Path Semantics

Path semantics are a core concept in causal process modeling, helping distinguish between desired, observed, and undesired behavior in business processes. Unlike traditional discovery methods that only reflect recorded event sequences, causal process models interpret paths using predefined causal knowledge and domain expertise. This allows analysts to detect conforming behavior, hypothetical alternatives, omissions, shortcuts, backjumps, and critical deviations such as prohibited transitions or skip-reverse sequences. By embedding causal expectations into the analysis of observed data, path semantics improve transparency, reduce ambiguity, and support more precise diagnosis of process deviations.

Conformance path

The semantics of the conformance path relates to a combination of desired and observed behavior. On the one hand, desired behavior connects to the causal process knowledge, which the analyst predefines as a working hypothesis. By that, analysts presuppose, based on their own expertise, that within the very specific context, the process is supposed to flow through this particular path. It is implicitly assumed that process behavior not flowing through this path is understood as a deviation or at least as an unexpected behavior. On the other hand, the conformance path additionally incorporates the observed behavior that is recorded in the data source. Hence, the semantics of the conformance path can be considered both an actually observed behavior in the source data and a desired behavior, as intended by the analyst. The visual representation takes the form of an arrow with a solid gray line connected to a filled arrowhead. The structure of this path runs angularly and has no curvatures. The intention behind the visualization is to convey the impression of desired behavior that is not explicitly prominent.

Hypothetical path

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.

Omitted path

The semantics of the omitted path also relates to unobserved yet desired behavior. As opposed to the hypothetical path, here, the intended sequence flow is considered mandatory, but with no data recorded that confirms its execution. If an omitted path occurs, it can be concluded that certain process activities have been skipped unintentionally or that the order of activities has been reversed. The visual representation takes the form of an arrow with a gray dashed line connected to an unfilled (empty) arrowhead. It also runs in an angular course. The unfilled arrowhead should give the impression that the path is mandatory, thus its exaggerated appearance.

Allowed shortcut path

The semantics of the allowed shortcut path relates to desired and observed behavior. Therefore, the causal process knowledge indicates that the process is allowed to 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 the model, a hypothetical path can be linked to it because a circuitous route via the activities skipped, in reality, would also have been possible. The visual representation takes the form of an arrow with a solid gray line connected to a filled arrowhead. The structural appearance, again, follows an angular course with the intention to convey expected and desired behavior. However, this path can often be recognized as flowing in parallel to the direction of other conformance paths.

Prohibited shortcut path

The semantics of the prohibited shortcut path relates to undesired yet observed 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 omitted path can be linked to the prohibited shortcut path because other activities 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. Here, contrast is to be conveyed in relation to the allowed shortcut path, which indicates an undesirable behavior through the round and less structured-appearing course.

Allowed backjump path

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.

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.

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.