; 3. reify the original relation à la RDF, turning the property into a class (Manola and Miller, 2004);
4. employ a fact identifier à la YAGO, implicitly leading to quads (Hoffart et al., 2011); 5. wrap the range arguments in an object, called N-ary relation encoding by W3C (Hayes and Welty, 2006); 6. encode a perdurantist/4D view in OWL (Welty and Fikes, 2006); Figure 1: Different ways of representing the atemporal statement (the "fluent") marriedTo(p, p ) between two people p and p , being true for the time period t = [s, e]. " −→" should be read as rewrite to. The last representation schema only works if the original property (here: marriedTo) is inverse functional for all relation instances (which needs not to be the case).
7. interpret the original entities as time slices (Krieger, 2008); 8. encode the temporal extent through new synthetic properties (Gangemi, 2011); 9. use relation composition applied to the second argument which does not work in general, but only if original relation is inverse functional.
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 (Hayes, 2004) and OWL Horst/OWL 2 RL (ter Horst, 2005;Motik et al., 2012) can be adjusted, so that rule-based reasoners that go beyond symbol matching, such as Jena (Reynolds, 2006) or HFC (Krieger, 2013), are still able to perform extended entailments under these new encoding schemas. 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.
Approach 1 is pursued in the temporal database community under the heading valid time (Snodgrass, 2000). 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."
We would like to make our preference towards a direct rep- The additional left hand side four-place relation Intersec-tionNotEmpty from the @test section of the rule simply checks whether the two temporal intervals [s 1 , e 1 ] and [s 2 , e 2 ] have a non-empty intersection, indicated by xxx below:
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. 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.
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.
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. And finally, certain temporal inferences such as p( x, s, t) entails p( x, s , t ) in case s ≤ s ≤ t ≤ 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.
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 (Hayes, 2004) and OWL (ter Horst, 2005) entailment, as shown in Krieger (2012). 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 t (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 (Adolphs et al., 2010).
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 TREND-MINER ONTOLOGIES) which are interlinked to one another through the use of interface axioms (Krieger and Declerck, 2014). These interface axioms either relates classes (TBox) and properties (RBox) from different subontologies through the use of description logic axiom constructors, e.g., 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: ∀op:hasHolder − . op:Opinion However, hasHolder consciously lacks its range, since this information should only be added when several ontologies are brought together. The above axioms together with the two terminological axioms from the biography (prefix bio) and the politics (prefix pol) ontologies bio:Person bio:Agent pol:Journalist 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.
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.
3.1 Overall Guidelines 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 Protégé can be used for this task.
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 SHIN (D), according to the Ontology metrics pane of Protégé, version 4.3.0. A partial view of the three subclasses and properties linking them is given in Figure 3.
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).
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 hap-pening 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).
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.
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).
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 → ?y owl:sameAs ?z @test IntersectionNotEmpty ?s1 ?e1 ?s2 ?e2
Here, as in the former example, the additional left hand side test IntersectionNotEmpty checks whether the two temporal intervals [s 1 , e 1 ] and [s 2 , e 2 ] 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: "2014-12-20"ˆˆxsd:date "2014-12-20"ˆˆxsd: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.
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 (ter Horst, 2005), makes sure that even 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: 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).
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 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:
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:
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.
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 (Davidson, 1967, p. 83):
Jones buttered the toast in the bathroom with a knife at midnight.
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. Jones buttered the toast in the bathroom. Jones buttered the toast with a knife. Jones buttered the toast at midnight. Jones buttered the toast in the bathroom with a knife. Jones buttered the toast in the bathroom at midnight. ..... etc.
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).
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):
∃e . butter(e, Jones, toast, at midnight) ∧ 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 (Parsons, 1990) 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.
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 (Segers et al., 2015), Wikidata (Erxleben et al., 2014), the BiographyNet ontology (Ockeloen et al., 2013), the BBC Storyline Ontology (Wilton et al., 2013), SEM (van Hage et al., 2011), FRBR OO (Le Boeuf, 2010), LODE (Shaw et al., 2009), or Event-Model-F (Scherp et al., 2009). 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 (Shaw et al., 2009 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.
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).
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 (Moreau and Missier, 2013). 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 (Ockeloen et al., 2013) 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.
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.