questions. The causal pattern is a proposed ontology design pattern for representing the structure of causal relations in a knowledge graph. This pattern is grounded in the concepts defined and used by the CausalAI community i.e., Causal Bayesian Networks and do-calculus. Specifically, the pattern models three primary concepts: (1) causal relations, (2) causal event roles, and (3) causal efect weights. Two use cases involving a sprinkler system and asthma patients are provided along with their relevant competency causal pattern, causality, causal bayesian network, causal relation, causal events, causal efects ∗Corresponding authors. †These authors contributed equally.
CEUR ceur-ws.org
Causality is a relation between events in which the occurrence of one event leads to the
occurrence of another. In other words, the first event is deemed responsible for the occurrence
of a second event [
The current state-of-the-art in modeling causality within the CausalAI community revolves
around using Causal Bayesian Networks (CBN) and the do-calculus [
Within the CausalAI field, a defined set of terminology exists to describe and model causal relations. This terminology serves as a foundation for a design pattern representing causal relations, to support integration, interoperability, and data reuse. In this paper, we present the causal pattern, a design pattern that captures the structure of causal relations. This pattern is designed to be compatible with current state-of-the-art models and applications while also adopting best practices and designs from the ontology design pattern (ODP) community. The proposed pattern models three key concepts from CausalAI: causal relations, causal event roles, and causal efect weights.
1. Causal relation: A causal relation represents a relation between events such that the occurrence of one event leads to the occurrence of the other. The direction of the causal relation between events is captured by the CBN as a directed edge between nodes in the graph. 2. Causal event role: A causal event role represents the role an event plays within the context of a causal relation. Events play three distinct causal roles: treatment, mediator, and outcome. The treatment role is played by some initial event, which is deemed responsible for the occurrence of a subsequent event. The outcome role is played by the subsequent event, which occurs because of the treatment. The mediator role is played by zero-or-more events that influence the causal relation between the treatment and outcome (further described in section 4.3.3), and 3. Causal efect weight: The causal efect weight represents strength of a causal relation; i.e., a higher efect weight implies a higher level of responsibility assigned to the treatment for the occurrence of the outcome event.
The causal pattern is the first attempt to model concepts from CBNs within an ontology design pattern. This pattern contains information from CBN – such as causal relations, causal event roles, and causal efect weights – allowing query on a conformant KG. Additionally, grounding the causal pattern in CBN enables compatibility with causal reasoning.
The paper is organized as follows: In section 2, a summary of relevant literature on causal representation in ontologies, ontology design patterns, and knowledge graphs is provided. In section 3, several relevant use cases are introduced, along with competency questions. The proposed causal pattern is defined and discussed in Section 4, including its primary concepts and axioms. Section 5 presents a version of the causal pattern for hyper-relational knowledge graphs. Discussion of the causal pattern with future work is outlined in Section 6, followed by the conclusion in Section 7.
Several past eforts have been made to represent causal relations in knowledge graphs. ConceptNet2 is a partially crowd-sourced knowledge graph that connects common words and phrases through named relations. It contains a notion of cause3, with details on related types (e.g. antecedent, etiology, factor), word forms, and antonyms.
CauseNet is a large scaled knowledge graph that models causal relations between two
concepts (words or noun phrases) that are extracted from the web [
One of the early attempts to represent causality was proposed in the DOLCE ontology as a relation between events [10]. DOLCE makes a distinction between causality and causation, in which causality is defined as a relation between abstract events and causation as a relation between concrete events. The causal pattern in this paper also captures this distinction (see Section 4). DOLCE also recognizes causation as a complex relation between events that could involve intermediary events. These are referred to as mediators in the causal pattern (see Section 4.3.3). The QualityCausation4 ontology design pattern aims to identify causal relations between the properties of objects in an event [11]. For example, in the domain of disaster risk management, an object participating in a hazardous event will have properties such as susceptibility, fragility, resilience, and vulnerability. An increase in susceptibility and a lack of resilience will cause an object to be more vulnerable. The causal relation helps determine which property causes an object to be most vulnerable and at risk.
The CausalEvent pattern is a recent efort at representing causality by grounding the causal relation in space-time [12]. This work also borrows the distinction between abstract and concrete events from DOLCE. It provides a framework to model spatiotemporal events and capture the implicit causal relation between them using the PossiblyCausesRelation concept and hasPossiblyCausesRelation object property. The pattern formalizes concepts that are needed to examine the causes of a disaster event. While there are similarities between the CausalEvent pattern and the proposed pattern, the latter is focused on representing concepts from CBNs, specifically to capture the role of an event and to quantify the strength of a causal relation.
