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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>An OWL Ontology for Biographical Knowledge. Representing Time-Dependent Factual Knowledge</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Hans-Ulrich Krieger</string-name>
          <email>krieger@dfki.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Thierry Declerck</string-name>
          <email>declerck@dfki.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>! ?y owl:sameAs ?z @test IntersectionNotEmpty ?s1 ?e1 ?s2 ?e2</institution>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>German Research Center for Artificial Intelligence (DFKI), Universita ̈t des Saarlandes</institution>
          ,
          <addr-line>Allgemeine Linguistik</addr-line>
        </aff>
      </contrib-group>
      <fpage>101</fpage>
      <lpage>110</lpage>
      <abstract>
        <p>Representing time-dependent information has become increasingly important for reasoning and querying services defined on top of RDF and OWL. In particular, addressing this task properly is vital for practical applications such as modern biographical information systems, but also for the Semantic Web/Web 2.0/Social Web in general. Extending binary relation instances with temporal information often translates into a massive proliferation of useless container objects when trying to keep the underlying RDF model. In this paper, we argue for directly extending RDF triples with further arguments in order to easily represent time-dependent factual knowledge and to allow for practical forms of reasoning. We also report on a freely available lightweight OWL ontology for representing biographical knowledge that models entities of interest via a tri-partite structure of the pairwise disjoint classes Abstract, Object, and Happening. Even though the ontology was manually developed utilizing the Prote´ge´ ontology editor, and thus sticking to the triple model of RDF, the meta-modelling facilities allowed us to cross-classify all properties as being either synchronic or diachronic. When viewing the temporal arguments as “extra” arguments that only apply to relation instances, universal biographical knowledge from the ontology can still be described as if there is no time. Linguistics and philosophy make a distinction between synchronic and diachronic relations in order to characterize statements whose truth values do or do not change over time. Synchronic relations, such as dateOfBirth, are relations whose instances stay constant over time, thus there is no direct need to attach a temporal extent to them. Consider, e.g., the natural language sentence: Assuming a RDF-based N-triple representation (Carothers and Seaborne, 2014), an information extraction system might yield the following set of triples: tb rdf:type Person tb hasName ”Tony Blair” tb dateOfBirth ”1953-05-06”^^xsd:date Since there is only one unique date of birth, this works perfectly well and properly capture the intended meaning.</p>
      </abstract>
      <kwd-group>
        <kwd>OWL biography ontology</kwd>
        <kwd>representation of time-dependent information</kwd>
        <kwd>practical temporal reasoning</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>Diachronic relationships, however, vary with time, i.e.,
their truth value do change over time. Representation
frameworks such as OWL that are geared towards unary
and binary relations can not be extended directly by further
(temporal) arguments. Consider the following biographical
information:</p>
      <p>Christopher Gent was Vodafone’s chairman until
July 2003. Later, Chris became the chairman of
GlaxoSmithKline with effect from January 1st, 2005.
From these two sentences, the information extraction
system might discover the following underspecified
timedependent facts:
Applying the synchronic representation schema for
dateOfBirth from above would give us:
However, the association between the original statements
and their temporal extents get lost in the resulting RDF
graph:
as the second and third association are not supported by the
above natural language quotation.</p>
      <p>2</p>
    </sec>
    <sec id="sec-2">
      <title>Approaches for Representing</title>
    </sec>
    <sec id="sec-3">
      <title>Time-Dependent Knowledge</title>
      <p>
        Several well-known proposals have been presented in the
literature in order to equip (binary) relation instances with
time or other kinds of information. The individual
rewriting schemas are depicted in Figure 1; see Welty and Fikes
(2006) and Krieger (2014) for a closer overview:
1. directly equip the relation instance
tional/temporal arguments
        <xref ref-type="bibr" rid="ref13">(Krieger, 2012)</xref>
        ;
with
addi2. apply a meta-logical predicate as used in the situation
      </p>
      <p>
        calculus
        <xref ref-type="bibr" rid="ref18">(McCarthy and Hayes, 1969)</xref>
        ;
3. reify the original relation a` la RDF, turning the
prop
      </p>
      <p>
        erty into a class
        <xref ref-type="bibr" rid="ref17">(Manola and Miller, 2004)</xref>
        ;
4. employ a fact identifier a` la YAGO, implicitly leading
      </p>
      <p>
        to quads
        <xref ref-type="bibr" rid="ref9">(Hoffart et al., 2011)</xref>
        ;
5. wrap the range arguments in an object, called N-ary
      </p>
      <p>
        relation encoding by W3C
        <xref ref-type="bibr" rid="ref33 ref7">(Hayes and Welty, 2006)</xref>
        ;
6. encode a perdurantist/4D view in OWL (Welty and
      </p>
      <p>Fikes, 2006);
approach
1
2
3
4
5
6
7
8
9
rewriting schema</p>
      <p>marriedTo(p; p0; s; e)
marriedTo(p; p0) 7 !
