Semantics for interoperability of distributed data and models: Foundations for better-connected information

1.1. Background and rationale

The vision of a Semantic Web^7,8 brought semantics to the foreground as an instrument to integrate diverse, independently developed information. The use of digitally stored ontologies (formal vocabularies paired with logical axioms describing their relationships and intended meaning⁹) has since become commonplace for annotating informational assets, i.e. adding concepts from ontologies to the associated metadata to enable their integration and reuse (e.g. 10,11). Research and progress in ontology-mediated interoperability have been significant, and interest in it remains high. Yet, the promise of semantic annotation has often been disappointing in practice, as describing the conceptual underpinnings of information in a way that is complete, consistent and understandable across disciplines and communities has proven difficult and elusive. Attributing stable, reliable and shared meaning to information is difficult because of a lack of accepted best practices, confusion about the phenomenological nature of observed entities and attributes, lack of accepted rules on how to choose, specialize and connect concepts, among other inevitable logical challenges. The result has been a confused landscape of mixed, incompatible attempts, which Goguen¹² described as “… the creation of a constantly shifting foreground and background, with the latter being called ‘context’”.

Ontologies for science come in many varieties. Foundational (also upper or reference) ontologies aim to provide philosophical foundations upon which to build lower level, domain-specific ones. They describe abstract, high-level concepts with the aim of establishing foundational logic for the definition of domain-specific concepts in derived ontologies¹³. For example, they may define the difference between abstract and concrete or establish the logical underpinnings of spatial, temporal, or part-whole relationships. Well-known foundational ontologies include DOLCE¹⁴, BFO (15, also see 16), and more comprehensive efforts like SUMO¹⁷, endorsed by the IEEE. Foundational ontologies have been successfully used and some have seen relatively broad adoption, but due to their high abstraction they cannot alone solve the issue of “what is what”, aside from providing a base for more specific domain ontologies (see below).

A second class of conceptualizations, observation ontologies (e.g. OBOE¹⁸, Ο&Μ¹⁹), also includes high-level concepts, but uses the notion of observation as the main device to introduce semantics, focusing on the “how” of observation rather than the “what” of phenomena. Emphasis is given to aspects such as the type of observation (e.g. measurements vs. rankings vs. classifications) and their use context. Observation ontologies thus try to occupy a foundational niche without committing to a specific phenomenology. Observation ontologies have been relatively successful in terms of adoption, but due in part to the lack of a phenomenological underpinning they cannot guide investigators in choosing appropriate observables, nor, by themselves, guarantee any of the FAIR principles for interoperability.

Domain ontologies, in contrast, describe specific areas of interest. Although in principle they should be used in conjunction with foundational ontologies, they are typically produced to serve the needs of a specific community, and are seldom committed to interoperability with ontologies from other domains¹³. The interoperability enabled in such a situation is primarily syntactic (“we use the same vocabulary, even if the semantics are not well thought out”) and therefore limited to users of the same ontology. Commonly these are formed as taxonomies, using a hierarchy of specialization (is-a relationships, for example: Precipitation is-a AtmosphericPhenomenon) to organize and systematize the terms used within the communities endorsing their development. Examples abound in various domains, including earth and environment: for example, SWEET²⁰, ENVO²¹, SPAN/SNAP²², Gene Ontology²³, and PlantOntology for plant anatomy and morphology²⁴. Some of them, such as the Gene Ontology²³, have been highly successful; yet the terminology is easily drained of meaning when confronted with other disciplinary contexts that use the same terms differently. For example, a crop is, to an agricultural economist, the agricultural product that reaches the market, possibly further processed after harvest, while to an agronomist the same term refers to the producing plant species. In general, domain ontologies commonly strive to endorse the term usage that is most popular in a community; this is both the reason for their success within those communities and their primary limitation.

