=Paper=
{{Paper
|id=Vol-3645/forum1
|storemode=property
|title=Multi-perspective path semantics in process mining based on causal process
knowledge
|pdfUrl=https://ceur-ws.org/Vol-3645/forum1.pdf
|volume=Vol-3645
|authors=Lukas Pfahlsberger,Christoffer Rubensson,Steven Knoblich,Maxim Vidgof,Jan Mendling
|dblpUrl=https://dblp.org/rec/conf/ifip8-1/PfahlsbergerRKV23
}}
==Multi-perspective path semantics in process mining based on causal process
knowledge
==
https://ceur-ws.org/Vol-3645/forum1.pdf
Multi-perspective path semantics in process mining
based on causal process knowledge
Lukas Pfahlsberger1,˚ , Christoffer Rubensson1 , Steven Knoblich1 , Maxim Vidgof2 and
Jan Mendling1
1
Humboldt-Universität zu Berlin (HU Berlin), Rudower Chaussee 25, 12489 Berlin-Adlershof, Germany
2
Wirtschaftsuniversität Wien (WU), Welthandelsplatz 1, 1020 Wien, Austria
Abstract
Process mining allows process analysts to investigate business processes with the help of algorithms
and event log data. To better identify and understand inefficiencies in discovered process models,
various visualization techniques have been proposed to enhance these models with further information,
such as displaying the duration of execution time between activities using sequential color schemes
or integrating statistical metrics into the model through textual annotations. However, it remains a
challenge for analysts to identify interesting behavioral patterns in directly follows graphs. Consequently,
this may lead process analysts to draw incorrect conclusions or be unable to identify the root causes for
answering their analytical questions. This paper proposes a novel set of path semantics based on causal
knowledge. We further examine how several combined path semantics, referred to as pattern types, may
provide analysts with additional information on the underlying behavior. By examining an order-to-cash
process in the real world, we demonstrate the usefulness and additional benefits of these path semantics
for process analysts.
Keywords
Process mining, visual analytics, path semantics, causal process knowledge, directly follows
1. Introduction
Over the last two decades, a plethora of different techniques, methods, and approaches for
visually representing business processes discovered from event-log data has been developed
to support analysts in making better and faster decisions [1]. However, an essential part of
these proposed process representations hardly differs in the semantic meaning of the visual
components. In particular, the semantics of the paths are almost without exception limited to a
single meaning, namely, a directly follows relationship.
Companion Proceedings of the 16th IFIP WG 8.1 Working Conference on the Practice of Enterprise Modeling and the 13th
Enterprise Design and Engineering Working Conference, November 28 – December 1, 2023, Vienna, Austria
˚
Corresponding author.
$ lukas.pfahlsberger@hu-berlin.de (L. Pfahlsberger); christoffer.rubensson@hu-berlin.de (C. Rubensson);
steven.knoblich@hu-berlin.de (S. Knoblich); maxim.vidgof@wu.ac.at (M. Vidgof); jan.mendling@hu-berlin.de
(J. Mendling)
https://www.informatik.hu-berlin.de/en/forschung-en/gebiete/promis-en/team/pfahlsbl (L. Pfahlsberger);
http://hu.berlin/rubensson (C. Rubensson); https://nm.wu.ac.at/nm/vidgof (M. Vidgof); http://hu.berlin/mendling
(J. Mendling)
0000-0002-1367-9441 (L. Pfahlsberger); 0009-0004-4940-5866 (C. Rubensson); 0009-0002-8509-7042 (S. Knoblich);
0000-0003-2394-2247 (M. Vidgof); 0000-0002-7260-524X (J. Mendling)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
In this paper, we propose our vision for multi-perspective path semantics. To this end, we
integrate causal process knowledge [2] that allows differentiating between eight different path
semantics. Furthermore, we abstract the individual path semantics into distinguishable pattern
types that are categorized into allowed and prohibited behavior. This allows linking pattern
types directly to generic use cases for process analysis. Thereby, analysts can identify and
discover interesting behavior that indicates problems in visual process representations more
precisely.
We contribute to the field of visual analytics for process mining by proposing multi-
perspective path semantics based on causal process knowledge. Our approach improves the
precision and speed of the process analysis due to a linkage between the meaning of the paths
and suitable use cases. Previous studies have presented visualization frameworks for process
mining [3] that investigate the effectiveness of different ways of representing process mining
outcomes. However, these works often neglect the aspect of path semantics and instead focus
on alternative visual forms of aggregating, clustering, or sorting the process data. We further
contribute to the integration of prior domain-specific knowledge into existing process discovery
techniques [4, 5, 6, 7]. We thereby show that prior knowledge can not only help to improve the
structural aspects of the model (e.g., by reducing complexity) but also the visual representation
of its elements, such as paths.