holds(marriedTo(p; p0); t) 7 ! 9f : holds(f; t) ^</p>
      <p>type(f; Fluent) ^ subject(f; p) ^ predicate(f; marriedTo) ^ object(f; p0)
marriedTo(p; p0; s; e) 7 ! 9e : type(e; MarriedToEvent) ^</p>
      <p>person1(e; p) ^ person2(e; p0) ^ starts(e; s) ^ ends(e; e)
marriedTo(p; p0; s; e) 7 ! 9i : i := marriedTo(p; p0) ^ starts(i; s) ^ ends(i; e)
marriedTo(p; p0; s; e) 7 ! 9o : marriedTo(p; o) ^</p>
      <p>type(o; PersonTime) ^ person(o; p0) ^ starts(o; s) ^ ends(o; e)
marriedTo(p; p0; s; e) 7 ! 9t; t0 : marriedTo(t; t0) ^
type(t; TimeSlice) ^ hasTimeSlice(p; t) ^ type(t0; TimeSlice) ^ hasTimeSlice(p0; t0) ^
starts(t; s) ^ ends(t; e) ^ starts(t0; s) ^ ends(t0; e)
marriedTo(p; p0; s; e) 7 ! 9t; t0 : marriedTo(t; t0) ^
type(t; Person) ^ hasTimeSlice(p; t) ^ type(t0; Person) ^ hasTimeSlice(p0; t0) ^
starts(p; s) ^ ends(p; e) ^ starts(p0; s) ^ ends(p0; e)
marriedTo(p; p0; s; e) 7 ! marriedTo s e(p; p0) ^</p>
      <p>marriedTo s e v marriedTo ^ starts(marriedTo s e; s) ^ ends(marriedTo s e; e)
marriedTo(p; p0; s; e) 7 ! marriedTo(p; p0) ^ starts(p0; s) ^ ends(p0; e)
7. interpret the original entities as time slices (Krieger,</p>
      <p>2008);
8. encode the temporal extent through new synthetic</p>
      <p>
        properties
        <xref ref-type="bibr" rid="ref6">(Gangemi, 2011)</xref>
        ;
9. use relation composition applied to the second
argument which does not work in general, but only if
original relation is inverse functional.
      </p>
      <sec id="sec-3-1">
        <title>2.1 Discussion</title>
        <p>
          The above approaches are in a certain sense semantically
equivalent in that we can rewrite one approach to another
one without losing any information. It is worth noting that
all approaches invalidate standard OWL reasoning, even
though they can be implemented within the RDF
framework, and thus at least explicitly stated information can
be queried by, e.g., SPARQL engines. Nevertheless, the
non-temporal entailment rules for RDFS
          <xref ref-type="bibr" rid="ref8">(Hayes, 2004)</xref>
          and
OWL Horst/OWL 2 RL
          <xref ref-type="bibr" rid="ref20 ref31">(ter Horst, 2005; Motik et al., 2012)</xref>
          can be adjusted, so that rule-based reasoners that go beyond
symbol matching, such as Jena
          <xref ref-type="bibr" rid="ref25">(Reynolds, 2006)</xref>
          or HFC
          <xref ref-type="bibr" rid="ref14">(Krieger, 2013)</xref>
          , are still able to perform extended
entailments under these new encoding schemas.
        </p>
        <p>Most of the above approaches require to rewrite the
original ontology, sometimes by turning relations into classes.
With the exception of approach 1, all approaches require
to introduce one or even two brand-new individuals per
time-dependent fact (see Figure 1). As a consequence,
reasoning and querying with such representations is
extremely complex, expensive, and error-prone.
Furthermore, the representation schemas 2–7 bear the potential of
a non-terminating closure computation in case the newly
introduced individuals are viewed as existentially
quantified, i.e., anonymous logic variables (RDF: blank nodes).
Luckily, this last danger can often be avoided by
generating unique URI names that are deterministically generated
from their “parts” (i.e., from information that is accessible
through properties from the new individual)—this “trick”
reminds us of constructing perfect hash functions over
complex objects, as known from computer science.</p>
        <p>
          Approach 1 is pursued in the temporal database
community under the heading valid time
          <xref ref-type="bibr" rid="ref30">(Snodgrass, 2000)</xref>
          . The
measurements in Krieger (2012) and Krieger (2014) have
shown that this approach easily outperforms all other
approaches during querying and reasoning (computation of
the deductive closure) in the time domain by several orders
of magnitude. In some cases, this divergency can make
a difference between doable and intractable applications.
Consequently, we think the time now is ripe for allowing
nary relations, or as Schmolze (1989) once put it in the early
days of KL-ONE “... the advantages for allowing direct
representation of n-ary relations far outweigh the reasons
for the restriction.”
