In this short paper we introduce two main elements of a general methodology, called iTelos, for the management of knowledge diversity. The first is Knowledge Lotuses, a general purpose tool for the representation of knowledge diversity, while the second is a set of metrics which allow to quantify it, as it occurs within and across knowledge resources. Copyright c 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). 1https://lov.linkeddata.es/dataset/lov, http://lov4iot.appspot.com/.
We usually talk of Semantic Heterogeneity meaning the phenomenon which arises when multiple knowledge resources, e.g., ontologies or schemas, for the same domain, present differences in how the intended meaning is represented, most often as a consequence of the fact that they have been developed independently. Managing this phenomenon is crucial in order to enable the Semantic Interoperability of knowledge resources. The key intuition underlying most previous work is to reduce the input representations to a given reference representation, e.g., an ontology, still preserving the intended meaning. This problem has been extensively studied in the literature, leading to a substantial amount of results. As an example, LOV, LOV4IoT,1 three among the most relevant repositories of reference knowledge resources, collectively contain around 800 such resources, some of which contain thousands of elements.
This work has gone a long way with many success stories, in particular in high value, highly formalized, domains, e.g., health, manufacturing. However, a general solution to the semantic interoperability problem, applicable with sustainable costs and time effort, is yet to be found. The difficulties which arise are multifaceted. Some are related to the fact that different resources only consider different partial aspects of a domain, or that they represent it at different levels of abstraction and/or approximation. Furthermore, last but not least, no matter how it is built, any resource will be hardly reusable in novel contexts and it will most often need to be adapted and evolve in time.
These difficulties are deeply rooted into the nature of knowledge. People adapt their
representations of the world as a function of their goals, focus and many other factors [
In this paper, we propose a novel methodology, called iTelos,2 for the management
of the diversity of knowledge [
Within this framework, our goal below is to introduce two new key elements of iTelos, namely Knowledge Lotuses, as a general tool for representing and visualizing knowledge diversity (Section 2) and an initial set of metrics which quantify the level of diversity within and across teleologies (Section 3).
Let us assume that a teleology represents knowledge in terms of (types of ) entities (e.g.,
Person, Place, Event), each being associated with a set of properties (e.g., birth-date,
height, near-to, father-of, has-capital), as it is the case in, e.g., knowledge graphs or
relational models. As from Formal Concept Analysis (FCA) [
We represent the diversity which occurs within and across teleologies with Knowledge Lotuses. Fig 1 provides three knowledge lotuses for (parts of) four state-of-theart knowledge schemas, namely OpenCyc, (the) DBpedia (ontology), Schema.org, and 2From the Greek word telos, meaning “end, purpose”. The “i” stands for “integration”. SUMO.3;4 Knowledge lotuses are Venn Diagrams5 defined as follows. Let us assume that we are interested in analyzing the diversity of certain a set of contexts C, e.g., the four resources mentioned above. Knowledge lotuses model the three core elements of contexts, namely, (i) the set of contexts themselves and, for each context, (ii) its set of entities and, for each entity, (iii) its set of properties. The key intuition is to fix one of these three elements (namely the context(s), or the entity(ies), or the property(ies)) and then, under this assumption, to study the diversity of the second element against the third element. Clearly, several combinations are possible and each of them provides a different perspective on diversity. As an example, let us consider the three cases in Fig 1. (a) Schema.org (b) Organization (c) All properties
Lotus (a) fixes the context (Schema.org) and it represents the diversity of entities in terms of their (un)shared properties. The dual case of comparing properties in terms of the entities in their domain is also possible. These types of lotuses represent the diversity internal to a context, in terms of their entities or their properties. Lotus (b) fixes the entity (Organization) and it represents the diversity of teleologies in terms of their (un)shared properties (for that entity). The dual case of comparing properties in terms of the teleologies where they occur is also possible. These types of lotuses represent the diversity across teleologies, for any given entity. Lotus (c) fixes the properties (all of them) and it represents the diversity of teleologies in terms of the (un)shared entities. The dual case of comparing entities in terms of the teleologies where they occur is also possible. These types of lotuses represent the diversity across teleologies, for any given property.
For instance, looking at Fig1(a), in Schema.org, “Person” and “Organization” share 30 property terms, while they are distinguished by 31 and 23 terms respectively. Looking 3www.cyc.com, wiki.dbpedia.org, www.schema.org, www.adampease.org.
4The data in Fig 1, as well as the quantitative analysis below, have been generated via a simple NLP pipeline which performs the following main steps: a) split a string every time a capital letter is encountered (e.g., birthDate ! birth and date); b) lower case all characters; c) filter out stop-words (e.g., hasAuthor ! author).