Large investments have been made in developing controlled vocabularies to describe and discover artifacts of interest for specific disciplinary sectors, meant to facilitate annotation and sharing of information objects. Controlled vocabularies are typically domain-centered, with little or no pretension of phenomenological adequacy, but have strong links to the culture, language and applications in their community of origin, usually endorsing terms and assumptions that are best recognized in a community of reference. When formally expressed, their structure is often inspired by organizational, rather than logical, reasons. Many high-adoption examples exist, including e.g. AGROVOC²⁵ and CABT²⁶ for agriculture, CUAHSI for hydrology²⁷, and MESh for medicine²⁸. Generally, vocabularies contain a large number of terms (e.g., for taxonomic or chemical species of interest), are often multilingual, and can grow rapidly with use, while, by contrast, ontologies strive for minimality and robust logics. The differences between ontologies and controlled vocabularies are often misinterpreted, and in common practice the terms are sometimes used interchangeably.

Exploring ontology repositories, such as the OBO Foundry²⁹, immediately shows that notable inroads have been made in both fundamental and domain ontologies, and that efforts to produce multi-domain conceptualizations based on common semantics are made regularly. Despite these attempts, duplications, ambiguities and inconsistencies continue to hamper the development and adoption of semantic annotation standards in practitioner communities. With the current state of the art, and with the semantic web community seemingly more interested in enabling technologies than in the conceptual aspects of interoperability, FAIR+ interoperability remains all but impossible, perhaps aside from within very restricted communities. In our view, a major need for progress towards this goal is a solid, uncontroversial phenomenological base, i.e. the basic semantics for the types of phenomena and entities that can be understood by human observers. This phenomenology needs to be general enough to work across domains and worldviews. Formalisms and toolsets must be built to support it, to ease the specification of domains and allow for extension, while enforcing a consistent design discipline. We need clear best practices for specialization and connection of terms, and guidelines on how to integrate always growing, and potentially infinite, domain content from vocabularies without breaking the logical integrity of the resulting annotations. We start our discussion by focusing on the definition and preconditions of interoperability itself, before illustrating the details of the approach we have found useful as a possible starting point towards FAIR+ interoperability.

1.2. Interoperability of observations

In this article, we are concerned with the process of creating informational artifacts describing an observable concept in a chosen context, to provide evidence for a scientific deduction or computation. By observation we refer any artifact that is resolved from the perspective of a scientific process, i.e. can be used without requiring any further observation. Observations in this sense are commonly called “data”; yet, this term can be ambiguous with respect to the semantics of the observables involved, as we will explore later.

Definitions for interoperability vary by purpose, and while emphasis is sometimes given to formats and protocols for encoding and transmission (syntactic), legal compatibility (i.e., copyright and licenses) or organizational aspects (e.g., openness and purposes of the data), most definitions involve semantics - the meaning of what the information represents. The most rigorously structured information, such as scientific data and models, present the most stringent challenges in establishing semantic equality. Interoperability in such situations concerns links between two informational endpoints: for example, finding data to link to model inputs, or linking the outputs of one model to the inputs of another, so that a single computational chain can be established without fear that its results will be invalid. We term observations compatible to refer to this definition of interoperability between two informational endpoints (we will provide a more formal definition in Section 2.6).

We maintain that this kind of information alignment has three nearly independent semantic dimensions: semantics of the observable, the observation and the context.

Observable semantics describes what observations are about: physical objects, events, processes, agents, or characteristics that may be “observed” or measured. The human observer recognizes relevant observables, e.g. elevation (a quality pertaining to a location on Earth), households (subjects, part of villages or cities), or surface water flow (a process observable in watersheds). Much of what we call “data” consists of observations of qualities; their inherent subjects (e.g., the location on Earth whose elevation we observe) are often specified indirectly or implicitly. In order for observations to be made, and for their interoperability to be possible, it is crucial that such identities are fully specified and unchanging. For two observations to be compatible, their observables must be described by the same concept.