OntoBayes models Bayesian network (BN) probabilities and conditional dependencies in the Ontology Web Language (OWL) to enhance knowledge representation in uncertain systems [13]. Similarly, ByNowLife creates a knowledge base by integrating logical information from an ontology into a BN and probability information from a BN into an ontology [14]. The proposed causal pattern does not focus on modeling the probability and conditional dependency aspects of BN or CBN.
Two use cases are provided to motivate the need for the proposed causal pattern. The first use case describes a scenario involving a sprinkler system and slippery pavement. This scenario is commonly used in textbooks and tutorials to illustrate the basic structure of causality. The second use case describes a scenario involving asthma patients in a healthcare setting.
The sprinkler use case is a well-known example often used in the CBN literature [
CQ 3.1.1 What events are responsible for the pavement being slippery? CQ 3.1.2 What would be the outcome of turning the sprinkler system on(of)? CQ 3.1.3 How strong is the causal link between the sprinkler being on and the pavement being wet? CQ 3.1.4 What if the pavement is not wet, how would it efect the pavement being slippery?”
The use case described in this section is part of the kHealth-Asthma project [15, 16]. Asthma is a complex disease with multiple factors afecting a patient’s condition. kHealth-Asthma is a continuous self-monitoring project involving pediatric asthma patients and aiming to understand the efects of outdoor environmental allergens on the patient’s symptoms and their medication intake. The data collected about asthma patients include their (1) symptoms, such as cough, chest tightness, wheezing, and breathing patterns, (2) intake of medications, and (3) outdoor environment features, such as pollen and air quality index (AQI). Figure 1(B) shows a CBN with nodes representing events such as the presence of outdoor allergens (i.e., pollen and AQI), the patient experiencing coughing symptoms, and the intake of medication. The edges represent the causal relations with efect weights. For example, the presence of outdoor allergen: pollen/AQI causes the patient to experience a cough with causal efect weight “0.8” and “0.4”, respectively. An ODP for causal relations should be able to support questions about the asthma use case, such as:
CQ 3.2.1 Is the medication intake by the patient caused by the presence of outdoor environmental allergen such as pollen or AQI? CQ 3.2.2 How much does the presence of an asthma symptom efect the intake of medication? CQ 3.2.3 How does an outdoor environmental allergen afect the patient? CQ 3.2.4 What is the probable cause of the cough experienced by the patient? CQ 3.2.5 What if pollen (or AQI) allergen was not present in the outdoor environment, how would it efect the intake of medication? CQ 3.2.6 What if the patient did not experience a cough, how would it efect the intake of medication? Long-term analysis involving questions of this type would help clinicians better understand and treat their patients. For example, this could lead to early intervention in a patient’s treatment plan, either by suggesting preventive measures (i.e., avoiding outdoor exposure when environmental allergens are present) or changing the dosage and/or type of medication prescribed. Eventually, this may lead to more personalized treatment plans that are customized toward a patient’s specific health condition [ 15].
Causality is a relation between events, in which an initial treatment event (i.e. the cause) causes
an outcome event (i.e. the efect). This notion of causality is grounded in Causal Bayesian
Networks (CBN) and do-calculus [
In the causal pattern, the causal relation is reified as a class, C a u s e s (see Figure 2). Events are linked through C a u s e s using the causal role properties, defined in Section 4.3. The efect weight of a causal relation is defined as a property of C a u s e s in Section 4.4.
An E v e n t is an occurrence, and thus has a direct temporal quality and indirect spatial quality (via its participants).An e v e n t can have more than one cause (i.e. treatment), and may cause more than one efect (i.e. outcome). As shown in the sprinkler CBN use case from Figure 1(A), pavement is wet has two causes: sprinkler is on and it is raining. Similarly, it is rainy season has two causal efects: sprinkler is on and it is raining. An e v e n t may either be abstract or concrete. The conceptual distinction of abstract and concrete events was first introduced by DOLCE [ 10] and then formalized within an ontology design pattern by [12]. 4.2.1. Event(Abstract) An abstract event, E v e n t ( A b s t r a c t ) , is a general type of E v e n t ; e.g. it’s rainy season, patient is coughing. The events described in CBNs, such as those from the use cases above, are often abstract.
Event(Abstract) ⊑ Event (1) 4.2.2. Event(Concrete) A concrete event, E v e n t ( C o n c r e t e ) , is a specific E v e n t that has transpired in the world; e.g. it’s rainy season in Spring 2023, John Doe is coughing.
Event(Concrete) ⊑ Event (2)
A concrete event may belong to a type of abstract event. For example, the concrete event John Doe is coughing is of type patient is coughing.