The remainder of the paper is structured as follows. Section 2 presents the theoretical
background focusing on visual analytics, graph types in process mining, with a focus on arc
semantics, and causal process knowledge. Section 3 introduces our vision for multi-perspective
path semantics. Section 4 derives pattern types based on distinct combinations of path semantics
on a process instance level. Section 5 links the pattern types to use cases, thus evaluating our
vision for multi-perspective path semantics based on a real-world order-to-cash process. Section
6 points out implications for future research and limitations. Finally, Section 7 concludes this
paper.
2. Background
In this section, we discuss three distinct areas of research. First, we briefly introduce the topic
of visualization and how it is utilized for analytical purposes. Second, we introduce previous
works on the semantics of arcs in process models. Finally, we define causal process knowledge
and explore its applications in process mining.
2.1. Visualization & visual analytics
Visualization can be seen as the process of converting data into graphical representations [8,
p. 3], enabling the derivation of insights otherwise difficult to discern from raw data sets.
Visual analytics is a multidisciplinary field that employs visualization techniques for graphically
representing knowledge and enhancing analytical reasoning [9, p. 4]. Many visualization
techniques are available to accomplish this objective (cf., [10, 11]).
Visual analytics relies on active interaction between users and data [9, p. 4], making human
judgment a crucial component. Munzner’s nested model [12], a design and validation framework
for visualizations, emphasizes a human-centered approach with a four-layer design process. The
framework takes the domain problem and its intended user as a starting point. This is followed
by translating the problem into a computer science context, designing the visualization, and
finally creating its rendering mechanism. McKenna et al. [13] extend the nested model [12]
with the overlapping activities understand, ideate, make, and deploy that further emphasize
the user-centric motivation and their design outcomes for each step in the process. In another
framework, Moere and Purchase [14] define roles with domain-specific needs for visualizations,
which could facilitate the quality of the design solutions when met. These roles comprise the
visualization studies (researchers), with the aim for utility and soundness; the visualization prac-
tice (businesses), with the need for market-oriented solutions; and the visualization exploration
(artists), who strive to create visually appealing yet workable designs [14, pp. 366-368]. Lastly,
Moody [15] developed the Physics of Notations, a theory comprising a set of design princi-
ples to support the creation and validation of cognitively effective visualizations in software
engineering. An example principle is the Principle of Semiotic Clarity that ascribes designers
to ensure a one-to-one relationship between graphical symbols and the semantic construct
they represent [15, pp. 762-763]. Failure to adhere to this principle may result in ineffective
visualizations, such as a symbol deficit whenever a semantic is not represented by any symbol or
a symbol redundancy whenever multiple symbols refer to the same semantic [15, pp. 762-763].
The process of visualizing the data involves a range of dimensions to consider (cf., [15]).
While we only provide a few examples, one aspect involves using geometrical objects to depict
data, such as glyphs in different shapes [8]. A well-known depiction of data in statistics is
the boxplot (e.g., [16, pp. 45-46]), in which numerical data is grouped into a single box with
extending lines (whiskers) to indicate, i.a., data variability. In process science, a standard for
visualizing processes is the Business Process Model and Notation (BPMN) standard1 , which, i.a.,
uses boxes, rhombuses, and arrows to, respectively, depict activities, gateways (decision points),
and sequence flow between activities. Another aspect to consider is color, or color mapping,
which can be used to map data to certain attributes [8, p.5]. Despite appearing trivial, color
in visualization is a highly complex topic as it is closely linked to human perception through
various channels, such as color properties (e.g., hue and saturation), color combinations, and
geometrical patterns (e.g., [17]). Brewer [18] makes an important contribution that provides
insights and guidelines on color mapping based on data types and human perception, further
demonstrating the topic’s complexity.
2.2. Arc semantics in process models
Some of the existing process modeling languages already provide arcs with different semantics.
However, the purpose and concepts behind such differentiation is not the same across languages.
On the other hand, some languages do not distinguish between different arc semantics. In
directly-follows graphs [1], for instance, there is only a single type of arc connecting two
activities. Its arc semantics simply considers observed events that follow the path between
the two activities. These arcs can store additional information (e.g., the number of instances
following the arc) or durations of transitions. In BPMN, there are two kinds of arcs, namely,
control flow and message flow. The semantics of the former is that a process instance transitions
1
https://www.bpmn.org (Last accessed: 2023-12-10)
from one activity to another. The semantics of the message flow is that a message from an
external pool (e.g., sent from an external party such as an organization) is received by an activity
or event in another pool or vice versa [19].