If a physical object, event, process or relationship can be simply acknowledged to exist in a context of interest, qualities, such as the elevation of a mountain or the temperature of a body, can only be observed indirectly, i.e. by comparison with reference observations. Units of measurement, currencies, rankings and classification systems define the ways human observers quantitatively or qualitatively describe such observations. Observation semantics describe how the observation activity is carried out, detailing the choice of reference metrics to ensure that a state can be understood and mediated. Mediation between different observation semantics is often possible, sometimes exactly (units of measurement, typically converted with negligible loss of precision), sometimes approximately (prices in different currencies can be more roughly compared by adjusting for inflation and purchasing power) and sometimes hardly (e.g. different land cover classifications systems are often extremely difficult to mediate). To be assessed for compatibility, qualities need the full statement of how they are observed; mediation operations may be necessary to harmonize two observations before computation involving both can take place.

Observation always happens in a context, providing observables with a when and a where. The context is usually chosen a priori by the actor who created the original artifacts, and may differ, subtly or greatly, between two compatible observations. Just like the scale of a geographical map determines what entities are visible in it (urban streets disappear in a 1:2,000,000 map), certain observables only come into focus at a given geographical scale, and certain phenomena emerge only at a given temporal scale. Context semantics describes these aspects for an observation. While differently scaled observation can be mediated to some extent through aggregation or propagation (with loss of information), scale also reflects deeply on semantics; large scale shifts will determine incompatible semantic misalignments, with (e.g.) uncountable processes becoming countable events when their time scale is changed beyond a threshold. For example, lightning is seen as an event by a meteorologist and as a process by a high-energy physicist; subjects, e.g. the microorganisms in a lake, become visible only through qualities (the color of the lake) over a spatial extent that makes the observer lose sight of them. For this reason, scale is key to establishing meaning in more ways than usually recognized; scale depends entirely on the chosen observation context, therefore on the human decision of what to observe. The semantics of scale largely deal with space/time, and as such, can be formalized independently from the observables’.

The ability to accurately characterize semantics along observable, observation and context dimensions addresses the interoperable and reusable FAIR criteria. Semantic specifications can be rewritten into queries that select interoperable counterparts for an observation, addressing the findable and accessible requirements. If queries embodying all three dimensions can be executed and the resulting observations can be ranked for appropriateness, unsupervised linking becomes possible. While observation and context semantics are relatively well-understood, the characterization of what things are - observable semantics - remains difficult and uncertain, even with increasing investments in ontologies and vocabularies and an engaged community behind the current state of the art.

The rest of this article details our approach to building foundations for FAIR+ interoperability through semantics, using examples. We describe a conceptual framework and examples of reasoning and specifications to support the characterization of observable semantics, resulting from field-testing in years of initial application, followed by a discussion of goals already achieved and those that remain. Here, and in all applications of these principles and methods, we argue for SMM as a driver for a semantics-first workflow, where the lifecycle of information begins, before data collection or model development, with the understanding of semantics, which in turn guides data collection, organization and processing up to eventual documentation, storage and curation. This contrasts with the more commonly adopted annotation approach¹⁰ where data represent the first-class artifacts, collected and stored with a logic dictated primarily by practical constraints, and semantics may complement the artifacts “after the fact” to suit the data to specific applications.

2.1. A simple metaphysics for scientific observables

We briefly articulate the phenomenological basis for our approach below, starting with the fundamental logical dichotomy of universals vs. particulars and further dividing particulars into continuants and occurrents. In our interpretation, these terms all refer to concepts; we are not concerned here with concrete instances (e.g., the individual tree, as opposed to the idea of a tree) as our only aim is to produce observations - informational artifacts generated through the process of observing concepts in the world.

