: Application of the technique over mixed declarative-imperative models User-defined criteria for constraints sorting/selection Heuristics for a more efficient exploration of the search space are currently under

investigation http://www.promtools.org/prom6/nightly

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Ensuring Model Consistency in Declarative Process DiscoveryClaudio Di Ciccio, Fabrizio Maria Maggi, Marco Montali and Jan Mendling

13th International Conference on Business Process ManagementInnsbruck, Austria

claudio.di.ciccio@wu.ac.at

Ensuring Model Consistency in Declarative Process DiscoveryClaudio Di Ciccio, Fabrizio Maria Maggi, Marco Montali and Jan Mendling

13th International Conference on Business Process ManagementInnsbruck, Austria

Extra slides deck

The application of the method to minimise the model

Rationale:1. How to find redundancies among constraints?

Use the automaton-model correspondence Same language recognised after the product?

Main difference with the inconsistency-checking algorithm

Constraints having support 100% are checked for redundancies

More details in the paper

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The application of the method to minimise the model

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BPIC 2012

The algorithm /4

4. Return the process model made of:

safe constraints, and unsafe constraints not

leading to automata recognising empty languages

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<a, b, a, b, a, b, c><a, b, a, b, a, c>