Extending Temporal Business Constraints with Uncertainty
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The document discusses extending temporal business constraints to incorporate uncertainty using a framework based on linear temporal logic over finite traces, particularly through the Declare model. It elaborates on how probabilistic constraints can yield different conforming scenarios and the importance of addressing consistency and probability in business processes. Key reasoning tasks include probabilistic conformance checking and constraint entailment to assess compliance with business rules.
![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](https://image.slidesharecdn.com/caise-forum-2020-probdeclare-montali-220819222912-976b99e8/85/Extending-Temporal-Business-Constraints-with-Uncertainty-2-320.jpg)
Extending Temporal Business Constraints with Uncertainty
- 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.