=Paper=
{{Paper
|id=None
|storemode=property
|title=A Logical Model of an Event Ontology for Exploring Connections in Historical Domains
|pdfUrl=https://ceur-ws.org/Vol-779/derive2011_submission_16.pdf
|volume=Vol-779
|dblpUrl=https://dblp.org/rec/conf/semweb/CordaBD11
}}
==A Logical Model of an Event Ontology for Exploring Connections in Historical Domains==
https://ceur-ws.org/Vol-779/derive2011_submission_16.pdf
A Logical Model of an Event Ontology for Exploring
Connections in Historical Domains
Ilaria Corda, Brandon Bennett, and Vania Dimitrova
School of Computing, University of Leeds
ilaria,brandon,vania@comp.leeds.ac.uk
Abstract. Exploring connections between events is paramount to any historical
investigation. In the course of human occurrences, historians have been always
interested in unveiling connections between events for the purpose of establish-
ing the significance of certain happenings and measure their impact. The paper
describes a formal model for representing events and comparing temporal di-
mensions as the backbone for drawing connections and exploring relationships
between happenings. The approach is illustrated in a case study from the Astro-
nomical Revolution, a sub-domain of History of Science.
1 Introduction
Historical information is not just a collection of the most significant happenings, treated
as distinct and unchained entities. It tells a story, forms a narrative which describes a
chronological order and also suggests deeper connections. Hence, the ability to repre-
sent events and reason about their temporal relationships are paramount requirements
when building a framework for exploring connections between historical occurrences.
Understanding historical facts requires knowledge of many aspects of events such as:
when and where an event happened, what events preceded or succeeded it, and whether
its participants are involved in other events. Whereas ontological approaches are already
established within subjects such as Biology and Medicine, domain ontologies for mod-
elling historical domains, e.g. History or Philosophy, are still a relatively unexplored
area. This may be attributed to a number of factors: historical domains tend to be both
complex and loosely structured, they involve a wide variety of different kinds of en-
tity and relation including temporal, conceptual and physical entities. There is clearly
a need for a well-founded and general ontology applicable across historical domains
which rigorously characterises the notion of events and formalises their key role within
temporal information.
The remainder of this paper is organised as follows. First, we will describe the mod-
elling decisions underpinning our model of an Event Ontology and temporal frame-
work. In Section 4, we will illustrate a formal model of an Event Ontology, which
includes vocabulary, domain, syntax and rules. Furthermore, in Section 6 the notion of
semantic links will be introduced and exemplified as a means to construct sequences
of semantically-related information. Finally, we will review related works and outline
application domains in which our model can be employed.
2
2 Modelling Events
Events are situated occurrences incorporating complex and rich information which nor-
mally refers to the 5W: Who (subject of the event), What (object), When (temporal
dimension), Where (spatial dimension) and Why (causes and effects). We have devel-
oped a generic approach, applicable across historical domains, for modelling historical
events and comparing time between them. This was inspired by Davidson’s theory of
events [5], which lays on the idea that each event-forming predicate is enriched with
an extra argument-place to be filled with a variable ranging over event-tokens, which
stands for particular dated occurrences. The main advantage is the ability to associate
multiple properties to events, such as time, location, and other additional information,
thereby avoiding adding extra relations to handle different event dimensions:
(∃e)(born(Galileo Galilei, e) ∧ Time(e, 1564) ∧ Place(e, 1564))
Davidson’s theory of events enabled us to deal with a wide range of historical events,
such as scientific events, e.g. observation, discovery, human and social happening, e.g.
births, deaths, cooperations and conflicts. In many cases, references to event tokens are
hidden within the verbs that are used to describe them and, as in the above example, an
additional event token variable is required to articulate the logical form. However, in the
historical domain there are also cases where an event token is referred to directly by a
naming phrase (what philosophers usually call a definite description). For instance wars
and battles often have a specific name such as the “battle of Hastings”, and historical
periods are also referred to in this way, e.g. “Early Modern”, and “Scientific Revolu-
tion”. In such cases a term of the form named de(”Scientific Revolution”) is used to
refer directly to an event token.
named e(“Scientific Revolution”) ∧
Time-start(named e(“Scientific Revolution”), 1543) ∧
Time-end(named e(“Scientific Revolution”), 1750) ∧
Place(named e(“Scientific Revolution”), Europe)
In the next section, we will discuss the issues of dealing with temporal information in
historical domains and present our modelling decisions in that respect.
