In System Alignments we Trust! Explainable Alignments via Projections

TL;DR

This work addresses the challenge of reconciling imperfect system logs and normative models in processes with interacting objects. It introduces relaxed alignments based on projections to enable partial, multi-perspective matching between the complete system behavior $S$, the log $L$, and the model $M$, capturing inter-object dependencies more faithfully. The authors formalize relaxations across the model, the log, and the object-matching function, including a correlation-creation/destruction mechanism via $N^C$, and propose a cost-driven optimization to produce relaxed alignments that maximize multi-object synchronization while minimizing over-relaxation. The approach yields a richer, locally trustable representation of reality, supporting targeted log/model repair and enabling more accurate downstream analysis in performance and decision-point contexts. Overall, the framework advances conformance checking for multi-object systems by making the alignment process robust to partial information and inter-object semantics.

Abstract

Alignments are a well-known process mining technique for reconciling system logs and normative process models. Evidence of certain behaviors in a real system may only be present in one representation - either a log or a model - but not in the other. Since for processes in which multiple entities, like objects and resources, are involved in the activities, their interactions affect the behavior and are therefore essential to take into account in the alignments. Additionally, both logged and modeled representations of reality may be imprecise and only partially represent some of these entities, but not all. In this paper, we introduce the concept of "relaxations" through projections for alignments to deal with partially correct models and logs. Relaxed alignments help to distinguish between trustworthy and untrustworthy content of the two representations (the log and the model) to achieve a better understanding of the underlying process and expose quality issues.

Figures (8)

• Figure 1: System log $L$ and process model $M$ in relation to the system $S$.
• Figure 2: Example of a poset and two projections.
• Figure 3: Example labeled Petri net $N_1$ with marking $m$ such that $m(p_5) = m(p_6) = 0$ and $m(p_{11}) = 2$.
• Figure 4: Visualization of the $S_1$, $L_1$, and $\varphi_1 \in \mathcal{L}(M)$ regarding packages 1 and 2.
• Figure 5: Running example $M = (N, m_i, m_f)$ with t-PNID $N$ and initial and final markings $m_i=m_f$. Furthermore, $M$ contains object roles $\mathcal{R} = \{ p,d,w \}$ and variable sets $\mathcal{V}_p = \{ \nu_p,p \},\mathcal{V}_d = \{ d \}$, and $\mathcal{V}_w = \{ w \}$.

Theorems & Definitions (13)

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