2.2
        </p>
      </sec>
      <sec id="sec-3-2">
        <title>Tuples vs. Triples: Representation &amp; Reasoning</title>
        <p>We would like to make our preference towards a direct
representation of additional (temporal) arguments more clear
by looking at concrete examples. Consider the Wikipedia
entry for Tony Blair which says he married Cherie Booth
on 29th March 1980 (today = 2015-05-08), leading to the
quintuple representation:
tony blair marriedTo cherie booth</p>
        <p>”1980-03-29”^^xsd:date ”2015-05-08”^^xsd:date
A meaning-preserving triple representation which adheres
to a W3C best practice recommendation, called N-ary
relation encoding (see rewrite schema 5 in Figure 1) would
instead result in five triples, a new individual :ppt, a new
type ValuePlusTime, and the three “accessor” properties
hasValue, starts, and ends:
tony blair marriedTo :ppt
:ppt rdf:type nary:ValuePlusTime
:ppt nary:hasValue cherie booth
:ppt nary:starts ”1980-03-29”^^xsd:date
:ppt nary:ends ”2015-05-08”^^xsd:date
Such a representation has a three times larger memory
footprint, a slightly more complex structure, and is a bit harder
to read. However, as indicated above, the new individual
(in our example blank node :ppt) might turn out to be
problematic during entailment reasoning (no longer guaranteed
to terminate).</p>
        <p>
          Now let us focus not only on the representation of (static)
knowledge, but on the (dynamic) derivation of new
knowledge through entailment rules in order to see how much
worse a (recommended) triple representation becomes.
Consider the following entailment schema for functional
diachronic datatype properties (in Section 3.3, we will look
at the corresponding entailment schema for functional
diachronic object properties). The original non-temporal
schema looks like this (we use the rule syntax of HFC
          <xref ref-type="bibr" rid="ref14">(Krieger, 2013)</xref>
          in the examples below):
?p rdf:type owl:FunctionalProperty
?p rdf:type owl:DatatypeProperty
?x ?p ?y
?x ?p ?z
Such a rule schema is useful, e.g., for detecting
contradictory birth dates for one and the same person (famous
example: Louis Armstrong; right: August 4, 1901, wrongly
claimed by him: July 4, 1900). Such a schema matches, for
instance,
louis armstrong dateOfBirth ”1901-08-04”^^xsd:date
louis armstrong dateOfBirth ”1900-07-04”^^xsd:date
and binds louis armstrong to ?x, dateOfBirth to ?p,
”190108-04”^^xsd:date to ?y, and ”1900-07-04”^^xsd:date to ?z.
Having found problematic cases is signaled by assigning
the “bottom” type owl:Nothing to the subject element of the
triple bound to the logical variable ?x (= Louis Armstrong)
on the right hand side of the rule.
        </p>
        <p>Adding time to this rule schema makes it applicable to
other functional relations such as hasSalary which do
change over time, as indicated by the property
characteristics time:DiachronicProperty in the rule below. Extending
the rule schema is quite easy by equipping the fourth and
fifth left hand side clauses with a temporal extent (things
that have been added are underlined):
?p rdf:type owl:FunctionalProperty
?p rdf:type time:DiachronicProperty
?p rdf:type owl:DatatypeProperty
?x ?p ?y ?s1 ?e1
?x ?p ?z ?s2 ?e2
!
?x rdf:type owl:Nothing ?s ?e
@test
?y != ?z
IntersectionNotEmpty ?s1 ?e1 ?s2 ?e2
The additional left hand side four-place relation
IntersectionNotEmpty from the @test section of the rule simply
checks whether the two temporal intervals [s1; e1] and
[s2; e2] have a non-empty intersection, indicated by xxx
below:</p>
        <p>p(x;y)
jxxx————j
p(x;z)
j——xxxj
———s1—s2–e1———e2————. t
If this is the case, we mark the subject bound to ?x being
of type owl:Nothing (same as for the original rule), but this
type assignment now only holds for the overlapping
observation time, given by the maximum of the starting times (=
?s) and the minimum of the ending times (= ?e), as
computed in the @action section of the rule.</p>
        <p>The above natural extension of the non-temporal rule,
however, turns into an awfully looking and terribly inefficient
rule when being couched in a triple-based setting:
?p rdf:type owl:FunctionalProperty
?p rdf:type time:DiachronicProperty
?p rdf:type owl:DatatypeProperty
?x ?p ?blank1
?blank1 rdf:type nary:ValuePlusTime
?blank1 nary:hasValue ?y
?blank1 nary:starts ?start1
?blank1 nary:ends ?end1
?x ?p ?blank2
?blank2 rdf:type nary:ValuePlusTime
?blank2 nary:hasValue ?z
?blank2 nary:starts ?start2
?blank2 nary:ends ?end2
!