3 Modelling Time
Temporal information in events has been embedded employing a calendar structure
consisting of year, month and day in the form of YYYY-MM-DD. Temporal entities
are represented as time grains which correspond to particular years, months, and days
within the Gregorian calendar structure, also known as a Western calendar. In historical
domains, temporal information can be missing due to the fact that historical sources
3
cannot fully reconstruct when exactly a given event occurred, and because of that time
dimensions are only partially provided. Time grains refer to temporal entities that are
considered as atomic, with respect to the temporal granularity with which information
can be specified within the historical knowledge base. They correspond to particular
time periods embedded within a calendar structure. More specifically, they refer to par-
ticular years, months or days within the calendar structure. We have mostly dealt with
years as a minimum requirement and months. Instead, the finer day granularity is un-
usual in our domain. For instance, we are generally aware of the date of birth and death
of a scientific figure, e.g. Isaac Newton died the 20th of March 1727, whereas it is
quite unusual to hold complete information for events such a conducted experiment,
e.g. Galileo Galilei conducted the experiment of falling bodies during 1604. Hence, the
granularity in which the temporal information is expressed can vary, and our model
needed to allow representing both coarse and fine-grained time dimensions. This par-
ticular modelling challenge has been taken into account when defining the semantics
of ordering relations over the domain for comparing temporal information in events
holding different time granularity. For instance, the time point 1564 is potentially coin-
cident with 1564-04 as both occurred within the temporal span of that year. Comparing
time points of different granularity was possible by introducing a weaker form of time
inclusion based on the idea of incidents. Incidents define events that are temporally sub-
ordinated or included within a main event and can be applied between different levels of
granularity. 1610-10 refines 1610 meaning that 1610-10 is incident within 1610. Hence,
the first time grain is temporally within the second. In [1] a theory of time which takes
intervals as primitives is presented, however the interval relations can be specified in
terms of ordering constraints on their end points. We have employed Allen’s vocabu-
lary of interval relations to describe temporal relation between events on the basis of
their start and end points. All 13 relations, including the converses, have been repre-
sented within our model. For instance, the relation meet(e1 , e2 ) holds when the end
point of e1 is equal to or incident within the beginning e2 , as follows:
Meet(e1 , e2 ), Time-end(e1 , t2 ) = Time-end(e2 , t4 ) or refines(e1 , e2 )
In the next section, we will illustrate our Event Ontology Model, which includes vocab-
ulary, domain, syntax and a set of inference rules.
4 An Event Ontology Model: Vocabulary and Domain
An Event Ontology is a logical structure such that:
Ω = hV, D, Φ, 4, begin, end, location, δi
where: V is a vocabulary of symbols; D is a domain representing all entities in the
real world; Φ is the set of all asserted and inferred formulae; 4 is an order relationship
4
over the domain D; begin and end, location are functions over the domain; δ is an
interpretation structure.
The vocabulary V specifies the sets of non-logical symbols:
V = hVc , Vn , Vt , Vh , Vr , Vv i
where Vc is the set of concept symbols; Vn is the set of name symbols; Vt is the set of
time grain symbols; Vh is the set of symbols associated with event tokens (happenings);
Vr is the set of binary relation symbols; Vv is the set of event-verb symbols.
The domain D specifies the objects from the real world and includes three distinct
sub-domains
D = I∪E∪T
where I is the set of all individuals. For instance, these can include particular people,
places, physical objects and so forth; E is the set of all event tokens. These correspond
to particular instances of events, which happen over a particular interval of time. Each
event token has been defined following our adaptation of Davidson’s theory of events.
Event tokens are associated to particular event verbs which bind pairs of individuals
known as subject and object of the relation; T is the set of all time grains. Time grains
are particular years, months or days within the calendar structure and may be expressed
in terms of any of these different levels of granularity. For example, the year 1066 is
considered to be a time grain as is June 1965 and 1st April 2020. T consists of the
union of all individuals from the three types of temporal entity:
T = Y∪M∪D
where Y is the set of all years; M is the set of all event months; D is the set of all days.