Based on this reasoning, we use the term particular to refer to concepts that describe observables for which an observation can be made, as described above, although in some literature the term is used to refer to instances. Particulars include (1) physical objects, (2) their qualities, the (3) processes and (4) events that affect them (whose observation is likely to describe the qualities affected, causal pathways and component objects) and (5) the relationships that connect them. In contrast with particulars, we use the term universals to refer to concepts that cannot be observed directly. In much literature (e.g. 15), the term universal simply means a concept (the abstraction of an entity, as opposed to the entity itself), so it includes concepts that we classify as particulars, such as processes or physical objects. We take a stance closer to Platonic realism³¹, which defines universals as those notions that cannot be directly incarnated unless associated with a particular. This includes classes of concepts such as attributes (e.g. ‘black’ cannot have an instance, but it can qualify a physical object, e.g., a cat), roles and others. In SMM, we translate universals into entities that cannot be observed in their own right. Only observations of particulars can be made, and universals are attributed to them to further specify their semantics.

Within particulars, the continuant vs occurrent distinction reflects how observed entities stand with regard to space and time. This distinction is found in all foundational ontologies with slightly different definitions or terminology¹⁶: for example, DOLCE¹⁴ uses the terms perdurant and endurant instead. Continuants are entities that maintain their identity through time, including physical objects (named subjects in SMM) and their measurable qualities. For example, color or height, which can be observed only when linked to other entities through mandatory inherency: e.g., the height of a tree. While continuants are, occurrents, such as events and processes, happen: their definition is intimately tied to time. As discussed previously, a spatial shift in the observation point can morph continuants from countable subjects to uncountable qualities as spatial resolution moves upwards and small-scale subjects lose their individual visibility in favor of larger-scale ones. Similarly, countable events can morph into uncountable processes, as temporal resolution shifts to allow appreciating change within what was formerly seen as an individual event. Relationships between two observations also reflect the continuant-occurrent dichotomy; accordingly, they can be seen as structural (unconcerned with time, such as parent-child) and functional (such as flows, whose expression is a time-dependent process).

Figure 1 illustrates how observational scale and the categorization of particulars are intimately linked. A temporal scale gradient (Y axis) separates occurrents - for which fine temporal resolution allows an observer to appreciate change - from continuants, the meaning of which can be appreciated independent of time, due to the temporal scale being coarse enough to make change invisible. On a spatial scale gradient (X axis), “close” observation focuses within individual observations, impeding the appreciation of their individuality (therefore the “counting” of separate individuals), but enabling the observation of their inherent qualities and processes. As spatial scale is made coarser, the point of view moves outside the individual observation, allowing an observer to appreciate first the individual relationships between two of them, then an arbitrary number of them in the context of a larger-scale observation (not shown in the image). The property of countability tracks meaning along a spatial scale gradient in the same way that the dichotomy “happens/is” tracks meaning along time scale gradients. The diagram in Figure 1 has proven intuitive enough for ARIES users to remember and use as guidance in the first steps of semantic annotation.

Figure 1. A synthetic representation of how the spatial and temporal dimensions of observational scale influence the identification of the fundamental categories of observables discussed in the article.

Refer to the text for explanations.

2.2. A formal language to specify interoperable semantics

During the development of the ARIES project, it quickly became apparent that the explicit statement of semantics was key to achieving our goals of building and linking community-driven, interoperable repositories of independently developed data and models. At the same time, it became clear that no community of modelers, data scientists or other prospective users would consider an investment in OWL or other semantic web-endorsed formalism as the vehicle to express the semantics in data and models, and that a different approach was necessary. Our solution was the design of a custom semantic specification and annotation language, for which we laid out four main requirements.

The result of many years of design and user feedback is the k.IM language, which currently makes worldviews accessible to ARIES modelers. The k.IM (for “knowledge-Integrated Modeling”) language is complemented by an open source software stack named k.LAB, which provides integrated tools to develop and use conceptualizations and models using k.IM. The software, which in its current alpha stage requires training to be applied, will not be discussed here, but can be freely downloaded and explored in source form.