?x rdf:type ?new
?new rdf:type nary:ValuePlusTime
?new nary:hasValue owl:Nothing
?new nary:starts ?start
?new nary:ends ?end
@test
?y != ?z
IntersectionNotEmpty ?start1 ?end1 ?start2 ?end2
@action
?start = Max2 ?start1 ?start2
?end = Min2 ?end1 ?end2
?new = MakeUri owl:Nothing ?start ?end
Note how the relevant input information is hidden in the
two container individuals bound to ?blank1 and ?blank2
and how the output is wrapped in a brand-new individual
?new, generated by MakeUri from the @action section.</p>
      </sec>
      <sec id="sec-3-3">
        <title>2.3 Limitations</title>
        <p>Several points are worth mentioning here. Firstly, we are
not dealing here with duration time in order to resolve
expressions like Monday or 20 days against valid time. This
needs to be handled by a richer temporal ontology and
temporal arithmetic.</p>
        <p>Secondly, temporal quantification, such as four hours every
week, needs to be addressed by a richer temporal inventory.
Thirdly, even though underspecified time is handled by our
implementation through wildcards in the XSD dateTime
format (e.g., year missing in Over New Year’s Eve, I have
visited the Eiffel Tower), we do not focus on this here.
The solution requires to make certain rule tests sensitive to
the fact that underspecified time is only partially ordered.
These tests then return true, false, or don’t-know, whereas
only true indicates that the test has succeeded, leading to
the instantiation of the right hand side of the rule.
Fourthly, coalescing temporal information (i.e., building
larger intervals from intervals with overlapping parts)
should be addressed in custom rules and should not be
regarded as part of the extended RDFS/OWL rule set, since
this functionality depends on the (semantic) nature of
predicates and the assumption whether temporal intervals are
convex (i.e., contain no “holes”) or not.</p>
        <p>And finally, certain temporal inferences such as p(~x; s; t)
entails p(~x; s0; t0) in case s s0 t0 t should not be
handled in the below rules, since termination of the
computation of the deductive closure is no longer guaranteed.
Such information can only be obtained on the query level.
3</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>Ontology for Biographical Knowledge</title>
      <p>
        We already indicated that we favor approach 1 as it is the
most perspicuous of the nine approaches presented above,
shows the best memory and runtime footprint, and always
guarantees a terminating closure computation for extended
RDFS
        <xref ref-type="bibr" rid="ref8">(Hayes, 2004)</xref>
        and OWL
        <xref ref-type="bibr" rid="ref31">(ter Horst, 2005)</xref>
        entailment, as shown in Krieger (2012).
      </p>
      <p>
        In the introduction, we argued that axiomatic knowledge
about classes (TBox) and properties (RBox) does not need
to have a notion of time—this is universal knowledge which
we assume to be static. For instance, we do not assume that
the subtype relationship between two classes only holds for
some period of time or that an URI should be regarded as a
property at time t and as a class at a different time t0 (even
though this would be possible). The assertional knowledge
of an ontology (ABox), i.e., the set of relation instances,
however, is what we equip with time (see the various
approaches for the marriedTo example in Figure 1), as this is
knowledge that has undergone a temporal change.
In this section, we present the schema (the TBox and
the RBox) of an ontology that we had developed
originally for the TAKE project (http://take.dfki.de) and that was
used in the KOMPARSE project (http://komparse.dfki.de)
to represent biographical information about celebrities
        <xref ref-type="bibr" rid="ref1">(Adolphs et al., 2010)</xref>
        . This ontology has been
reused and extended in the EU projects MONNET
(http://cordis.europa.eu/fp7/ict/language-technologies) and
TRENDMINER (http://www.trendminer-project.eu). This
biography ontology is now part of a larger set of
independently developed ontologies (called TMO, for
TRENDMINER ONTOLOGIES) which are interlinked to one
another through the use of interface axioms
        <xref ref-type="bibr" rid="ref10 ref15 ref2">(Krieger and
Declerck, 2014)</xref>
        . These interface axioms either relates
classes (TBox) and properties (RBox) from different
subontologies through the use of description logic axiom
constructors, e.g.,
bio:Person
      </p>
      <p>pol:Person
or constrain the domain and range of potentially
underspecified properties, e.g.,</p>
      <p>&gt; v 8op:hasHolder . bio:Agent
The property hasHolder from the opinion ontology (prefix
op) is a good example of a property for which only the
domain has been specified, viz., op:Opinion:</p>
      <p>&gt; v 8op:hasHolder . op:Opinion
However, hasHolder consciously lacks its range, since this
information should only be added when several ontologies
are brought together.</p>
      <p>The above axioms together with the two terminological
axioms from the biography (prefix bio) and the politics (prefix
pol) ontologies
bio:Person v bio:Agent
pol:Journalist v pol:Person
guarantee to draw legal inferences, such as journalists are
holders of opinions, even though the interface axiom above
constrain holders of opinions to be of type bio:Agent.