To the best of our knowledge, Petri nets have the largest variety of arc semantics. While
the primary purpose of arcs in Petri nets is to represent the movement of the tokens between
places and transitions, the exact semantics may differ. First, there are differences in terms of
whether and how many tokens are moved. Traditionally, one token moves along the arc when
it is consumed or produced by a transition. However, there are also read arcs [20] requiring
tokens to be present in a place for a connected transition to fire but not consuming or producing
the tokens. There are inhibitor arcs [21] that, on the contrary, prevent an otherwise enabled
transition to fire if there are tokens in a specified place. Weighted arcs [22] specify exactly how
many tokens are consumed or produced by a transaction, allowing more than one token to be
moved along an arc. Finally, reset arcs [23] remove all tokens from respective places when a
transition fires.
Furthermore, the type of tokens being moved can also differ. Colored Petri nets [24] allow
distinguishing between different types of objects or object instances by assigning colors to
tokens. For the places, one can then define different capacities for tokens of different colors.
The firing semantics of the transitions can also depend on the color. Finally, the arcs ultimately
specify the colors of tokens to be consumed or produced.
2.3. Causal process knowledge in process mining
As a forefather of the philosophy of causation, Hume [25] noted that all knowledge comes from
experience and that it is based on associations between perceived events. Waldmann [26] adopted
this idea in his work on knowledge-based causal induction, indicating causal directionality as
the fundamental factor for determining how statistical correlations are understood. The term
causation can be further differentiated by Pearl’s [27] three-level causal hierarchy highlighting
the role of causal knowledge in helping to associate, intervene, or counterargue.
Regarding causal knowledge concerning business processes, experts with years of acquired
domain-specific experience represent a valuable resource for process improvement. Experience
provides process experts with a precise understanding of causal relationships between individual
activities of business processes. For instance, a process owner of an order-to-cash process might
readily understand that a customer order eventually leads to an invoice being created. Intuitively,
it is clear to the process owner that, oppositely, an invoice followed by the customer order
would contradict the causal logic of the process [2].
In the process mining research field, most discovery algorithms do not leverage causal process
knowledge [2, 4]. Instead, they consider data as the “single source of truths” to behaviors while
overlooking domain-specific reasons. In an experimental setting, Rembert et al. [4] develop and
test a process discovery algorithm that integrates prior knowledge. The results indicate that
prior knowledge increases the robustness against noise, subsequently reducing the likelihood of
measurement and ordering errors, particularly for processes with a higher degree of infrequent
behavior. Similarly, Diamantini et al. [5] exploit knowledge in complex domains with highly
variable processes as a means to repair event logs and produce more realistic models. Waibel et
al. [2] use a causal template that helps process analysts integrate a causal order into discovering
Conformance behavior type
Path
the processAllowed
combinations structures withProhibited
a focus on control-flow. Compared to approaches that do not
integrate
Skip-reverse/
Backjump
domain knowledge, the approach by [2] generates much simpler models with higher
2 2
conformance to the defined causality by reducing the number of self-loops and spurious arcs.
1,3 1,3
Conformance
Lu et al. [6] propose a semi-automated approach to detecting log patterns in process discovery,
Refinement Rework
using human reasoning to evaluate, modify, and extend pattern types.
2 2
1 1
3 3
Adjustment Correction
3. Multi-perspective path semantics
(Variation)
2 2
Skip-reverse/
In this section, we present our vision of multi-perspective path semantics. To this end, we
Backjump
Hypothetical/
develop eight path semantics through visual characteristics related to shape and color. The
3
1
Conformance 1
3
semantics differ
Reorder
based on whether
Disarray the path indicates desired or undesired behavior, observed or
unobserved
Shortcut behavior, and its flow direction.
1 1
Hypothetical/
Omitted
3.1. Conformance
Simplification pathNegligence
(Sloppiness)
The semantics of the conformance path relates to a combination of desired and
Conformance behavior type
Path
combinations Allowed
observed behavior. On the one hand, desired behavior connects to the causal
Prohibited
Skip-reverse/
2 process knowledge, which the analyst predefines as a working hypothesis. By that,
2
Backjump
Conformance
1,3 analysts presuppose, based on their own expertise, that within the very specific
1,3
Refinement context, the process is supposed to flow through this particular path. It is implicitly assumed
Rework
2 that process behavior not flowing through this path is understood as a deviation or at least as
2
1
3
an unexpected behavior. On the other hand, the conformance path additionally incorporates the
1
3
Adjustment
observed behavior
Correction
that is recorded in the data source. Hence, the semantics of the conformance
(Variation) path can be considered both an actually observed behavior in the source data and a desired
Skip-reverse/ 2 behavior, as intended by the analyst.
