This doctoral research integrates Probabilistic Logic Programming (PLP) with Declarative Process Mining (DPM) to address uncertainty in business process management. The research will have to address assumptions that are traditionally made in binary DPM but do not always hold in real cases, or are ignored in real world logs: (i) a process model able to perfectly distinguish between positive and negative examples; (ii) noise in the log, at the event level, or at the trace level; (iii) log incompleteness: for a variety of reasons some events could have not been recorded in the log (“missing events”); (iv) clarity and understandability of a declarative model, which might be undermined by the large number of its constraints.
CEUR Workshop
ISSN1613-0073 target the issues above by means of new combinations of declarative Process Mining with probabilistic and combinatorial approaches. The final aim is to produce more verifiable and understandable explanations of its processes to an organisation.
The Business Process Mining (BPM) community sees the integration of probability into various aspects
of process modeling as a growing research topic, reflecting an interest in enhancing process analysis
under conditions of uncertainty in real-world domains. Uncertainty can be found at various levels, such
as process constraints, events, event attributes, or traces. For instance, in declarative PM, [
Diferently from previous work, we propose a novel semantics to handle uncertainty at the level of: i) events in a trace, ii) traces in a log, iii) and constraints in process models, in a declarative PM setting.
In Process Mining a trace or process instance represents a distinct execution of a process, potentially repeated multiple times. A trace typically consists of a sequence of activity executions, each identified by a distinct name and associated with temporal information that defines their order. Definition 1 (Trace and Log ℒ). Given a finite set of symbols (i.e., activity names), a trace is a ifnite, ordered sequence of symbols over , i.e. ∈ ∗, where ∗ is the infinite set of all the possible finite sentences over . A log ℒ is a finite set of traces, such as
ℒ = { 1 = ⟨a, b, c⟩, 2 = ⟨a, b, a, d⟩, 3 = ⟨a, a, d⟩, 4 = ⟨a, b, c⟩}
Declarative PM represents a branch of PM that prioritizes flexibility rather than strictly defined
procedural workflows. Unlike procedural approaches that prescribe exact execution sequences, declarative
PM defines constraints that specify conditions that must or must not be satisfied during process
execution. Our work builds upon DECLARE [
Definition 2 (Compliance of a trace with a constraint). A trace is compliant with a DECLARE constraint if it satisfies the corresponding logical formula , denoted as ⊧ . Conversely, if ⊭ , we say violates the constraint.
In the following, we extend this notion with respect to a set of constraints, i.e. a process model, that we formally call Declarative Process Specification.
Definition 3 (Declarative Process Specification) . A Declarative Process Specification is a triple = ( , , ) , where is a finite set of constraint templates c( 1, … , ) (with arity ∈ ℕ ), is a finite set of activity names, and is a finite set of instantiated constraints c( 1, … , ) with ∈ . Definition 4 (Compliance of a trace versus a Declarative Process Specification) . A trace is compliant with a DS if it entails the conjunction of the formulas corresponding to the ∈ : ⊧ 1 ∧ … ∧ where is the cardinality of .
The proposed goal of this research is to develop a probabilistic framework for declarative Process Mining that integrates uncertainty in both event data and model specifications. The framework aims to support both validation (via conformance checking) and model extraction (through learning algorithms) under uncertainty. The research goals of this work are the following: RG1) how uncertainty can be represented across events, traces, and constraints in declarative PM;RG2) defining compliance evaluation on both uncertain traces and probabilistic constraints;RG3) learning probabilistic declarative models from uncertain logs; RG4) model evaluation and selection based on user preferences. These goals are detailed in the Introduction.
This section outlines our recent contributions, which are inspired by the Distribution Semantics [
Definition 6 (Probabilistic Trace [
Example 1. The trace: = ⟨0.9 ∶ register_order, approve_order, schedule_delivery, invoice_customer⟩ describes the situation where _ was not logged, however it is very probable that it happened due to the standard process (the associated probability is high). register_order is a probabilistic event, and is a probabilistic trace.