TMO has been assembled from 16 sub-ontologies, some of
them also dealing with the representation of biographical
knowledge, others describing concepts that can be found in
politics and sociology. Especially the opinion ontology can
be used to model provenance information, important for
biographical knowledge; for instance, information about the:
holder of the opinion: hasHolder;
source from which the info was taken: extractedFrom;
time when the opinion was published: utteredAt;
trustworthiness of the holder: holdersTrust;
polarity of the opinion: hasPolarity.</p>
      <p>The TMO ontology suite is freely available for
academic research and to other sites upon request (see
http://www.dfki.de/lt/onto/). Parts of the taxonomic structure
of the biography ontology is depicted in Figure 2.</p>
      <sec id="sec-4-1">
        <title>3.1 Overall Guidelines</title>
        <p>TMO, and thus the biography ontology, implements several
“guidelines” that we have found useful in many projects
which have dealt with the representation of time-dependent
knowledge (some of the arguments have already been
presented):
1. model the TBox and RBox axioms of an ontology as if
there is no time, since the ontology schema is regarded
to be immutable; consequence: standard ontology
editors, such as Prote´ge´ can be used for this task.
2. cross-classify all properties as being either synchronic
or diachronic; advantage: these property
characteristics can be used, amongst other things, as
distinguishing marks in entailment rules (see examples).
3. populate the ABox of an ontology with extended
relation instances, i.e., with quintuples whose fourth and
fifth argument encode the temporal extent of the
preceding atemporal statement (the triple).
4. extend the RDFS/OWL entailment rules by a
temporal dimension; example: use XSD’s date or dateTime
format to implement an interval-based calendar time
(used by the examples in this paper).
The biography ontology assumes a tri-partite structure,
defining a most general class Entity, having pairwise
disjoint subclasses Abstract, Happening, and Object. TMO is
a lightweight ontology that consists of 146 classes and 80
properties, and is of expressivity S HIN (D), according to
the Ontology metrics pane of Prote´ge´ , version 4.3.0. A
partial view of the three subclasses and properties linking them
is given in Figure 3.</p>
        <sec id="sec-4-1-1">
          <title>3.2.1 Abstract</title>
          <p>Ontological categories that do not fit into Happening or
Object are regarded to be of type Abstract, thus this class is a
kind of “remainder” category. Abstract things can be used
to describe literal concepts, e.g., activities, academic
degrees, ideas, inventions, the life, or personal, professional,
and social roles. An abstraction manifestsIn real-world
happenings, whereas the outcome of a happening leadsTo
virtually everything (= Entity). For example: a specific
military activity (the invasion of Poland) manifested in World
War II. The outcome of WW-II has led to military
inventions (Abstract), has led to the Cold War (Happening), and
has led to the building of 86 U2 aircrafts (Object).</p>
        </sec>
        <sec id="sec-4-1-2">
          <title>3.2.2 Happening</title>
          <p>Happenings are things that “happen” or “unfold” and are
disjointly categorized as being either static atomic
Situations or dynamic decomposable Events. They come with a
(possibly underspecified) startDate and endDate. A
happening is basedOn or leadsTo entities (i.e., either abstract
things, further happenings, or concrete objects), thus these
properties can be used to encode pre- and post-conditions of
a happening. An instance of this class also involves Agents
and happensAt a Location. Situations help to “terminate”
the decomposition of a Happening. The other subclass
Event can be used to model simple unordered processes,
as it comes with three relational properties of its own, viz.,
startsWith, continuesWith, and endsWith, all mapping to
Happening (see Figure 2).
3.2.3 Object
Objects are “physical” things and mostly deal with Agents
(an exhaustive disjoint partition between Person, Group,
and political State) and other categories that we think are
relevant for biographical information, e.g., Location,
material Property, or WorkAndProduct. A Person isAwareOf
a Happening: (s)he “owns” it, can be part of it, or learns
about a happening. As isAwareOf is a diachronic property,
awareness of a happening might even turn into oblivion.</p>
        </sec>
      </sec>
      <sec id="sec-4-2">
        <title>3.3 Practical Temporal Reasoning</title>
        <p>For a larger non-trivial example, let us again turn our
attention to the marriage of Tony Blair and Cherie Booth.
marriedTo is at the same time a symmetric, a diachronic,
a functional, and an object property (see the Types pane at
the bottom of Figure 4).</p>
        <p>We mentioned that we have cross-classified every property
from the biography ontology as being either synchronic
or diachronic and have already discussed the temporal
extension of the entailment rule for functional diachronic
datatype properties in Section 2.2. Let us now focus on the
complementary rule for functional diachronic object
properties which is applicable to the marriedTo relation:
?p rdf:type owl:FunctionalProperty
?p rdf:type time:DiachronicProperty
?p rdf:type owl:ObjectProperty
?x ?p ?y ?s1 ?e1
?x ?p ?z ?s2 ?e2
Here, as in the former example, the additional left hand side
test IntersectionNotEmpty checks whether the two
temporal intervals [s1; e1] and [s2; e2] have a non-empty
intersection. Assuming that a person is not married to more than
one partner at the same time, such a rule is able to
identify individuals/URIs bound to ?y and ?z for two properly
overlapping observations through the use of owl:sameAs.