2
Backjump
Hypothetical/
The visual representation takes the form of an arrow with a solid gray line connected to a
3
filled arrowhead. The structure of this path runs angularly and has no curvatures. The intention
1
Conformance 1
3
Reorder
behind the visualization is to convey the impression of desired behavior that is not explicitly
Disarray
Shortcut 1 prominent. 1
Hypothetical/
Omitted
Simplification 3.2. Hypothetical
Negligence path
(Sloppiness)
The semantics of the hypothetical path relates to an unobserved yet desired behavior.
This means that the causal process knowledge allows the process to flow through this
particular path with no record in the data confirming this behavior. If a hypothetical
path occurs, this always implies that there is at least one other path option over
which the process can flow as well. For instance, this can be attributable to the causal process
knowledge allowing for the parallel execution of two activities with a time offset or a passage
in the process that allows for an arbitrary choice of follow-up options.
The visual representation takes the form of an arrow with a gray dashed line connected to a
filled arrowhead with an identical angular course. The visualization is supposed to convey the
indefinite characteristics of a non-conforming behavior.
2 2
Skip-reverse/
Backjump
Hypothetical/ 3
1
Conformance
Conformance behavior type 3
1
Allowed Reorder Disarray
Prohibited
2 2
Shortcut 1 1
1,3 Hypothetical/ 1,3
Omitted
Refinement Rework
3.3. Omitted path
Simplification Negligence
2 2 (Sloppiness)
1
3
1
3
The semantics of the omitted path also relates to unobserved yet desired behavior.
Adjustment Correction
As opposed to the hypothetical path, here, the intended sequence flow is considered
(Variation) mandatory, but with no data recorded that confirms its execution. If an omitted
2 2 path occurs, it can be concluded that certain process activities have been skipped
unintentionally or that the order of activities has been reversed.
3
The visual representation takes the form of an arrow with a gray dashed line connected to an
1
1
3
Reorder
unfilled (empty) arrowhead. It also runs in an angular course. The unfilled arrowhead should
Disarray
r type
1 give the impression that the path is mandatory, thus its exaggerated appearance.
1
Prohibited
2
Simplification 3.4. Allowed shortcut path
Negligence
1,3 (Sloppiness)
Rework The semantics of the allowed shortcut path relates to desired and observed behavior.
2 Therefore, the causal process knowledge indicates that the process is allowed to
1
3
skip one or more process activities without following up on them at later points,
and the data recorded indicates that this, in fact, happened. If this path appears in
Correction
the model, a hypothetical path can be linked to it because a circuitous route via the activities
2 skipped, in reality, would also have been possible.
3
The visual representation takes the form of an arrow with a solid gray line connected to a
1
filled arrowhead. The structural appearance, again, follows an angular course with the intention
Disarray
rmance behavior type
to convey expected and desired behavior. However, this path can often be recognized as flowing
1
Prohibited
in parallel to the direction of other conformance paths.
2
Negligence
1,3
3.5. Prohibited shortcut path
(Sloppiness) Rework
2
The semantics of the prohibited shortcut path relates to undesired yet observed
1 behavior. In this case, the causal process knowledge explicitly does not allow the
process to jump over a specific activity but is recorded in the data. Here, at least one
3
Correction
omitted path can be linked to the prohibited shortcut path because other activities
2
not intended to be executed were left out and not followed up on.
The visual representation takes the form of an arrow with a solid red line connected to a
filled arrowhead. In this case, as opposed to the allowed shortcut, it has a curvilinear course.
3
1
Disarray Here, contrast is to be conveyed in relation to the allowed shortcut path, which indicates an
1
undesirable behavior through the round and less structured-appearing course.
n Negligence 3.6. Allowed backjump path
(Sloppiness)
The semantics of the allowed backjump path relates to observed and desired behavior.
The causal process knowledge indicates that the process can jump back to already
executed process activities. Once an allowed backjump occurs, there are multiple
follow-up options leading to an increased level of complexity.
The visual representation takes the form of an arrow with a solid gray line connected to a
filled arrowhead. Thereby, the path runs in an angular course in the opposite direction of other
conformance paths. Even though backjumps in processes may be negatively conjugated, this
path semantics emphasizes the acceptance to repeat an activity already executed before.
3.7. Prohibited backjump path
The semantics of the prohibited backjump path relates to observed yet undesired
behavior. In this case, the causal process knowledge restricts the process from not
returning to a previously performed activity despite the recorded data indicating
otherwise. With these paths, a large variety of follow-up options becomes possible,
which usually leads to higher degrees of complexity.
The visual representation takes the form of an arrow with a solid red line connected to a filled
arrowhead with a curvilinear course. In most cases, this path runs in the opposite direction of
other conformance paths, indicating an undesired behavior.
