=Paper=
{{Paper
|id=Vol-3636/paper4
|storemode=property
|title=An Ontology Design Pattern for Representing Causality
|pdfUrl=https://ceur-ws.org/Vol-3636/paper4.pdf
|volume=Vol-3636
|authors=Utkarshani Jaimini,Cory Henson,Amit Sheth
|dblpUrl=https://dblp.org/rec/conf/wop/JaiminiHS23
}}
==An Ontology Design Pattern for Representing Causality==
https://ceur-ws.org/Vol-3636/paper4.pdf
An Ontology Design Pattern for Representing
Causality
Utkarshani Jaimini1,∗,† , Cory Henson2,∗,† and Amit Sheth1
1
Artificial Intelligence Institute, University of South Carolina, Columbia, SC, USA
2
Bosch Center for Artificial Intelligence, Pittsburgh, PA, USA
Abstract
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 effect weights. Two use
cases involving a sprinkler system and asthma patients are provided along with their relevant competency
questions.
Keywords
causal pattern, causality, causal bayesian network, causal relation, causal events, causal effects
1. Introduction
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 [1, 2]. For example, it may be stated that rain causes wet pavement if the rain
can be deemed responsible for the pavement being wet. Causality has applications in many
domains, including healthcare, economics, and social science [3]. There is a growing need for a
design pattern that captures the fundamental structure of causality, as it is used in CausalAI1 .
The current state-of-the-art in modeling causality within the CausalAI community revolves
around using Causal Bayesian Networks (CBN) and the do-calculus [4, 5, 6]. A CBN expresses
causal knowledge in a visually intuitive and human-readable graphical representation. More
specifically, a CBN is a directed acyclic graph where the nodes denote variables of interest
(i.e., the occurrence of an event or a feature of an object), and a directed edge between two
nodes indicates a causal relation [7]. In the absence of a direct edge between two nodes, the
causal relation could be mediated by one-or-more intermediary event nodes (discussed in
detail in section 4.3.3). The do-calculus, developed by Judea Pearl, is used for causal reasoning
i.e., interventional and counterfactual reasoning [8]. An interventional reasoning simulates
WOP’23: Workshop on Ontology Designs and Patterns, ISWC 2023,November 6-10, 2023. Athens, Greece
∗
Corresponding authors.
†
These authors contributed equally.
Envelope-Open ujaimini@email.sc.edu (U. Jaimini); cory.henson@us.bosch.com (C. Henson); amit@sc.edu (A. Sheth)
Orcid 0000-0002-1168-06843 (U. Jaimini); 0000-0003-3875-3705 (C. Henson); 0000-0002-0021-5293 (A. Sheth)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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Workshop ISSN 1613-0073
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a physical intervention on a causal model and helps identify its effects in a model without
running any actual experiment, which saves a significant amount of time, effort, and money.
To accomplish this, do-calculus assigns a value to a node (e.g., sprinkler is on) and analyzes
the effect of this intervention assignment on the model. In addition, CBNs and do-calculus
also support counterfactual reasoning, which answers what-if questions based on hypothetical,
unknown, and unseen scenarios.
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 effect 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 effect weight: The causal effect weight represents strength of a causal relation; i.e.,
a higher effect 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 effect 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.
2. Related work
Several past efforts have been made to represent causal relations in knowledge graphs. Concept-
Net2 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 [9]. The causal relations
are extracted from the ClueWeb12 web crawl and Wikipedia based on linguistic patterns and
represent causality within different domains, such as science, health, society, business, and
news. CauseNet is the first work in knowledge graphs to introduce the notion of mediator as a
transitive relation.
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 effort 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.
2
https://conceptnet.io/
3
https://conceptnet.io/c/en/cause
4
https://mazimweal.github.io/onto/
Figure 1: A causal bayesian network with causal effect weights on the edges for (A) the sprinkler
use case and (B) the asthma use case. The nodes represent events and edges between the two nodes
represent their causal relation. The literals on the edges denote causal effect weights.
3. Use cases
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.
3.1. Sprinkler use case
The sprinkler use case is a well-known example often used in the CBN literature [7]. A CBN, as
seen in Figure 1(A), is used to reason about the cause of a slippery pavement. This model has
five nodes representing the following events: it is rainy season, the sprinkler is on, it is raining,
the pavement is wet, and the pavement is slippery. The directed edges between nodes represent
the causal relations and their effect weights. For example, the rainy season causes rain with an
effect weight of “0.6”. Now consider the causal relation between the rain and slippery pavement
event. While rain does not directly cause the pavement to be slippery, the effect of rain on
slippery pavement is mediated by the pavement being wet. An ODP for causal relations should
be able to support questions about the sprinkler use case, such as:
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(off)?
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 effect the pavement being
slippery?”
3.2. Asthma use case
The use case described in this section is part of the kHealth-Asthma project [15, 16]. Asthma
is a complex disease with multiple factors affecting a patient’s condition. kHealth-Asthma
is a continuous self-monitoring project involving pediatric asthma patients and aiming to
understand the effects 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 effect weights. For example, the presence of outdoor allergen:
pollen/AQI causes the patient to experience a cough with causal effect 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 envi-
ronmental allergen such as pollen or AQI?