Consider again the Wikipedia entry for the marriage of
Tony Blair and Cherie Booth that we used in the example
from Section 2.2:
tony blair marriedTo cherie booth</p>
        <p>”1980-03-29”^^xsd:date ”2015-05-08”^^xsd:date
and furthermore assume that the Economist article The
loneliness of Tony Blair from December 2014 mentioned
that Cherie Blair is Blair’s wife (quintuple again):
tony blair marriedTo cherie blair</p>
        <p>”2014-12-20”^^xsd:date ”2014-12-20”^^xsd:date
Now it is safe to assume that Cherie Booth and Cherie Blair
are in fact the same person, according to the successful
application of the above temporal entailment rule:
cherie booth owl:sameAs cherie blair
It is worth noting that sameAs statements will not be
equipped with a temporal extent—commonsense dictates
that once we do identify individuals, they will never fall
apart.</p>
        <p>
          At every moment in time, we never know how long a
person is married to his/her partner in advance. That is
why we introduced another property divorcedFrom,
being the temporal disjoint object property to marriedTo (see
the owl:disjointObjectProperty pane in Figure 4). As the
Economist article does not specify the date of marriage, we
better opt for a moment in time, when Blair and Booth were
definitely married (actually a day: start = end). Luckily,
the right hand side sameAs inference from above, together
with another extended OWL entailment rule, called rdfp11
          <xref ref-type="bibr" rid="ref31">(ter Horst, 2005)</xref>
          , makes sure that even
tony blair marriedTo cherie blair
        </p>
        <p>”1980-03-29”^^xsd:date ”2015-05-08”^^xsd:date
is a valid entailment, exactly what we expect.
3.4</p>
      </sec>
      <sec id="sec-4-3">
        <title>Temporal Arguments as Extra Arguments</title>
        <p>So far, our approach has argued for a direct encoding of the
temporal extent through two further arguments, turning a
binary relation, such as marriedTo Person Person into a
quaternary one: marriedTo Person Person date date.
Given the original relation signature, the non-temporal
entailment rule schema for symmetric binary relations from
ter Horst (2005) thus leads to the following instantiation:
marriedTo(p; p0) ! marriedTo(p0; p)
as symmetric relations swap their domain and range
arguments (p; p0 being two people).</p>
        <p>Now, if we add time (b = begin; e = end), we obtain:1
marriedTo(i; j; b; e) ! marriedTo(j; b; e; i)
Clearly, something has gone wrong here because
symmetric relations assume the same number of arguments in
domain and range position. One solution would be to
reduplicate the starting and ending points, so we would end up
in sexternary relation:</p>
        <p>marriedTo(i; b; e; j; b; e) ! marriedTo(j; b; e; i; b; e)
This is not an appealing solution as the structures become
larger, and rules and queries are harder to formulate, read,
debug, and process. What we would like to see is
something like:</p>
        <p>marriedTo(i; j; b; e) ! marriedTo(j; i; b; e)
whereas the second semicolon should indicate that the
additional temporal arguments are extra arguments, belonging
to the relation instance as such (a kind of relation instance
annotation, not possible in OWL). Thus with this idea in
mind, we can still keep the idea of having only binary
relations, without introducing any new identifier (contrary to
the rewrite schemas 2–7 from Figure 1).</p>
        <p>Nevertheless, we are not arguing against arbitrary n-ary
relations as we are convinced that many binary relations in
today’s ontologies are ignoring additional arguments (e.g.,
properties oriented towards ditransitive verbs or having
additional modifiers/adjuncts) or come along with
unsatisfactory means to encode the additional arguments (relation
composition, by taking the object of a binary relation
instance into account). The current biography ontology, for
instance, poorly models the property obtains as a relation
1For better readability, we separate the domain and range
arguments from one another by using a semicolon.
between people and (academic) degrees. In order to
obtain the educational organization where the degree was
obtained, we employ relation composition at the moment,
using an additional property obtainedAt between degree and
education:</p>
        <p>obtainedAt obtains Person EducationalOrganization
This way of representing the additional argument is related
to approach 9 from Figure 1 and only works because
obtains is inverse functional (a characteristics applicable to
properties in OWL). Ideally, obtains should be modeled as
a quinternary relation, having one domain argument, two
range arguments, and two extra temporal arguments:
obtains Person</p>
        <p>Degree EducationalOrganization
xsd:dateTime xsd:dateTime
// domain
// range
// extra
In order to easily define such non-binary relations, ontology
editors need to be extended by Cartesian types. In Krieger
and Willms (2015), we described -Prote´ge´ , an extension
of the Prote´ge´ ontology editor that provides means to define
such Cartesian types and to use them to type the domain,
range, and extra arguments of non-binary relations. A first
public version of -Prote´ge´ will be available in mid 2015.