3.8. Skip-reverse path
The semantics of the skip-reverse path relates to observed yet undesired behavior,
which inevitably occurs in combination. This means that the recorded behavior
indicates that the process activities were executed in an order that the causal process
knowledge forbids. This triggers at least one path that skips a considered follow-up
activity and at least one reverse path that continues where another activity was left out. However,
even though all intended process activities were executed, the order of activity execution was
incorrect. If this path is shown in the model, an omitted path can always be linked to a pair of
reverse and skipped paths.
The visual representation takes the form of an arrow with a solid red line connected to a
filled arrowhead with a curvilinear course. Together with the inseparably connected path to the
follow-up activity and the omitted path between the activities in the original order, the path
semantics intends to create a complex-appearing and slightly chaotic impression that conveys
that something is not going as desired.
4. Pattern types
This section briefly demonstrates how the context, meaning various arrangements of different
path semantics, may emphasize an underlying behavior that is otherwise hard to distinguish
when examining one single path semantics in isolation. We refer to these path semantics
ensembles as patterns or pattern types on a process instance level. An example of this is the
allowed backjump path, which could denote a wrong-order execution of events if it is proceeded
by a hypothetical path rather than when proceeded by a conformance path.
We identify eight possible patterns, all listed in Table 1. The patterns are divided into two
categories, allowed and prohibited, whether they include allowed or prohibited path semantics.
Each pattern is given a name for easy recognition of an underlying behavior. We also exemplify
the patterns from the perspective of an order-to-cash process.
To further enhance understandability, we define a pattern as a sequence of directly follows
relations x𝑎1 Ñ 𝑎2 ... Ñ 𝑎𝑛 y that is part of a process instance, where 𝑎1 ...𝑎𝑛 are activities of the
Conformance behavior type
Path
combinations Allowed Prohibited
2 2
Skip-reverse/
Backjump 1,3 1,3 2 2
Conformance behavior type
Conformance
Path
Conformance behavior type 1,3 1,3
combinations
Path Allowed Refinement
Prohibited Rework
combinations Allowed Prohibited
2 2 2 2
Skip-reverse/
2
Conformance behavior 1,3type
Backjump Skip-reverse/ 2 2 2
Path Conformance
Backjump
1,3 1 1 2 2
1,3 3 3 1 1
combinations Table 1
Allowed ConformanceProhibited
Refinement Rework
1,3
1,3
2
1,3 3
2
3
Conformance behavior type 1,3 1,3
Path An2 overview of some possible 2
pattern types that
Refinement result
Reworkfrom a unique
Adjustment set
Correctionof path semantics. The numbers
Skip-reverse/
combinations 2 (Variation)
Allowed 2
Backjump indicate
1,3
the execution
Prohibited order,
1,3
with
2
"1" denoting the 2
first
2
execution. 22 2
Conformance 2 2
1 1
2 2 2
Skip-reverse/ Path combinations3 1Skip-reverse/ 3
1,3
2
1 1
1,3
1
Backjump 1,3
Refinement 1,3
Rework 3Backjump 2
3 3
2
1
3
1 2 2
3
Conformance
nformance behavior type Adjustment Hypothetical/ Correction
3
3
Conformance behavior type Conformance1,3 1
Refinement 2 Backjump
Rework Backjump/Shortcut
(Variation)2 Adjustment
3
Correction
1,3
Backjump1
Shortcut 1
3
1
3
Allowed Prohibited (Variation)
Prohibited
2
1 Conformance 1
2
Conformance
Reorder 2
Hypothetical/Omitted
2
2
Disarray Hypothetical/Omitted
2
2 2 3 Skip-reverse/ 3 1 1
2 2 2
Backjump Skip-reverse/ 3 2 3 2 2 2
1
Backjump
Hypothetical/
1 Shortcut 1 1 2 2
1,3
3 Adjustment
2 23
Hypothetical/ 1 Correction
1,3 1,3 2 2 1 1
3 Hypothetical/ 1 1
Conformance 3
ior type (Variation) Conformance
1,3 3 1,3
1Omitted
1,3
3 1 3 1
3
1
3
1,3
ent
Refinement ReworkRework
AdjustmentAllowed Correction
1 1 1
3
Reorder 3
Disarray 3
Prohibited (Variation) 2 Refinement 2
Reorder Adjustment Disarray
Simplification Reorder
Negligence Simplification
2 Skip-reverse/
2
2 2 (Sloppiness)
Backjump Shortcut 1
2 2 12 2
2 2
1
Hypothetical/
Skip-reverse/ 2 1 1
Shortcut 2