CQ 3.2.2 How much does the presence of an asthma symptom effect the intake of medica-
tion?
CQ 3.2.3 How does an outdoor environmental allergen affect 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 effect the intake of medication?
CQ 3.2.6 What if the patient did not experience a cough, how would it effect 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].
4. Causal Pattern
Causality is a relation between events, in which an initial treatment event (i.e. the cause) causes
an outcome event (i.e. the effect). This notion of causality is grounded in Causal Bayesian
Networks (CBN) and do-calculus [5, 7, 4]. The causal pattern models three primary causal
concepts: causal relation, causal event roles, and causal effect weights5 . These concepts will
be described in the subsequent sections, along with formal axioms and examples. The scoped
domain and range axioms are defined, which limits the overall impact of the axiom on the
5
Note that these 3 concepts, of course, do not constitute the entire set of concepts and terminology used by CBNs
and do-calculus. They do, however, constitute terminology needed to describe a causal relation.
Figure 2: The schema diagram for the Causal pattern
rest of the concepts [12]. The proposed causal pattern provides a template to represent
causal relations and can be turned into an ontology using module ontology modeling and
template-based instantiating [17, 18]. The causal pattern OWL file can be found online6 .
4.1. Causes
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 effect weight
of a causal relation is defined as a property of C a u s e s in Section 4.4.
4.2. Event
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 effect (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 effects: 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)
6
https://github.com/utkarshani/CausalPattern
Figure 3: Knowledge graphs representing causal relations from the use cases, conformant to the Causal
pattern: (A) the sprinkler use case described in Section 3.1, and (B) the asthma use case described in
Section 3.2. The blue oval represent E v e n t ( A b s t r a c t ) class, yellow circle are the instances of C a u s e s class,
and the white box represents the causal effect weight literals.
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.
∃ofType.Event(Abstract) ⊑ Event(Concrete) (Scoped Domain) (3)
Event(Concrete) ⊑ ∀ofType.Event(Abstract) (Scoped Range) (4)
4.3. Causal Event Role
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 different 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 different 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.
∃hasTreatment.Event ⊑ Causes (Scoped Domain) (5)
Causes ⊑ ∀hasTreatment.Event (Scoped Range) (6)
Causes ⊑ ⩾ 1hasTreatment.Event ⊓ ⩽ 1hasTreatment.Event (7)
4.3.2. hasOutcome
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 (Scoped Domain) (8)
Causes ⊑ ∀hasOutcome.Event (Scoped Range) (9)
Causes ⊑ ⩾ 1hasOutcome.Event ⊓ ⩽ 1hasOutcome.Event (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 (Scoped Domain) (11)
Causes ⊑ ∀hasMediator.Event (Scoped Range) (12)
Causes ⊑ ⩾ 0Mediator.Event (13)
4.4. Causal Effect Weight
Causal effect weight represents the strength of a causal relation; i.e., a higher effect 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 .
∃hasEffectWeight.EffectWeight ⊑ Causes (Scoped Domain) (14)
Causes ⊑ ∀hasEffectWeight.EffectWeight (Scoped Range) (15)
Figure 4: The schema diagram for the hyper-relational causal pattern, causalHR.
In practice, the specific representation, generation, and use of effect weight is highly application
dependent. For example, an effect 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
effect weight may be a quantitative value represented as a numeric literal, perhaps ranging
from 0 to 1. For this reason, effect weight is only loosely defined and should be adapted based
on the use case. In the case of effect weight represented as a literal, as seen in Figure 3(A), 3(B),
then the axioms may be formalized as such:
∃hasEffectWeight.rdfs:Literal ⊑ Causes (Scoped Domain) (16)
Causes ⊑ ∀hasEffectWeight.rdfs:Literal (Scoped Range) (17)
In the CausalAI domain, several different types of causal effects are defined and used: total
causal effect (TCE), natural direct effect (NDE), and natural indirect effect (NIE). The strength
of these causal effects are represented using causal effect weights, which may be defined as sub-
properties 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 effect weight), hasNDEW (natural direct effect weight),
and hasNIEW (natural indirect effect weight), respectively. These more specific effect weights
are estimated with do-calculus and are used for intervention and counterfactual reasoning. As
an example, TCE weight is a measure of the effect on the outcome of an intervention done on
the treatment; i.e., measuring how much the change in the treatment effects the outcome. In the
sprinkler use case, TCE measures the strength of the effect 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 effect 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 effects and their weights is out-of-scope
of this paper, the reader may refer to [5] for more information.
5. Causal pattern for hyper-relational knowledge graphs
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 official 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
Figure 5: Comparison between CausalEvent pattern, and causal pattern. Sprinkle use case as repre-
sented using (A) CausalEvent pattern, and (B) causalHR pattern
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 effect 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» hasEffectWeight
“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 effect 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.
6. Discussion and future work
The proposed causal pattern focuses on modeling (1) causal relations, (2) causal event roles, and
(3) causal effect 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 effect 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 effect
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 [1, 24]. In other words, a causal relation between events implies a
temporal ordering of the events.
7. Conclusion
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.
Acknowledgment This research was conducted during an internship at Bosch and supported
by NSF Awards #2133842 and #2119654. The opinions are of the authors and not the sponsors.
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