5All the lotuses in Fig 1 represent four sets. Simpler/complex lotuses can be depicted to represent the diversity of lower/ higher numbers of resources. at Fig 1(b), the four representations of “Organization” share only one property, while two of them, i.e., OpenCyc and DBpedia share 12 properties.
One observation. Consider Fig 1(c). If one looks at the central part, there are only
four entities which are shared by all resources. These entities are Event, Place, Person
and Organization, namely the entities for time and space, i.e., the two a priori of
perception [
We analyze first the diversity within a resource and then across multiple resources. Our
key insight for analyzing a resource internal diversity is based upon Rosch’s cue validity
[
PoE(p; e) jdom(p)j (p, e) returns 0 if p is not associated with e and 1/n, where n is the number of entities in the domain of p, otherwise. In particular, if p is associated to only one entity its cuep-validity is maximum and equal to one. Given the notion of cuep-validity we define the notion of cue validity of an entity, also called cuee-validity, as the sum of the cue validities of the properties associated with the entity, namely:
jprop(e)j Cuee(e) = å Cuep(pi; e) = c 2 [0; prop(e)] (3)
i=1 where prop(e) is the set of properties which are associated with e. The intuition is the same as Rosch’s: the entities with higher cuee-validity will be the easiest to recognize. In fact, the cuee-validity increases with the number of the properties, while decreasing, for each property, with the number of entities which share that property.
However, the cuee-validity does not tell us anything about how many properties an entity shares with other entities in the same context. To make an example, assume that we have two entities and two properties. Assume the following two situations: (i) both entities share both properties and (ii) the two entities are each associated to one property. In both cases the cuee-validity of the two entities is 1 but, while in the first case they are indistinguishable, in the second case they are highly identifiable. We capture this distinction via the notion of cueer-validity, as:
Cueer(e) =
Cuee(e)
jprop(e)j
The higher the cueer-validity the more distinguishable an entity is, for a given value of the
cuee-validity. Thus, for instance, in the first case in the example above, the cueer-validity
of the both entities will be 0.5 while in the second case it will be one. As an example
let us analyze the internal diversity in SUMO and Schema.org as from Fig 2, where the
x-axis and y-axis are cueer and cuee, respectively. A few observations are in order. The
first is that both resources have a few outlier entities (e.g., “GeopoliticalArea”, “Person”
and “CreativeWork”) with higher values of cuee-validity. Furthermore, there seems to be
a pattern by which, the more the cuee-validity decreases, the more entities there are with
the same cueer-validity, this meaning the fact that there is an area with a cloud of entities
which are not easy to distinguish among one another. Furthermore, the outlier entities are
the only ones which high values of cuee-validity. By looking then into the specifics, it
seems that the outliers are mostly those entities of higher interest (e.g., “CreativeWork”
and “Person” in Schema.org) as, maybe, was to be expected (in anything we do, we all
tend to focus on what is of highest interest). This confirms once more the role of diversity
in capturing not only what is formalized (as well in knowledge lotuses) but also the
quality of the formalization (via metrics). We define the basic diversity measure across
resources via the Jaccard index [
Simc(CA;CB) = jprop(CA) \ prop(CB)j = c 2 [0; 1] jprop(CA) [ prop(CB)j (5) Simc(CA;CB) is a symmetric measure which tells us how much is (not) shared across two resources. If this measure is 1 then the two resources coincide, if it is 0 then they are disjoint. As an example of use, take the two contexts to be a single entity, for instance as formalized in two different resources. Clearly the value of this resource is independent of the actual name of the entity itself. This measure will thus allow, for instance, to realize that the two input entities are the same despite the fact that they have different names and also the vice versa. Fig 3 below shows some examples of similarity of entities from SUMO and Schema.org. In the y-axis we have the value of SimC(CA;CB) with CA being the entity written above the graph as formalized as formalized in either SUMO (SU) or Schema.org (SC), while in the x-axis we have other entities from both resources (each entity being taken as CB), in decreasing order of similarity. For instance, “Apartment” in SC is essentially a synonym of “SingleFamilyResidence” in SC with a similar situation with “MoveAction”. Notice how the two entities in SC, which are synonyms of “MoveAction”, are, by transitivity, also synonyms (where it is not clear whether this was actually what the modeler really wanted to do). The other diagrams report much lower levels of similarity, where for instance “Person” in SC has the highest similarity with “Organization” as in SC or SU, namely the other entity for agenthood.
(a) Apartment (b) MoveAction (c) Person
We see this as just the beginnings of a quantitative study of knowledge diversity. We see potential from a scientific point of view, towards the study of knowledge as an emerging natural phenomenon, but also from an engineering point of view, towards a widespread reuse of existing resources (teleologies). This work is part of a long term effort aimed at providing iTelos, a general methodology for managing knowledge diversity and, in particular, for performing knowledge and data integration in a cost-effective way.