In k.IM, particulars and universals are combined to specify observables; these can later be used to annotate data and models. Keywords and syntax rules are designed to make k.IM statements readable and understandable by mimicking English syntax, while specifying much more complex, correct and consistent OWL³² axioms. All k.IM statements compile to OWL2, the most widely used and accepted representational standards for ontologies. Conceptualizations written in k.IM can thus be exported and used in OWL-based systems with no loss of information.

Experience with developing and teaching k.IM has highlighted three clearly distinguishable tiers of sophistication in semantic annotation practice, arranged here by decreasing levels of experience required and progressively shorter learning curves. Tier 1 is annotation of data and models, performed by minimally trained users utilizing the terms from domain ontologies, facilitated by context-aware search tools. Tier 2 is domain definition, where domain experience is the essential skill, but an investment in knowledge engineering remains necessary. Tier 3 is worldview definition, limited to knowledge engineers with ample time to invest in work with domain experts. All three tiers are enabled in the k.LAB community and will be discussed and exemplified below. Tier 3 usage is discussed in Section 2.3. Examples from tiers 2 and 1 will be given in Section 2.5.

2.3. Building a worldview: Definition of domains

The following examples, taken from the socio-ecological system worldview used in ARIES, illustrate some of the most important aspects of k.IM and their role in facilitating the conceptualization of domains. For clarity, the examples are highlighted in the same way the k.LAB editor does: keywords (identifiers recognized as part of the language) are in purple; user-generated text (including concept identifiers) is in black; literal text (such as quoted strings) is in blue. Table 1 provides a more systematic list of keywords with their associated meanings. We only discuss the features of the language used to specify concepts; those concerned with data annotation will only be briefly described, while the features concerned with modeling will be discussed in a forthcoming contribution.

Geographical elevation is a quality inherent to regions of Earth, whose full specification involves different notions, some specific to the geographic domain, others of more general relevance. We use namespaces, associated with separate URLs or files, to separate concepts from different knowledge domains; a namespace can import another (through a using clause as shown below), so that the concepts defined in it can be referenced. Concepts from imported namespaces are referred to using the namespace identifier as a prefix to the concept name, separated by a colon (for earth:Region, the concept Region is defined in the earth namespace). The specification in definition (1) comes from the geography namespace, declared at the beginning along with its imports.

namespace geography using im, earth; 
		
length Elevation
  "Geographical elevation above sea level, as described by a digital                         (1)
   elevation model."
  is im:Height of earth:Terrain within earth:Terrestrial earth:Region;
	

In this specification, the length keyword establishes the fundamental character of geographical elevation, including its physical nature (an extensive property whose value changes with the extent of the inherent subject) and the base unit for its measurement. This is done by tying the concept being defined to the core observation ontology, which lays out the phenomenological categories defined above, along with constraints and relationships for all common scientific observables, unseen by users. The language contains keywords for many fundamental quantities, allowing users easy specification in most situations (Table 1). It also provides semantic operators to easily and systematically modify existing concepts obtaining derived quality concepts:

event Earthquake;
                                                                                                       (2)
model table(“data/earthquakes.csv”) as probability of Earthquake;

Example (2) needs only one concept, Earthquake, as the annotation of its probability can be done through a semantic operator (probability of), which can only be followed by a concept describing an event and produces a concept for its probability. Similar operators allow the expression of presence, occurrence, distance, proportion, ratio and value (Table 2). The use of semantic operators greatly reduces the number of concepts needed in the worldview and enables validation of the modified observable.

As concrete qualities (those of which observations can be made) can only exist inherently to a direct observable, the observable must be made explicit before the concepts can be used (e.g., earth:Region in the previous elevation example). In example (1), the concept statement starts with a description (highlighted in blue) that is indexed in the k.LAB software, so that users can easily locate concepts by textual searching. The is keyword introduces the semantic specification for the term Elevation. In it, im:Height (from the base namespace im, for “integrated modeling”, also the name of the containing worldview) is first established as its fundamental nature; then, inherency is established by means of the keywords of and within. Inherency enables validation of the contexts in which the qualities are used. For example, after the definitions in (1), it will be correct to annotate elevation within a watershed, as long as a previous statement defines the Watershed concept as a type of earth:Region. In many situations, specifying within is enough to establish inherency. The of keyword is used when the quality refers to a second, implicit observable in the context of inherency. For example, the “height of trees” quality in a region is inherent to that region, but implicitly describes tree subjects in it. In keeping with our readability requirement, we only allow two levels of specification and use two different keywords (within and optionally of). We found that legitimate chained specifications, such as “x within y within z within …”, were awkward and difficult to understand in usage tests and decided against allowing such statements. Multiple chains of inherency of this kind can be defined using intermediate concepts.