Hypothetical/ 1 1 1 1
3 1,3 2 3 2 1 1
3
BackjumpConformance 3 1
Omitted Hypothetical/1 1 1 1
3 1 3 1
3
Hypothetical/ 3 1,3
Omitted
3
1,3 3
1
3
Rework 3
Adjustment
Conformance
ent
1
Correction Prohibited
Correction
Reorder Disarray
1 Simplification Negligence
(Variation)
n) 3 Rework Simplification Correction (Sloppiness)Negligence Disarray Negligence
2
Reorder Disarray (Sloppiness)
2 2
2 Shortcut
1 2 1
1
2 1
Hypothetical/
3
1
same sequence with different activity types so that 𝑎 ‰ ... ‰ 𝑎𝑛 holds. The timestamps of two
1 1
ShortcutOmitted
1
3 1
Hypothetical/
3
3
1
activities in a directly follows relation 𝑎 Ñ 𝑎 must be different so that 𝑡p𝑎1 q ă 𝑡p𝑎2 q holds. If
1
Correction
Omitted 3
1
1 2
3
Simplification
1 Negligence
Reorder an activity (type)
Disarray is executed twice in the instance, the timestamps must be different so that
𝑎1(Sloppiness)
Negligence
Simplification
Disarray
2
holds. The arrow symbol Ñ denotes a directly follows relations between two
𝑡p𝑎1 q ă 𝑡p𝑎11 q (Sloppiness)
activities 𝑎1 and 𝑎2 in a pattern, which is further assigned a letter to indicate its path semantics
1 1
1
as either a backjump path Ñ𝐵 , a shortcut path Ñ𝑆 , a conformance path Ñ𝐶 , a hypothetical
3
1
Disarray
Simplification
path Ñ𝐻 , or an omitted path Ñ𝑂 . A crossed-out arrow Û emphasizes a prohibited path. Note
Negligence
ation that we do not differentiate between designed and executed sequences since the path semantics
(Sloppiness)
Negligence
(Sloppiness)
1
imply it.
Negligence
4.1. Allowed pattern types
(Sloppiness)
The allowed pattern types comprise path combinations, which are allowed by design. These
include: refinement, adjustment, reorder, and simplification.
Refinement is characterized by a backjump path that follows and is followed by two identical
conformance paths leading to the emerging sequence x𝑎1 Ñ𝐶 𝑎2 Ñ𝐵 𝑎1 Ñ𝐶 𝑎2 y. Since the
same directly follows relations 𝑎1 Ñ𝐶 𝑎2 is executed twice, this pattern indicates a revising
behavior (e.g., when a customer proofreads an order detail before purchase).
Adjustment is characterized by a conformance path followed by a backjump path, which
sequentially is followed by a shortcut path, leading to the emerging sequence: x𝑎1 Ñ𝐶 𝑎2 Ñ𝐵
𝑎1 Ñ𝑆 𝑎3 y. Here, only the first activity 𝑎1 is executed twice (cf., refinement), thus indicating a
re-routing of an intended activity sequence (e.g., when a customer cancels a requested credit
card payment and, instead, decides to pay in installments).
Reorder is characterized by a backjump path that follows a hypothetical path, which sequen-
tially is followed by a shortcut path leading to the emerging sequence: x𝑎1 Ñ𝐻 𝑎2 Ñ𝐵 𝑎1 Ñ𝑆
𝑎3 y. This means that the intended activity sequence is executed in reverse (e.g., when an order
foresees a purchase-for-delivery procedure when, in fact, customers purchase items (through
bill) after delivery).
Simplification is characterized by a shortcut path that skips a sequence of hypothetical paths,
such that the following pattern occurs: x𝑎1 pÑ𝐻 ... Ñ𝐻 𝑎𝑛 , Ñ𝑆 𝑎𝑛`1 qy. This pattern suggests
redundancies in the process design (e.g., when customers use an autofill function to fill out their
demographic details before purchase).
4.2. Prohibited pattern types
The prohibited pattern types are analogous to the allowed patterns but contain at least one
prohibited path, thus indicating violations of an intended process design. These include: rework,
correction, disarray, and negligence.
Rework is the analog to refinement yet with prohibited paths, such that the following pattern
emerges: x𝑎1 Ñ𝐶 𝑎2 Û𝐵 𝑎1 Ñ𝐶 𝑎2 y. Here, a refining behavior is instead a source of
frustration or an unnecessary emendation (e.g., when a customer has to re-purchase an order
after discovering the purchase of the wrong items).
Correction is the analog to adjustment yet with prohibited paths, such that the following
pattern emerges: x𝑎1 Ñ𝐶 𝑎2 Û𝐵 𝑎1 Û𝑆 𝑎3 y. In comparison, whereas an adjustment may
improve a process towards a better outcome, in correction, an avoidable mistake is adjusted to
prevent harm (e.g., when a customer must be contacted after they were able to purchase an
order with a suspended credit card successfully).