∃of Type.Event(Abstract) ⊑ Event(Concrete) Event(Concrete) ⊑ ∀of Type.Event(Abstract)
A causal event role is a role performed by an event within the scope of a causal relation. There are three distinct causal roles that an event may play: treatment, mediator, and outcome. An event may play only one role within a given causal relation, but may play diferent roles within other causal relations. For example, consider the situation in which it’s raining causes the pavement to be wet, which in turn causes the pavement to be slippery. Notice that the pavement is wet event plays three diferent roles – as treatment, outcome, and mediator – within three distinct causal relations (see Figure 3(A) ). The three causal roles are represented as object properties – h a s T r e a t m e n t (Section 4.3.1), h a s O u t c o m e (Section 4.3.2), and h a s M e d i a t o r (Section 4.3.3) – with the C a u s e s class as the domain and E v e n t as the range. 4.3.1. hasTreatment The treatment role is defined as the initial event that is responsible for the occurrence of some subsequent event. It is represented as an object property, h a s T r e a t m e n t , with the domain C a u s e s and range E v e n t . In the sprinkler use case, Figure 3(A), for the causal relation between it’s raining and pavement is wet, the event it’s raining plays the role of treatment. Similarly, in the asthma use case, Figure 3(B), for the causal relation between pollen allergen and medication intake, pollen allergen is present plays the role of treatment and is linked using the h a s T r e a t m e n t object property. 4.3.2. hasOutcome ∃hasTreatment.Event ⊑ Causes Causes ⊑ ∀hasTreatment.Event Causes ⊑ ⩾ 1hasTreatment.Event ⊓ ⩽ 1hasTreatment.Event The outcome role is defined as the event which occurs as a result of the treatment event. It is represented as an object property, h a s O u t c o m e , with the domain C a u s e s and range E v e n t . In the sprinkler use case, Figure 3(A), for the causal relation between it’s raining and pavement is wet, the event pavement is wet plays the role of outcome. Similarly, in the asthma use case, Figure 3(B), medication intake plays the role of outcome in two causal relations with treatment events pollen allergen is present and patient is coughing.
∃hasOutcome.Event ⊑ Causes Causes ⊑ ∀hasOutcome.Event Causes ⊑ ⩾ 1hasOutcome.Event ⊓ ⩽ 1hasOutcome.Event (Scoped Domain) (Scoped Range) (8) (9) (10) 4.3.3. hasMediator The causal relation is transitive. For example, given events {A, B, C}, if A causes B causes C, then this would imply that A causes C (i.e., A holds some responsibility for the occurrence of C). In this case, the causal relation between A and C is said to be mediated by B. A causal relation may have zero-or-more mediator events. The mediator role is represented as an object property, h a s M e d i a t o r , with the domain C a u s e s and range E v e n t . In the sprinkler use case, Figure 3(A), for the causal relation between it’s raining and pavement is slippery, the event pavement is wet plays the role of mediator. Similarly, for the asthma use case, Figure 3(B), patient is coughing plays the role of mediator in a causal relation between pollen allergen is present and medication intake.
∃hasMediator.Event ⊑ Causes Causes ⊑ ∀hasMediator.Event Causes ⊑ ⩾ 0Mediator.Event
Causal efect weight represents the strength of a causal relation; i.e., a higher efect weight implies a higher level of responsibility assigned to the treatment for the occurrence of the outcome. In the causal pattern, this is represented as a property, h a s E f f e c t W e i g h t , with domain C a u s e s and range E f f e c t W e i g h t .
∃hasEfectWeight .EfectWeight ⊑ Causes Causes ⊑ ∀hasEfectWeight .EfectWeight (14) (15)
In practice, the specific representation, generation, and use of efect weight is highly application
dependent. For example, an efect weight may be a qualitative value, enumerated as {Strong,
Middling, Weak}, and represented as an instance of the E f f e c t W e i g h t class. Alternatively, an
efect weight may be a quantitative value represented as a numeric literal, perhaps ranging
from 0 to 1. For this reason, efect weight is only loosely defined and should be adapted based
on the use case. In the case of efect weight represented as a literal, as seen in Figure 3(A), 3(B),
then the axioms may be formalized as such:
∃hasEfectWeight.rdfs:Literal ⊑ Causes
Causes ⊑ ∀hasEfectWeight.rdfs:Literal
(Scoped Domain)
(Scoped Range)
(16)
(17)
In the CausalAI domain, several diferent types of causal efects are defined and used: total
causal efect (TCE), natural direct efect (NDE), and natural indirect efect (NIE). The strength
of these causal efects are represented using causal efect weights, which may be defined as
subproperties of h a s E f f e c t W e i g h t . In Figure 3(A), 3(B), the reader may notice that these properties
are named as: hasTCEW (total causal efect weight), hasNDEW (natural direct efect weight),
and hasNIEW (natural indirect efect weight), respectively. These more specific efect weights
are estimated with do-calculus and are used for intervention and counterfactual reasoning. As
an example, TCE weight is a measure of the efect on the outcome of an intervention done on
the treatment; i.e., measuring how much the change in the treatment efects the outcome. In the
sprinkler use case, TCE measures the strength of the efect of rain on the wet pavement (“0.6”
as shown in 3(A)). Similarly, in the asthma use case, TCE measures the strength of the efect of
the presence of the pollen allergen on the medication intake (“0.9” as shown in Figure 3(B)).