We can define ordering relations on each of the sets of Y, M and D using the order
relation 4. For instance, Y is a totally ordered set (Y, 4) such that:
∀y1 , y2 ∈ Y : y1 4 y2 ∨ y2 4 y1
Each time grain in T is a tuple including at least an element from Y. There are three
possible combinations:
hyi or hy − mi or hy − m − di where y ∈ Y, m ∈ M, d ∈ D
We define two temporal functions begin and end to map happenings from E to time
grains from T, as follows:
begin : E → T
end : E → T
where for every event token e ∈ E begin(e) is the time grain when e started and end(e)
is the time grain when e ended; begin(e) always precedes end(e).
Similarly, we define the spatial function location to map happenings from E to individ-
uals from I, as follows:
location : E → I
5
where for every event token e ∈ E location(e) is the place where e occurred.
The interpretation structure
δ = hδc , δn , δt , δh , δr , δv i
interprets the non-logical symbols from the vocabulary by mapping them to the seman-
tics:
– δc : Vc → 2I assigns to each concept symbol a subset of individuals in I;
– δn : Vn → I assigns to each name symbol an individual from I;
– δt : Vt → P assigns to each time grain symbol a time point from P;
– δh : Vh → E assigns to each event token symbol an event token from E;
– δr : Vr → 2I×I assigns to each binary relation a subset of pairs from I;
– δv : Vv → ((I × I) → 2E ) assigns to each event-verb symbol a mapping
from the set of pairs of individuals I × I to a subset of event tokens from E.
Example
We illustrate δc , δr and δh :
δc (astronomer) = {galileo, ptolemy, brahe . . . }
δr (explain) = {h‘galilean theory of tides’, tidei, h‘keplerian moon theory’, tidei . . . }
δv (observe) = {hhgalileo, sunspoti, {Gal Observe Sunp1, Gal Observe Sunp2}i,
hhbrahe, supernovai, {Brahe Observe Sup1, Brahe Observe Sunp2}i, hhbrahe, star spoti, {}i, . . . }
5 An Event Ontology Model: Syntax
Our syntax consists of atomic terms and propositions. The terms include Individuals
Vn = {a, b, c, . . . }; Time points Vt = {t1 , t2 , t3 , . . . }; Concepts Vc = {C1 ,C2 ,C3 , . . . }; and
Event tokens Vh = {e1 , e2 , e3 , . . . }. The propositions are either atomic propositions or
propositional constructs. We have defined four types of declared propositions: Con-
cepts and Individuals Propositions, Binary Relations Propositions, Time Propositions
and Event Propositions.
Concepts and Individuals Propositions. Concepts and Individuals propositions in-
clude atomic propositions which deal with concepts and individuals from the domain.
– C1 v C2 where C1 , C2 ∈ Vc ;
– C1 (a) where C1 ∈ Vc and a ∈ Vn ;
– a = b where a, b ∈ Vn .
Binary Relations Propositions. Binary relations propositions include binary relations
between individuals over the domain.
– R(a, b) where R ∈ Vr and a, b ∈ Vn ;
6
– t(R)(a, b) where t(R) ∈ Vr is a transitive relation where a, b ∈ Vn ;
– inv(R)(a, b) where inv(R) ∈ Vr is an inverse relation where a, b ∈ Vn ;
– sym(R)(a, b) where sym(R) ∈ Vr is a symmetrical relation where a, b ∈ Vn ;
– Binary relations introducing a lattice order between individuals. Lattice binary re-
lations resemble the general binary relations between individuals, although they are
used to cluster individuals that stand in a hierarchy based on their conceptual gen-
erality and specificity. The complete list of lattice relations have been defined, as
follows:
• sub field(a, b) where R ∈ Vr and a, b ∈ Vn ;
• sub phenomenon(a, b) where R ∈ Vr and a, b ∈ Vn ;
• sub theory(a, b) where R ∈ Vr and a, b ∈ Vn ;
• sub law(a, b) where R ∈ Vr and a, b ∈ Vn ;
• sub doctrine(a, b) where R ∈ Vr and a, b ∈ Vn ;
• sub historical period(a, b) where R ∈ Vr and a, b ∈ Vn .
Time Propositions. Time propositions model temporal relations between time grains.