In knowledge domains (as opposed to physical ones), the implicit inherent subject is often a configuration. This is a perceived, measured or inferred arrangement of observables that can be experienced and recognized by humans without being directly amenable to providing the observable of an informational artifact. For example:

namespace earth using physical;

configuration Terrain                                                                       (3)
  "The three-dimensional configuration of land surfaces"
  is physical:PhysicalConfiguration within Terrestrial Region;

In k.IM, configurations can only follow of in inherency specifications. This constraint allows the construction of clear and unambiguous statements that relate well to scientific discourse while remaining logically consistent. Common logical errors stem from confusing legitimate observables (such as qualities, subjects or events) with “objects of study” in science that are part of daily discourse but are not actually amenable to being directly described by informational artifacts. Configurations often allow keeping such concepts (such as Terrain above) in a specification without compromising logical integrity. Other examples of configurations include bathymetry, aesthetics and all types of networks, e.g. a stream network or a social network, whose observables are the actual subjects and relationships that create the perceived configuration.

The inherency requirement for qualities is one of the primary means for semantic inference and validation in SMM. Machine reasoning can be applied to ensure proper usage of each concept in data annotations and models. For example, models of a quality that is inherent to a specific subject or process are validated to ensure that all other qualities used for its computation are inherent to a compatible subject type (see below for a definition of compatibility). Any mismatch makes the model semantically inconsistent and must be solved before it can be computed. At the same time, many inferences are possible through reasoning on inherency. For example, a model’s requirement for “presence of biology:Tree” will automatically be satisfied if data for this specific concept are not available, by an observation of “im:Height of biology:Tree within earth:Region”. Because non-zero values of extensive physical properties imply the existence of their inherent subjects, a model for presence of trees can be automatically built using the height data and height > 0 as the criterion to establish presence. Interestingly, inherency underlies the mechanism through which shifts in a spatial scale affect identity and meaning in continuants. If a finer spatial scale resolves, e.g., the color of individual unicellular algae subjects in a volume of water, expanding the spatial extent and lowering the resolution may cause the algae subjects to go “out of focus”. Their color now becomes a quality inherent to a larger, previously invisible lake subject.

In specification (1), geographic elevation is established as a length by its fundamental keyword, but the definition introduced by is defines it as a Height, from the base im worldview namespace. The definition of Height shows the use of attributes to constrain the length concept to a specific orientation relative to the observer:

namespace im;
                                                                                                        (4)
abstract length Height inherits Vertical, Lineal;

The attributes Vertical and Lineal (whose definitions are not shown here) are attributed to Height using the keyword inherits, establishing characteristics of Height beyond its definition as a length. In this worldview, Lineal (as opposed to Areal or Volumetric) is used to ensure that transformations of qualities involving dimensional reasoning (e.g. dimensional collapse under scale aggregation) carry the information that is needed for the algorithms to properly mediate scales and values. While the concept of “length” belongs to the foundational observation ontology, outside the worldview, dimensionality is specific to worldviews, as it could be interpreted differently in other domains (e.g., in non-classical physics). The Height concept is declared abstract to ensure that observations cannot be made of it; any concrete concepts derived from it - omitting the abstract keyword, such as elevation in (1) - must specify their inherency or the k.IM parser will flag an error.