Definition 7 (Probabilistic Log [
Example 2. The probabilistic log ℒ = { 1, 0.9 ∶ 2, 3} describes the case in which the process instances1 and 3 were observed and recorded, while 2 was not observed but there is a high probability (0.9) that it happened.
Definition 8 (Probabilistic Declarative Specification [
Example 3. The following PDS: includes one probabilistic constraintc1 which indicates that the fact thatregister_order is potentially followed by approve_order carries relatively high importance in the business process.
Constraints with probability = 1 are termed crisp constraints. When all constraints are crisp, the specification is equivalent to a standard Declarative Specification. Following Distribution Semantics principles, a PDS defines a probability distribution over possible worlds where constraint c is included with probability or excluded with probability 1 − . The probability of each resulting DS, denoted ()
, is the product of the probabilities for selected, and 1 − for excluded constraints. This distribution ensures ∑ (
In [
) is the probability associated with each deterministic specification.
Example 4. Let us consider the following PDS:
4, i.e. those specifications that do not contain c2, since the first event of the trace is not register_order. ’s probability of compliance is (, ) = ( 2) + ( 4) = 0.08 + 0.02 = 0.1.
Declarative Process Specification (DS) 1 = {response(register_order, approve_order), init(register_order)} ( 2 = {response(register_order, approve_order)} 3 = {init(register_order)} 4 = { } ( ) ( ( 1) = 0.8 × 0.9 = 0.72 2) = 0.8 × 0.1 = 0.08 3) = 0.2 × 0.9 = 0.18
9, we assess compliance by examining each regular trace generated from a probabilistic trace against every Declarative Specification DS derived from the PDS.
Definition 10 (Compliance of a probabilistic trace versus a PDS). Given a a Probabilistic Declarative Process Specification PDS and a Probabilistic Trace t, let us consider all possible selections over the PDS and all possible selections over t. Let us consider all the Declarative Specifications generated from PDS and all regular traces () generated from t as a result of the selections.
We define the compliance Comp(t,PDS) of a probabilistic trace w.r.t. as: (, ) =
( ∑ { () 0 ()) ⋅ ( ) if () is compliant with , otherwise.
Unlike traditional conformance checking, which yields a binary outcome (either compliant or noncompliant), compliance in the probabilistic setting becomes a weighted evaluation over all possible DSs, where the weight is the probability of a regular trace compliant to the ℎ DS.
Up to now we used the implementation already available in [
Process Specifications results in an exponential growth in execution time as the number of probabilistic constraints and events increases. We are currently exploring more eficient methods for computing compliance that bypass the need for full enumeration.
This research aims to develop a comprehensive probabilistic framework for declarative Process Mining that integrates uncertainty in both event data and model specifications, and returns to the user preferable models. So far, it has provided a formal probabilistic semantics that captures how uncertainty can be represented across events, traces, and constraints (addressing RG1), along with a definition of probabilistic compliance that accounts for uncertainty in both traces and process models (addressing RG2). Preliminary implementations demonstrate the feasibility of our approach on realistic datasets, including a medical protocol case study, validating the practical relevance of the proposed semantics. However, open issues in RG2 regard the development of scalable algorithms to avoid the exponential cost of enumerating all possible worlds to perform the task of compliance. To addressRG3, we plan to design learning methods that extract probabilistic constraints from uncertain logs. We aim to leverage both positive and negative traces to improve learning accuracy and model quality. In line withRG4, we are exploring how to incorporate user preferences into model evaluation to enhance interpretability and trust.
Research funded by the Italian Ministerial grant PRIN 2022 “Probabilistic Declarative Process Mining (PRODE)”, n. 20224C9HXA - CUP F53D23004240006, funded by European Union – Next Generation EU. Research funded by the Italian Ministry of University and Research through PNRR - M4C2 - Investimento 1.3 (Decreto Direttoriale MUR n. 341 del 15/03/2022), Partenariato Esteso PE00000013 - ”FAIR - Future Artificial Intelligence Research” Spoke 8 ”Pervasive AI” - CUP J33C22002830006, funded by the European Union under the NextGeneration EU programme”. The authors declare that in the planning, drafting, and/or revision of the work have made no use of generative AI tools.