Synchronizing Process Model and Event Abstraction for Grounded Process Intelligence (Extended Version)

TL;DR

This work closes the gap between model abstraction (MA) and event abstraction (EA) in process intelligence by formalizing a synchronization framework. It introduces a BPA-based non-order-preserving MA, paired with a synchronized EA that preserves grounding by producing a minimal directly-follows complete log $L_a$ corresponding to $M_a = ext{ma}_{bpa}(M)$, and proves their isomorphic rediscoverability under df-complete logs via a Main Synchronization Theorem. The approach hinges on two components: adapting BPA for synchronization and designing $ ext{ea}_{bpa}$ to mirror abstractions while maintaining behavioral relations, validated through a rigorous theoretical treatment (no reliance on empirical experiments). A bank/finance illustrative example demonstrates how synchronized artifacts enable downstream process intelligence tasks on abstracted yet grounded representations. The framework paves the way for extending to more discovery techniques and richer event-log abstractions, broadening the practical impact of grounded process intelligence.

Abstract

Model abstraction (MA) and event abstraction (EA) are means to reduce complexity of (discovered) models and event data. Imagine a process intelligence project that aims to analyze a model discovered from event data which is further abstracted, possibly multiple times, to reach optimality goals, e.g., reducing model size. So far, after discovering the model, there is no technique that enables the synchronized abstraction of the underlying event log. This results in loosing the grounding in the real-world behavior contained in the log and, in turn, restricts analysis insights. Hence, in this work, we provide the formal basis for synchronized model and event abstraction, i.e., we prove that abstracting a process model by MA and discovering a process model from an abstracted event log yields an equivalent process model. We prove the feasibility of our approach based on behavioral profile abstraction as non-order preserving MA technique, resulting in a novel EA technique.

Figures (3)

• Figure 1: Process Intelligence in the Financial Domain (Example)
• Figure 2: Running example: Process tree $M$ and abstracted process tree $\operatorname{ma}_{bpa}(M)$smirnov_businessm_2012 for threshold $w_t =0.5$.
• Figure 3: Modular decomposition of two order relation graphs $G(p_{M_a})$ and $G(p_{M_a^{\prime}})$ that are derived by $\operatorname{ma}_{bpa}$ from the running example $M$ for two different parameters $w_t$. For $w_t = 0.5$ (a-c), AND-complete module $C_1$, linear module $C_2$, XOR-complete module $C_3$ and linear module $C_4$ are discovered. For $0.5 < w_t \leq 0.66$ (d-e), AND-complete module $C_1$, linear module $C_2$, and primitive module $C_3$ are discovered.

Theorems & Definitions (35)

• definition thmcounterdefinition: Synchronizability
• definition thmcounterdefinition: Behavioral profile, adapted from smirnov_businessm_2012
• definition thmcounterdefinition: Behavioral Profile Abstraction (adapted from smirnov_businessm_2012)
• definition thmcounterdefinition: Class $C_{c}, C_{a}$
• lemma thmcounterlemma: Process trees in $C_{a}$ are isomorphic rediscoverable
• lemma thmcounterlemma: $\operatorname{ma}_{bpa}$ abstracted process trees are in $C_a$
• lemma thmcounterlemma: Number of traces and size of $\mathcal{L}_m(M).\text{log}$
• lemma thmcounterlemma: Operator ordering wrt. their mdf-complete log
• proof
• definition thmcounterdefinition: Restricted event log