Presentation of the paper "Extending Temporal Business Constraints with Uncertainty" at the CAiSE2020 Forum. The paper is available here: https://link.springer.com/chapter/10.1007/978-3-030-58135-0_8 Abstract: Conformance checking is a fundamental task to detect deviations between the actual and the expected courses of execution of a business process. In this context, temporal business constraints have been extensively adopted to declaratively capture the expected behavior of the process. However, traditionally, these constraints are interpreted logically in a crisp way: a process execution trace conforms with a constraint model if all the constraints therein are satisfied. This is too restrictive when one wants to capture best practices, constraints involving uncontrollable activities, and exceptional but still conforming behaviors. This calls for the extension of business constraints with uncertainty. In this paper, we tackle this timely and important challenge, relying on recent results on probabilistic temporal logics over finite traces. Specifically, we equip business constraints with a natural, probabilistic notion of uncertainty. We discuss the semantic implications of the resulting framework and show how probabilistic conformance checking and constraint entailment can be tackled therein.

1. Extending temporal
business constraints
with uncertainty
Fabrizio M. Maggi
Marco Montali
Rafael Peñaloza CAiSE Forum 2020
1

2. Constraints predicating on the execution of activities over
time.
Notable examples: DCR Graphs [Slaats et al, BPM13] and
Declare [Pesic et al, EDOC17].
• Declarative speci
fi
cation and enactment of business
processes.
• Formalization of business rules and policies in monitoring
and conformance checking [___,BPM14].
Declare uses LTL over
fi
nite traces and its automata-theoretic
characterization to provide support in the whole lifecycle.
Temporal business constraints
2

3. A front-end for linear temporal logic over
fi
nite traces
The Declare framework
3
accept reject
1..* 1..*
Crisp semantics of constraints: an execution trace
conforms to the model if it satis
fi
es every constraint in
the model.

4. A front-end for linear temporal logic over
fi
nite traces
The Declare framework
4
accept reject
1..* 1..*
Crisp semantics of constraints: an execution trace
conforms to the model if it satis
fi
es every constraint in
the model.
Inconsistent model:
no conforming trace

5. • Best practices: constraints that must hold in the majority, but
not necessarily all, cases.
90% of the orders are shipped via truck.
• Outlier behaviors: constraints that only apply to very few, but
still conforming, cases.
Only 1% of the orders are canceled after being paid.
• Constraints involving external parties: contain uncontrollable
activities for which only partial guarantees can be given.
In 8 cases out of 10, the customer accepts the order and also
pays for it.
Some examples
Uncertainty is pervasive
5

6. Uncertainty as conformance ratio
6
multiset of traces
for n cases
constraint “C”

7. Uncertainty as conformance ratio
7
multiset of traces
for n cases
constraint “C”
conforms to C?

8. Uncertainty as conformance ratio
8
multiset of traces
for n cases
conforms to C?
constraint “C”
…

9. Uncertainty as conformance ratio
9
multiset of traces
for n cases
k
conforming
traces
constraint “C”
k
n

10. Uncertainty as conformance ratio
10
multiset of traces
for n cases
k
conforming
traces
constraint “C”
holds with
probability k/n
k
n

11. Uncertainty as conformance ratio
11
multiset of traces
for n cases
k
conforming
traces
n-k
nonconforming
traces
constraint “C”
holds with
probability k/n
k
n
constraint “C”
is violated with
probability 1-k/n

12. Uncertainty as conformance ratio
12
multiset of traces
for n cases
k
conforming
traces
n-k
nonconforming
traces
constraint “C”
holds with
probability k/n
k
n
constraint “not C”
holds with
probability 1-k/n

13. Extending Declare with probabilities
ProbDeclare
13
accept reject
1..* {0.8} 1..* {0.1}
Constraints have an associated probability.
• Crisp constraints: those with probability 1 (must hold in every
trace).
• Truly probabilistic constraints: may hold or not.