Disarray is the analog to reorder yet with prohibited paths, such that the following pattern
emerges: x𝑎1 Ñ𝑂 𝑎2 Û𝐵 𝑎1 Û𝑆 𝑎3 y. Here, a rearrangement of (strict) protocol procedure is
executed (e.g., when an order is marked as successful before verification).
Negligence is the analog to simplification yet with prohibited paths, such that the following
pattern emerges: x𝑎1 pÑ𝑂 ... Ñ𝑂 𝑎𝑛 , Û𝑆 𝑎𝑛`1 qy. Here, the complete skipping of an intended
activity sequence is considered wrong rather than as an improvement (e.g., when a customer is
warranted a replacement item after a filed complaint without the warranty not being properly
inspected by the company).
5. Use cases
Allowed patterns reflect expected behavior and give insights into how well a process is adopted.
Prohibited patterns are more complex. In this section, we focus on prohibited pattern types as
we expect more business value from their analysis. Therefore, we articulate three assumptions
and review the pattern according to four performance dimensions relevant to business processes.
In the second part of this section, we examine what a technical solution can look like and explain
the business impacts that can be derived from a specific process instance of an order-to-cash
process. We then further apply heuristics to improve the process.
5.1. Assumptions
Previous research addresses the speed of technical development and its adoption in business,
which leads to the clear call to action of transferring new developments in real-life use cases [28].
Some concepts are highly adopted in business, such as the Balanced Scorecard with its four
Table 2
Impact of prohibited pattern types on the performance perspectives time, cost, and quality
Performance Perspective
Time Cost Quality
Rework ÓÓ ÓÓ Ò
Pattern
Correction Ó l Ò
Disarray l l Ó
Negligence Ò Ò ÓÓ
Legend: Ò Ò high positive impact, Ò medium positive impact, l no impact, Ó medium negative impact,
Ó Ó high negative impact
perspectives financial, customer, learning, and growth as well as internal business process [29]2 .
The latter, namely the internal business process perspective, can be measured by the four
performance dimensions of the devil’s quadrangle, namely, (1) time, (2) cost, (3) quality, and (4)
flexibility [19]. We apply this to emphasize that the improvement of one or multiple perspectives
results in less performance of at least one other perspective [19]. For this paper, we review only
the prohibited pattern types of Section 4 and the impact on the four performance dimensions
with three assumptions, knowing that under realistic conditions, there are cases that will not
fulfill them. We use the following assumption:
1. With increasing complexity due to path variants and activity numbers, the average process
instance duration increases
2. Every activity has a cost, mainly labor costs, resulting in a negative financial impact per
executed activity.
3. Every activity adds value and, therefore, enhances the quality of the process outcome,
resulting in better quality the more (planned) activities are performed.
Based on these assumptions, the impact on process performance is summarized in Table 2.
As no impact on flexibility is identified, we do not address this perspective.
• The rework pattern repeats two events and adds two connections, resulting in a high
negative impact on cost. The quality is benefiting from the rework, as it repairs an error.
• The correction pattern repeats one event and adds one additional connection, resulting in
a medium negative impact on time and costs. The quality is benefiting as an unexpected
result is prohibited.
• The disarray pattern impacts time and cost under respecting the assumption, but a medium
negative impact on quality as the sequence of events is not followed.
• The negligence pattern is skipping one event and having one connection less, resulting
in a positive effect on costs and time. On the other hand, as an event is skipped, a high
negative effect on quality is expected.
2
https://www.bain.com/insights/management-tools-and-trends-2023/ (Last accessed: 2023-12-10)
5.2. Example
To illustrate the added value of multi-perspective path semantics for business process analysis,
we showcase its application using a real-world example of an order-to-cash process observed at
a German mid-sized company. To visualize this process, we use a tool of Noreja3 . This order-to-
cash process starts with placing a customer order, which is followed by the preparation and
shipping of digital or physical goods or services and ends with financial processing, including
the posting of an invoice and receiving of cash. This first extract of a process instance in Figure
1 represents the pattern type disarray4 . After the event Create Delivery Note (left of Figure 1),
the process continues with Receive Payment, skipping the actually desired follow-up activity
Post Invoice. This leads to an undesired order of the events Post Invoice and Receive Payment
that contradicts the causal process knowledge. Due to the particular semantics of the paths
and their highlighting in red, process analysts can now directly identify this pattern in order to
derive actions. The omitted paths indicate the desired process relations. In this case, the pattern
indicates that the organization takes a financial risk, as matching the payment against the actual
invoice is not secured. In this example, the payment terms for each customer order are highly
different and optimized by the sales department in terms of discounts, overdue fines, etc. The
lack of invoice-payment matching, therefore, causes significant problems. When receiving the
payment before the invoice, the potential of overpayment or underpayment is given, resulting
in lower customer satisfaction and more inaccurate financial planning.