– t1 = t2 and t1 ≈ t2 where t1 , t2 ∈ Vt . They define different types of time grains equal-
ity;
– t1 ≤ t2 and t1 . t2 where t1 , t2 ∈ Vt . They define different types of order relation;
– t1 ≥ t2 and t1 & t2 where t1 , t2 ∈ Vt . They have been defined as the converse of t1
≤ t2 and t1 . t2 ;
– begin(e, t) and end(e, t) where e ∈ Vh and t ∈ Vt . begin and end satisfy the con-
dition that for any e, where begin(e,t1 ) and end(e,t2 ), t1 and t2 are of the same
granularity.
Event Propositions. Event propositions include event verb relations and associated
properties such as location and the equality relation between event tokens. Similar to
begin and end, event properties are defined as functional properties mapping an event
token e to an individual from the class of places, respectively.
– token (e, V(a, b)) where e ∈ Vh , V ∈ Vv and a, b ∈ Vn ;
– location(e, a) where e ∈ Vh and a ∈ Vn . Begin, end and location are generic
functional relations across historical domains.
– e1 = e2 where e1 , e2 ∈ Vh .
Propositional Constructs Propositional constructs hold a newly introduced proposi-
tion name and combine one of more atomic propositions. They include the complete
set of Allen’s thirteen relationships which defines all possible relations that two distinct
time grain can have. Six pairs of the event-token propositions are converses.
7
– precede(e1 , e2 ) and preceded by(e2 , e1 ) where e1 , e2 ∈ Vh ;
– start (e1 , e2 ) and started by(e2 , e1 ) where e1 , e2 ∈ Vh ;
– finish(e1 , e2 ) and finished by(e2 , e1 ) where e1 , e2 ∈ Vh ;
– meet(e1 , e2 ) and met by(e2 , e1 ) where e1 , e2 ∈ Vh ;
– contain(e1 , e2 ) and during(e2 , e1 ) where e1 , e2 ∈ Vh ;
– overlap(e1 , e2 ) and overlapped by(e2 , e1 ) where e1 , e2 ∈ Vh ;
– equal(e1 , e2 ) where e1 , e2 ∈ Vh .
In addition, further propositional constructs can be defined to link elements from the
domain D. For example, we have included the following:
– participate(a,e) where a ∈ Vn and e ∈ Vh ;
– instrument(a,e) where instrument ∈ Vr and a ∈ Vn and e ∈ Vh
The semantic evaluation of each proposition is defined using the interpretation struc-
ture δ and standard set theory. For instance, C1 v C2 , t1 ≈ t2 and participate(a, e) are
evaluated as:
~C1 v C2 = true if δc (C1 ) ⊆ δc (C2 ), otherwise = false
~t1 ≈ t2 = true i f δt (t1 ), δt (t2 ), (t1 = t2 or refined-time(t1 , t2 )), otherwise = false
~participate(a, e) = true i f token(e, V(a, b)) or token(e, V(b, a)), otherwise = false
We use a set of rules in the form of ϕ1 , ϕ2 ⇒ ϕ3 classified in three main modes:
– Concept-based mode includes rules that determine direct and indirect concept-
individual inheritance. For instance: C1 (a), (C1 v C2 ) ⇒ C2 (a)
– Relation-based mode includes rules which define transitive, symmetrical inverse
relationship closures as well as transitivity on lattice relations. For instance:
trans(R)(a, b), trans(R)(b, c) ⇒ R(a, c) where R is a transitive relation (e.g. influ-
ence).
– Event-based mode includes rules which define reasoning upon events. For instance:
precede(e1 , e2 ), contain(e2 , e3 ) ⇒ precede(e1 , e3 )
Rules can be used to derive new knowledge on the basis of established information. In
our framework, we needed to derive implicit information from facts which are explicitly
declared in our historical knowledge base. For example, from the lattice binary relation
sub field(classical physics, mechanics) and sub field(mechanics, physics), we might
be interested to infer that classical physics is a sub field of physics, by applying tran-
sitive closure on the sub field relation.
8
6 Semantic Links
Semantic Links are the formal specifications of association patterns that we use to make
explicit the links between events and entities on the basis of both factual information
and structure of the ontology. Semantic Links follow the form of
semantic link(link type, χ1 , χ2 ) V Ω(χ1 , χ2 )
χ1 , χ2 are variables referring to elements in the Event Ontology Model Ω and link type
denotes specific connections between those variables, e.g. sub-concept relation.