Attributes are an important feature for k.IM to enable fluent specifications while enforcing our parsimony requirement. Definition (1) exemplifies the English-like syntax used to specify attributes that restrict the context to terrestrial regions without creating a new concept. The context for geography:Elevation is declared to be “earth:Terrestrial earth:Region”, combining two concepts at the time of usage by simply mentioning them in sequence. Instead of merging them into another concept, earth:TerrestrialRegion, the sequential specification follows the grammatical conventions of the English language and yields more parsimonious ontologies. The ubiquitous use of is-a specialization to add attributes to observables (BlackCat is-a Cat) is a major cause for explosion of terminologies in domain ontologies. While this is legitimate from a phenomenological perspective (a black cat certainly is a cat) and from a mathematical logics perspective (black cats certainly are a subset of the set of all cats), we adopt the convention that only clear semantic distinctions should reflect in is-a inheritance. As long as an attribute does not obviously modify identity (a black cat is just a cat) the specialization should be described without explicitly creating a new concept. Attribute composition through is-a relationships can also yield ambiguous inheritance graphs, logical errors and specification dead-ends when many attributes are used but subtypes are intended to inherit only some. As most universals apply to broad classes of observables (color is certainly not just an exclusive attribute of cats), the advantages of the quasi-natural k.IM syntax quickly become apparent in terms of parsimony and readability. This syntax enables the creation of ontologies that are small enough to be learned and used but retain high expressive power. The underlying infrastructure, such as k.LAB, is left in charge of handling, unseen, the axiomatic complexities of concept inheritance and attribute composition.

Attributes are often used to coarsely summarize the value of qualities. In k.IM, we preserve these relationships in order to allow inference of attributes:

namespace ecology using chemistry, earth;

abstract attribute Salinity
  describes chemistry:Salinity within earth:Aquatic earth:Region
  has children												(5)
    Saline,
    Brackish,
    Freshwater;

In definition (5), it is clear how an attribute (ecology:Salinity) with its “child” sub-categories is a synthetic and approximate way to describe the actual concentration of sodium chloride in a natural water body, defined in the chemistry namespace (see Section 2.4 for details on chemical identities, and Table 2 for the proportion of semantic operator):

namespace chemistry using im, physical;

quantity Salinity                                                                                     (6)
  is proportion of (NaCl im:Mass) to (Water im:Mass) within physical:DelimitedBody;

By establishing a semantic relationship between the salinity categories in the ecology namespace and the proper salinity definition in the chemistry domain, we open the way for classification models (not discussed in this article) to define specific ways to observe ecology:Salinity (i.e., establish the concrete sub-trait that applies to a chosen context). This occurs by observing and checking ranges of chemistry:Salinity that determine each category in context-specific ways (e.g. distinguishing brackish from fresh water; see 5 for practical examples of how similar models may be chosen, assembled and used).

To ease specification and enable inferences and functionalities, attribution in k.IM uses four categories of universals, collectively named traits, which correspond to different keywords used at declaration (Table 1). We distinguish general attributes from more specialized orderings (whose subtypes define an ordered sequence), realms (which identify mereologically arranged subdivisions of a context, such as atmospheric strata) and roles, which categorize the ways specific observables are seen when in the context of another. Each of these categories enables specific types of inference in applications; roles, in particular, are crucial for interoperability in modeling applications, and deserve a discussion that is outside the scope of this article. A final category of universals, identities, is instrumental for the use and reuse of external vocabularies and terminologies, and is described in detail in the next section.

2.4. Bridging to accepted terminologies: Identities and authorities

In semantic annotation practice, it is common to encounter situations when an abstract observable (such as an individual animal, plant, or a material object such as a delimited volume of matter) must be identified by a “species”, such as a taxonomic or chemical one. For such situations, k.IM recognizes specific types of universals we name identities, which can be bound to observable concepts so that the use of a given identity type becomes mandatory to further specialize the observable:

namespace biology using physical;

agent Individual                                                                                      (7) 
  is physical:SelfAssertedBody
  requires identity Species;

In this case, the set of possible identities may be very large or even infinite. Since it is of course impractical to expect that ontologies can list all possible identities, this presents a problem when reasoning must compare concepts at two separate endpoints, as the identity used at one may not be known at the other. Having users create concepts for identities whenever a new one is needed would break interoperability, and the alternative - adding them to the shared worldview on an as-needed basis - would make the worldview prohibitively difficult to coordinate and maintain.