4</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>Relation vs. Event Representation</title>
      <p>The approaches considered in Section 2 were investigated
on how well they perform w.r.t. binary relations whose two
arguments are considered to be obligatory. Such a kind of
relation is the default case in today’s popular knowledge
resources, such as YAGO, DBpedia, BabelNet, or Google’s
Knowledge Graph.</p>
      <p>
        In case more (e.g., time) and especially optional arguments
are investigated, our verdict concerning the different
approaches might turn into a different direction, so the
representation format needs to be updated (in the best case) or
changed (in the worst case). Consider the following
example, taken from
        <xref ref-type="bibr" rid="ref3">(Davidson, 1967, p. 83)</xref>
        :
      </p>
      <p>Jones buttered the toast in the bathroom with a knife
at midnight.</p>
      <p>The binary base relation butter (we assume a direct
mapping of the transitive verb to the relation name here) now
needs to be split and/or extended by further optional
arguments, as the following sentences are perfectly legal:
Jones buttered the toast.</p>
      <p>Jones buttered the toast in the bathroom.</p>
      <p>Jones buttered the toast with a knife.</p>
      <p>Jones buttered the toast at midnight.</p>
      <p>Jones buttered the toast in the bathroom with a knife.
Jones buttered the toast in the bathroom at midnight.
..... etc.</p>
      <p>In principle, the number of adjuncts is not bounded, thus
adding a large number of potentially underspecified direct
relation arguments is probably a bad solution. Today’s
technologies often address such hidden arguments through a
kind of relation composition as we have seen above for the
obtains example from the last section and listed as approach
9 in Figure 1. We think that this modeling “trick” is
unsatisfactory as it operates on the object of the binary relation
instance, but not on the relation instance itself (besides
being only correct if the original relation is inverse functional,
as explained before).</p>
      <p>Our personal solution would model the obligatory
arguments, including (under- or unspecified) time and perhaps
space, as direct arguments of the corresponding relation
instance or tuple (approach 1). A further argument, an event
identifier, also takes part in the relation. Optional
arguments, however, would be addressed through binary
relations, now working on the event argument. Applying this
kind of Davidsonian or event representation to the above
example gives us (informal relational notation):
9e : butter(e; Jones; toast; at midnight) ^</p>
      <p>
        location(e; bathroom) ^ instrument(e; knife)
It is worth noting that two of the approaches from Figure 1
are related to such an event representation, viz., 3 and 4.
Approach 3 (internal reification) can be seen as a kind
of “owlfication” of Neo-Davidsonian semantics
        <xref ref-type="bibr" rid="ref23">(Parsons,
1990)</xref>
        , as the original relation is always turned into an event
(an OWL class). Here the event identifier e from above
directly corresponds to a URI, referring to an instance of the
OWL class. For instance, the marriedTo relation is turned
into an event class, say Marry; thus:
tony blair marriedTo cherie booth
      </p>
      <p>”1980-03-29”^^xsd:date ”2015-05-08”^^xsd:date
needs to be expressed by (we use VerbNet terminology):
e rdf:type Marry
e agent tony blair
e co-agent cherie booth
e starts ”1980-03-29”^^xsd:date
e ends ”2015-05-08”^^xsd:date
Approach 4 (fact identifier) is a kind of external reification.
YAGO uses its own extension of the N3 plain triple
format, called N4, which associate unique identifiers i with
each time-dependent fact. However, the association i :=
marriedTo(p; p0) has the disadvantage of not being part of
the triple repository, as it is a quadruple technically. So we
guess that there exists a separate extendable mapping table
outside of the semantic repository, storing the triples.
Luckily, the biography ontology presented in Section 3 both
allows for extended relation instances (as shown before),
but also Davidsonian-like events through the class
Happening and its subclasses Event and Situation (see Figure 2). As
there does not exist a Marry event class so far (but only the
marriedTo property), such a class needs to be introduced as
a subclass of class Event, if needed.</p>
      <p>5</p>
    </sec>
    <sec id="sec-6">
      <title>Related Ontologies</title>
      <p>
        Several ontologies addressing the representation of
biographical information, cultural heritage information, and
news-related information exist today, all building on
Description Logics and Semantic Web technology
standards. These include ESO
        <xref ref-type="bibr" rid="ref28">(Segers et al., 2015)</xref>
        , Wikidata
        <xref ref-type="bibr" rid="ref4">(Erxleben et al., 2014)</xref>
        , the BiographyNet ontology
        <xref ref-type="bibr" rid="ref22">(Ockeloen et al., 2013)</xref>
        , the BBC Storyline Ontology
        <xref ref-type="bibr" rid="ref34">(Wilton
et al., 2013)</xref>
        , SEM
        <xref ref-type="bibr" rid="ref32">(van Hage et al., 2011)</xref>
        , FRBR OO
        <xref ref-type="bibr" rid="ref16">(Le
Boeuf, 2010)</xref>
        , LODE
        <xref ref-type="bibr" rid="ref29">(Shaw et al., 2009)</xref>
        , or Event-Model-F
        <xref ref-type="bibr" rid="ref26">(Scherp et al., 2009)</xref>
        . Some of these ontologies make use of
other resources, such as WordNet , FrameNet, Wikipedia,
SUMO , DOLCE , or CIDOC CRM . In order to represent
time-dependent knowledge, these approaches always need
to stick to an event-like representation in which all
information is hidden in an object and time is accessible through
properties, similar to approach 3 in Figure 1. None of them
are able to encode time as direct arguments of a relation
instance (approach 1). A comparison of some of these event
ontologies is presented in
        <xref ref-type="bibr" rid="ref29">(Shaw et al., 2009, section 2)</xref>
        and
        <xref ref-type="bibr" rid="ref32">(van Hage et al., 2011, section 5)</xref>
        .