While a comprehensive description of specific causal efects and their weights is out-of-scope
of this paper, the reader may refer to [
A hyper-relational knowledge graph is a knowledge graph that allows descriptions to be added to edges, or triples, in the graph [19]. This ability has a wide variety of uses, such as representing scores, weights, time, provenance, and other information that are relevant to a particular statement. Interest in the representation and use of hyper-relations has grown over the past few years, along with oficial standards and tooling with RDF-star and SPARQL-star [ 20]. The causal relation discussed in this paper represents a complex relationship that can be naturally modeled as a hyper-relation [21]. Figure 4 shows a graphical depiction of this alternative pattern, causalHR pattern, with causality (i.e., c a u s e s , a hyper-relation) modeled as a relation between events. This is similar to the causal relation structure in CBNs. Several additional statements can be made about a causal relation, including the event roles – treatment, outcome, mediator – and the causal efect weights, with the causal triple acting as the subject of these statements. As an example, in RDF-star syntax, this can be encoded as «event1 causes event2» hasEfectWeight “0.7”. However, causalHR pattern axioms can only be partially formalized in description logic. Intuitively, the c a u s e s hyper-relation should be the domain of the causal event role relations and the causal efect weight relations. As mentioned earlier, hyper-relational knowledge graphs, along with good tooling and support, are becoming more prevalent. The causalHR pattern provides an option for representing causality as a hyper-relation in such graphs.
The proposed causal pattern focuses on modeling (1) causal relations, (2) causal event roles, and (3) causal efect weights. To directly compare various models for causality, we can consider the sprinkler use-case from Section 3.1. Three distinct KGs for this use-case are depicted: the causal pattern is seen in Figure 3(A), the CausalEvent pattern [12] is seen in Figure 5(A), and the causalHR pattern is seen in Figure 5(B). The causal pattern and the CausalEvent pattern share a similar structure when representing causal relations between abstract events; i.e. Figure 3(A) and 5(A) respectively. Both reify the causal relation as an instance in the KG, with object properties linking to the two causal events. However, the CausalEvent pattern has no concept of causal event roles and no way of representing causal efect weights. These concepts are central to the representation of causal relations in CBNs, and thus are central to the representation of causal relations in the causal pattern. The knowledge graph conformant to the causalHR pattern, in Figure 5(B), contains all the same information as the causal pattern in Figure 3(A). The primary distinction, of course, is that the causal relation is encoded as a hyper-relation rather than an instance node. The causalHR pattern more closely matches the CBN from Figure 1(A) since the nodes in the graph represent events. Given that the knowledge graph conformant to the causal pattern and causalHR pattern contain information about event roles and efect weights, they are more closely aligned with CBNs and compatible with causal reasoning tasks such as interventional and counterfactual reasoning.
In future versions of the causal pattern, we can imagine extensions to integrate other
types of knowledge that would be relevant during practical use. Prominent examples include
provenance and time [22]. For provenance, consider that the structure of a CBN may be either
learned from data using existing structure learning algorithms [23] or determined by domain
experts. Explicit representation of this type of provenance information may be of critical
importance; e.g. for confidence and trust in the assignment of responsibility for a patient’s
asthma symptoms. Causality is also strongly associated with time. We may reasonably define
a temporal constraint on the causal relation stating that the treatment event always precedes
(in time) the outcome event [
In this paper, we proposed an ontology design pattern to represent the causal relation using concepts grounded in CBN and do-calculus. The pattern was exemplified through an intuitive and common sprinkler use case as well as a more complex health care use case involving asthma patients. Furthermore, we discussed how the causal pattern can be represented as a hyper-relation. In the future, the causal pattern template can be extended to integrate other types of relevant information, such as provenance and time.
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