14. The subtlety of probabilistic constraints
ProbDeclare
14
accept reject

15. The subtlety of probabilistic constraints
ProbDeclare
15
accept reject
in 100% traces:
accept and reject do not
coexist

16. The subtlety of probabilistic constraints
ProbDeclare
16
accept reject
1..* {0.8}
in 100% traces:
accept and reject do not
coexist
in 80% traces:
accept occurs

17. The subtlety of probabilistic constraints
ProbDeclare
17
accept reject
1..* {0.8} 1..* {0.1}
in 100% traces:
accept and reject do not
coexist
in 80% traces:
accept occurs
in 10% traces:
reject occurs

18. The subtlety of probabilistic constraints
ProbDeclare
18
accept reject
1..* {0.8} 1..* {0.1}
in 100% traces:
accept and reject do not
coexist
in 80% traces:
accept occurs
in 10% traces:
reject occurs
Can they overlap?
No: it is not possible to satisfy
all constraints at once!

19. The subtlety of probabilistic constraints
ProbDeclare
19
accept reject
1..* {0.8} 1..* {0.1}
in 100% traces:
accept and reject do not
coexist
in 80% traces:
accept occurs
in 10% traces:
reject occurs
Can they overlap?
No: it is not possible to satisfy
all constraints at once!

20. The subtlety of probabilistic constraints
ProbDeclare
20
accept reject
1..* {0.8} 1..* {0.1}
in 100% traces:
accept and reject do not
coexist
in 80% traces:
accept occurs
in 10% traces:
reject occurs

21. The subtlety of probabilistic constraints
ProbDeclare
21
accept reject
1..* {0.8} 1..* {0.1}
in 100% traces:
accept and reject do not
coexist
in 80% traces:
accept occurs
in 10% traces:
reject occurs

22. The subtlety of probabilistic constraints
ProbDeclare
22
accept reject
1..* {0.8} 1..* {0.1}
in 100% traces:
accept and reject do not
coexist
in 80% traces:
accept occurs
in 10% traces:
reject occurs
in 10% traces:
neither accept nor reject occur
⟹

23. The subtlety of probabilistic constraints
ProbDeclare
23
In how many traces is the order
accepted and then paid?
Not 70%… it is 50%!
accept
1..* {0.8}
0..1
pay
{0.7}

24. The subtlety of probabilistic constraints
ProbDeclare
24
accept
1..* {0.8}
0..1
pay
{0.7}
In how many traces is the order
accepted and then paid?
Not 70%… it is 50%!

25. Consider a ProbDeclare model with n constraints.
A constraint scenario picks which probabilistic constraints must hold,
and which are violated (i.e., their negated version must hold).
All in all: in principle, 2n scenarios, denoting di
ff
erent “process variants”.
Key point:
• Reasoning over a single scenario reduces back to standard LTLf
reasoning.
• Can be done with well-known automata-theoretic techniques.
A probabilistic version of “process variant”
Constraint scenario
25

26. Crisp constraints must hold in each scenario, so we only consider
choices for truly probabilistic constraints.
Constraint scenarios
Example
26
accept
1..* {0.8}
0..1
pay
{0.7}

27. Crisp constraints must hold in each scenario, so we only consider
choices for truly probabilistic constraints.
Constraint scenarios
Example
27
scenario
consistent? probability
0..1 acc precedence(acc,pay) 1..* acc response(acc,pay)
accept
1..* {0.8}
0..1
pay
{0.7}

28. Crisp constraints must hold in each scenario, so we only consider
choices for truly probabilistic constraints.
Constraint scenarios
Example
28
accept
1..* {0.8}
0..1
pay
{0.7}
scenario
consistent? probability
0..1 acc precedence(acc,pay) 1..* acc response(acc,pay)
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1

29. Do possible scenarios exist? Which ones are consistent? What is
their probability?
This depends on the logical interplay of constraints, and the
overall interplay of their probabilities.
Intuition
Probability of constraint scenarios
29