      </p>
      <p>
        As we have indicated in the beginning of Section 3
(Journalist example), OWL axiom constructors and
domain/range restrictions allow us to manually interface
our biography ontology with other ontologies, may they
be complimentary domain ontologies (opinion, politics,
sociology), overlapping biography event ontologies (see
above), or even OWL versions of upper ontologies (if
desired), such as DOLCE+DnS
        <xref ref-type="bibr" rid="ref5">(Gangemi et al., 2002)</xref>
        ,
SUMO
        <xref ref-type="bibr" rid="ref21">(Niles and Pease, 2001)</xref>
        , or Cyc
        <xref ref-type="bibr" rid="ref24">(Reed and Lenat,
2002)</xref>
        . For instance, if we would like to interface the BBC
storyline ontology, the following single axiom suffices:
bio:Happening
      </p>
      <p>nsl:Event
Connecting with LODE essentially reduces to:
bio:Happening lode:Event
bio:happensAt lode:atPlace
bio:involves lode:involvedAgent
bio:basedOn v lode:involved
bio:leadsTo v lode:involved
Other properties from LODE either do not have a
direct counterpart (lode:illustrate) or need to be
decomposed (lode:atTime onto bio:startDate and bio:endDate).
The sub-properties bio:startsWith, bio:continuesWith, and
bio:endsWith from the class bio:Event would even allow us
to decompose LODE events into smaller units, a feature
partially available in the SEM ontology:
bio:startsWith v sem:hasSubEvent
bio:continuesWith v sem:hasSubEvent
bio:endsWith v sem:hasSubEvent
As our ontology comes with the class bio:Happening, it is
possible to take advantage of the great effort invested in
the definition of event types in the ESO ontology. We
finally note that some of the mappings are not expressible
through simple OWL axiom constructors, because they
involve a translation from n-ary relation instances to sets of
triples (and vice versa). This would require to apply HFC
migration rules, similar to the rewrite rule of approach 3 in
Figure 1 which mediates between the quaternary marriedTo
relation and its event representation MarriedToEvent.
6</p>
    </sec>
    <sec id="sec-7">
      <title>Summary and Conclusion</title>
      <p>In this paper, we have presented an overview of nine
approaches to the representation of time-dependent
knowledge and have favored the direct encoding of the
temporal information as extra arguments of the original relation
instance. Nevertheless, allowing at the same time for an
event-based representation of situations, happening in the
real world, is profitable as a knowledge engineer might
choose the representation which fits her/his needs. For
instance, a marriage ceremony between two people is
probably modeled best as an event, whereas the fact that these
two people are married for a specific time period is
better represented as a quaternary relation. The lightweight
biography ontology, presented in this paper, allows both
views through the very general class Happening and
relations defined between classes which are extended by a
starting and ending time, expressing the temporal extent in
which the atemporal fact is true (called valid time in
temporal databases).</p>
      <p>
        Our debate on the right representation format can even be
viewed as the more general quest on how to integrate/add
important (meta) information that has been neglected in the
past for practical matters, but has gained a lot of
attention recently; see the W3C recommendation for the
provenance data model PROV-DM
        <xref ref-type="bibr" rid="ref19 ref34">(Moreau and Missier, 2013)</xref>
        .
This additional information might include the holder of a
time-dependent statement or event (person, website,
program/service), the spacial location of the holder, the time
when the statement/event was communicated by the holder
or made public on the Web (related to transaction time in
temporal databases), the trustworthiness of the holder, and
the attitude of the holder w.r.t. the statement/event
(sentiment/opinion). Ontologies for all these different aspects
already exist today (for instance, the BiographNet ontology
        <xref ref-type="bibr" rid="ref22">(Ockeloen et al., 2013)</xref>
        which incorporates a multi-level,
multi-perspective model for provenance), but a unified
standard is still missing. As a short-/mid-term workaround, we
suggest to manually interface these different sources of
information, as indicated in Section 5, thus making it possible
to incorporate work carried out by other researchers.
      </p>
    </sec>
    <sec id="sec-8">
      <title>Acknowledgements</title>
      <p>The work described in this paper has been partially
carried out in the ALL SIDES project, funded by the German
Federal Ministry of Education and Research under contract
number FKZ 01IW14002 and the PHEME project, funded
by the European Union’s 7th Framework Programme
under grant agreement no 611233. The authors would like to
thank our three reviewers and Antske Fokkens for their
useful comments, Hans Uszkoreit for giving the initial
impetus for the development of the biography ontology several
years ago, and Bernd Kiefer for always having an open ear
in many discussions.</p>
      <p>7</p>
    </sec>
  </body>
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