Ω(χ1 , χ2 ) is a constraint linking χ1 and χ2 expressed in terms of a set of formulas of
the Ontology language. Semantic Links can also make reference to common elements
occurring in facts, e.g. the same person participating in two or more events.
The set of pairs of ontology elements related by a semantic link of type link type will
be referred to by δl (link type).
Semantic Links are classified in three main modes:
– Semantic Links associated with Atomic Propositions. These are links that corre-
spond directly to atomic propositions asserted in the ontology. For instance, we
define a link corresponding to the primitive sub-concept relation:
semantic link(subclass, χ1 , χ2 ) V {χ1 v χ2 }
– Semantic Links associated with Inference Rules. These are links that correspond to
relations that can be inferred from the explicit facts in Ω by logical inference rules.
For instance:
semantic link(indirect sub concept, χ1 , χ2 ) V {indirect sub concept(χ1 , χ2 )}
– Semantic Links associated with a condition involving a common element. These
are links that correspond to relations between two elements from Ω depending on
their relation to a third intermediate element of Ω. For instance, two events may be
linked by having a common participant:
semantic link(common participant, χ1 , χ2 ), V {participate(ξ, χ1 ), participate(ξ, χ2 )}
For instance:
δl (common participant) = {hGal Improve Tel, Gal Publish Sidereusi,
hHar Observe Sunsp, Gal Observe Sunspi, . . . }
This indicates that the events of Galileo improving on the invention of the tele-
scope and Galileo publishing Sidereus Nuncius have a common participant, namely
Galileo; and the events of Harriot observing the sunspots and Galileo observing the
sunspots also have a common participant (the phenomenon of sunspots).
Sequences of Semantic Links form our notion of Semantic Trajectories, semantically
significant paths, which are derived from the Event Ontology Model by applying rules
to construct paths constituted from relational links among entities and events. Semantic
Trajectories support exploratory navigation of historical information, as introduced in
[2].
9
7 Related Work
Modelling of events is increasingly gaining widespread attention in the knowledge rep-
resentation community [15, 17]. There are mainly two kinds of event models: those
which facilitate interoperability in distributed event-based systems [12] or enhance ac-
cessibility to museum-related information [6], and those developed for specific appli-
cations [9] or domains [10]. In particular, there is a lack of event-centred approaches,
which provide formal syntax and semantics for modelling domain ontologies [7]. On
the other hand, domain-independent formal models of events [14] [12] are not often ade-
quate when modelling specific domains or families of domains, e.g. historical domains.
Event-centred approaches in historical domains are often associated with enhancing ac-
cess to Cultural Heritage collections [8, 16] and representing the underlying semantics
of bibliographic records [6]. In [13], events are extracted from various textual data and
an event model (SEM) is employed to interlink collection objects along the event di-
mensions. In [11] and [6] event-based models are employed for describing resources
across domains and facilitate semantic interoperability of metadata. Our logical model
is based on the event-token reification method as presented by [5], but also provides a
formal syntax and semantics for representing relationships between entities and events
which integrates our temporal representation. The resulting formal model of an Event
Ontology has the ability to make explicit connections between events and entities.
8 Conclusion and Application Domains
We have illustrated a logical model of an Event Ontology, which includes formal syn-
tax, semantics and reasoning rules for defining a generic approach applicable across
historical domains. Our approach for representing events was inspired by Davidson’s
theory of events [5], an event-token reification method which enables linking properties
(e.g. location, scientific instrument, and temporal information) to historical events. The
logical model of an Event Ontology enables one to make explicit links between events
and entities on the basis of both factual information and structure of the ontology. We
have envisioned that our logical model can be employed in a number of application
domains:
– Support search and browsing activities. The event ontology model would serve as
a resource gateway for retrieving information associated to each semantic link. A
prototypical implementation of the model has been presented in [3].
– Support essay writing. The event ontology model would help students discover key
ideas and elicit their connections to support essay writing.
– Construct narratives for museum collections. The event ontology model would as-
sist exploration in collections by generating historical narratives which describe the
contextual reference space [4] associated to each artefact.
We are currently using our event ontology model to facilitate knowledge discovery for
supporting essay writing in the History of Science domain.
10
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