Over the last decades, several redesign methodologies have been developed to improve process
performance, including redesign heuristics [19]. One of these heuristics is the case-base work
that removes the processing of cases in batches or at specific points in time (e.g., every Monday).
With handling individual cases, the time between two events can be shortened. Applying this
heuristic on the event post invoice can significantly reduce the time from creating the delivery
note to the invoice posting and reduce the risk of receiving payment with an invoice reference.
Applying this heuristic will, under assumption 2, result in additional costs, as the invoice posting
will happen more frequently. Another heuristic that can solve the downside of the case-based
work is the activity automation. Automating the posting of the invoice and executing this event
directly after the creation of the delivery note will reduce the time between these events and
the costs for the posting.
6. Limitations and future research
This paper presents multi-path semantics for process mining, pattern types, and possible
applications. This research stream is novel and promising, yet covering it entirely in one study
is infeasible. We acknowledge the limitations of our paper and use them to outline directions
for future research.
First, we must note the limitations of the scope of our paper. We explicitly exclude so-called
change activities5 . In addition, as the primary goal of this paper is to highlight the necessity for
3
https://noreja.com (Last accessed: 2023-12-10)
4
The blue symbols of the events themselves are not part of our proposed concept and therefore not explained.
5
Change activities cannot be sorted into the causal logic of a process, as they may appear randomly due to unplanned
occurrences. In an order-to-cash process, this takes the form of cancellations or price/quantity changes.
Figure 1: Visual representation of the pattern type disarray in a single process instance of an order-to-
cash process
multi-path semantics rather than to provide an exhaustive list, we note that other semantics,
including domain-specific ones, may be defined by future extensions. The same applies to
the patterns presented in this paper. While we identified some critical patterns using the
proposed multi-path semantics, additional patterns might also be observed, especially if new
path semantics are added.
Second, it must be noted that in this paper, we are only considering possible path semantics
for single cases. However, new challenges will arise as we try to raise the level of abstraction
(e.g., to a variant or even process level). Aggregating cases with paths of different semantics
between the same activities or aggregating path patterns is a non-trivial task. For instance, if,
in one case, activities 𝑎1 and 𝑎2 are connected via a conforming path. In another case, the same
activities are only connected via an omitted path. Then, it remains unclear which semantics
(and which visual representation) should be chosen when aggregating on a process level.
Third, while we do provide some visual descriptions of the paths with different semantics, it
must be noted that these descriptions should be treated as preliminary proposals for visualization
rather than fixed recommendations or guidelines. We explicitly leave the specific visualization
(e.g., a more differentiated coloring of paths) out of the scope of this paper. We also note that
further visual additions can be made (e.g., additional icons near the arc ends) for improved
visual differentiation and reduced cognitive load. Ultimately, we highlight that a user evaluation
is required to validate the visualization approach.
In future work, we plan to tackle the identified limitations. First, empirical research is needed
to evaluate both the relevance of the proposed path semantics in practice as well as the suitability
of various visualization approaches. Second, further path semantics and pattern types can be
obtained using both empirical and explorative studies. Finally, the impact of the observed paths
on flexibility – the fourth dimension of process performance – is yet to be studied.
7. Conclusion
In this paper, we envisioned a foundation for multi-perspective path semantics in process
mining. First, we presented eight distinct path semantics that can be derived by integrating
causal process knowledge. Second, we defined pattern types as unique sets of path semantics
on a process instance level to provide additional meaning about underlying behaviors. We
demonstrated the benefits of our approach by exemplifying the semantics in a use-case scenario,
examining various pattern types according to their business values using the devil’s quadrangle.
In addition, we gave some example visualizations from an existing process mining system. Our
work facilitates the interpretability and applicability of process mining outcomes by providing
a more fine-grained view of path semantics. By linking causal process knowledge to visual
elements, we further contribute by extending the graphical capabilities of process models.
In combination, both aspects facilitate the fast and purposeful acquisition of process-related
insights for analysts. In this way, our objective is to inspire future research to challenge the
still prevailing representational bias [30] in process mining, which oftentimes distorts the true
nature of the underlying process.
Acknowledgments
This work was supported by the Einstein Foundation Berlin [grant number EPP-2019-524, 2022]
and Deutsche Forschungsgemeinschaft [grant number ME 3711/2-1].
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