30. Combined approach, leading to a system of linear inequalities:
1. The probabilities of all constraint scenarios add up to 1.
2. The probabilities of constraint scenarios that require
constraint C to hold must add up to the probability of C.
3. Constraint scenarios that are inconsistent have probability 0.
(No trace conforms to them)
No solution: overall ProbDeclare model inconsistent.
One solution: gives the actual probability values.
Many solutions: can be used to compute probability ranges.
Approach
Probability of constraint scenarios
30

31. A scenario is consistent if it has at least one conforming trace.
Consistency of constraint scenario
Example
31
scenario
consistent? probability
1..* acc response(acc,pay)
0 0 N
0 1 Y
1 0 Y
1 1 Y
accept
1..* {0.8}
0..1
pay
{0.7}

32. • It is not possible to avoid accept while falsifying the response constraint.
• Two scenarios make 1..* accept true: their combined probability is 0.8.
• Two scenarios make response(accept,pay) true: their combined probability is 0.7.
Computing the probability of constraint scenarios
Example
32
scenario
consistent? probability
1..* acc response(acc,pay)
0 0 N
0 1 Y
1 0 Y
1 1 Y
accept
1..* {0.8}
0..1
pay
{0.7}

33. Computing the probability of constraint scenarios
Example
33
scenario
consistent? probability
1..* acc response(acc,pay)
0 0 N
0 1 Y
1 0 Y
1 1 Y
accept
1..* {0.8}
0..1
pay
{0.7}
• It is not possible to avoid accept while falsifying the response constraint.
• Two scenarios make 1..* accept true: their combined probability is 0.8.
• Two scenarios make response(accept,pay) true: their combined probability is 0.7.

34. Computing the probability of constraint scenarios
Example
34
scenario
consistent? probability
1..* acc response(acc,pay)
0 0 N 0
0 1 Y 0.2
1 0 Y 0.3
1 1 Y 0.5
accept
1..* {0.8}
0..1
pay
{0.7}
• It is not possible to avoid accept while falsifying the response constraint.
• Two scenarios make 1..* accept true: their combined probability is 0.8.
• Two scenarios make response(accept,pay) true: their combined probability is 0.7.

35. Probabilistic constraint entailment: given a business constraint of
interest, is it implied by the model? With which probability?
• Check which scenarios imply the constraint.
• Sum their probabilities.
Probabilistic conformance checking: given an execution trace, does
it conform to the model? With which probability (outlier vs mainstream)?
• Check conformance for each scenario.
• No scenario found: not conforming.
• One scenario found: conforming, with the corresponding probability.
Given a ProbDeclare model...
Key reasoning tasks
35

36. <pay>:
<accept>:
<accept,pay>:
Are these traces conforming? Are they “mainstream” or “outlier”?
Probabilistic conformance checking
36
scenario
consistent? probability
1..* acc response(acc,pay)
0 0 N 0
0 1 Y 0.2
1 0 Y 0.3
1 1 Y 0.5
accept
1..* {0.8}
0..1
pay
{0.7}

37. <pay>: not conforming (violates precedence)
<accept>: conforming, 30% variant
<accept,pay>: conforming, 50% variant
Are these traces conforming? Are they “mainstream” or “outlier”?
Probabilistic conformance checking
37
scenario
consistent? probability
1..* acc response(acc,pay)
0 0 N 0
0 1 Y 0.2
1 0 Y 0.3
1 1 Y 0.5
accept
1..* {0.8}
0..1
pay
{0.7}
<acc>
-
X
V
X
0.3
<acc,pay>
-
X
X
V
0.5

38. A framework that incorporates uncertainty into
temporal business constraints.
Combination of logical and probabilistic reasoning to
understand the resulting semantics, and to solve key
tasks.
“The future is uncertain, but the end is always near” (Jim Morrison)
Conclusion
38
Full technical framework +
monitoring techniques:
see our BPM20 paper.
Logical underpinning
via probabilistic LTLf:
see our AAAI20 paper.