In such situations, we use authorities to link authoritative terminologies and ontologies. In k.LAB, authorities are software components that translate terms provided by authoritative terminologies, maintained by standard-defining organizations such as IUPAC for chemical nomenclature, into logical axioms that can be inserted into the namespaces provided in the worldview to create stable concepts that are available at all points of use. Authorities are identified in k.IM by names bound to a specific identity in a worldview:

namespace biology;

abstract identity Species                                                                            (8)
  is Taxonomy
  defines authority GBIF.SPECIES;

This statement binds the GBIF.SPECIES authority to the biology:Species identity, requiring that any concrete biology:Individual is identified using it (based on definition 7, each Individual is in turn bound to adopting a biology:Species identity). For example, a spatial coverage (e.g., a raster GIS dataset) describing the counted occurrences of honeybee individuals (Apis mellifera) per square kilometer could be annotated as follows:

model raster(“data/bees.tif”) 
  as count biology:Individual identified as “1341976” by GBIF.SPECIES per km2;                  (9)

Code 1341976 in the GBIF catalogue³³ is the identifier for the Apis mellifera species, tracking its unchanging taxonomic identity through any changes in nomenclature that may have occurred over time. For increased readability, definition (9) can also be written with a concept declaration that makes the identity explicit for a reader:

agent HoneybeeIndividual
  is biology:Individual identified as “1341976” by GBIF.SPECIES;
										                	(10)
model raster(“data/bees.tif”) 
  as count HoneybeeIndividual per km2;

In such situations, the user-defined concept (HoneybeeIndividual) functions as an alias for the GBIF honeybee concept, so that independent uses of the concept will not produce ambiguity, even if different specifications like (10) are given and different concept names are used in them. The two specifications (9) and (10) are functionally identical and compile to the same OWL axioms. Within the GBIF.SPECIES authority, producing logical axioms for the GBIF code 1341976 entails verifying that the code is a valid species identifier: a different outcome, such as using a non-existent or, e.g., a family code, would result in a parsing error reported to the user. This mechanism guarantees the ability to reason across namespaces and allows full interoperability of taxonomic names when used at independent and uncoordinated endpoints. Multiple sub-authorities (such as GBIF.FAMILY, GBIF.CLASS, etc.) allow binding different classes of identifiers managed by the same organization. The GBIF web-accessible catalog service³³ provides codes that identify species and other taxonomic names in a stable and reliable way. It also provides metadata, such as labels, common names and broader terms, that are automatically linked to each concept created, allowing full specification of the identity and automated documentation of the resulting informational artifacts.

In addition to the identities managed by GBIF, representing the full taxonomic hierarchy from kingdom to variety, k.LAB provides authorities that recognize and interpret: (i) chemical identities (using the InChi naming conventions³⁴); (ii) soil taxa according to the World Reference Database nomenclature³⁵; and (iii) several classes of agricultural terms provided in AGROVOC²⁵ (Table 3). In most cases, authorities provide both validation of identifiers and search facilities, building on services provided by the managing institutions. For example, if a user refers to a chemical compound using a wrongly formatted InChi string, an informative error is reported. In contrast, a correct string can be translated by the IUPAC authority into a molecular diagram for the user to check. Availability of a specific authority within a worldview is equivalent to an endorsement of that authority in it. Authorities, complemented with search tools and validation, such as those provided in k.LAB, provide consistency and a sound annotation discipline in a usage landscape characterized by widespread redundancy and inconsistency. “Bridging” authorities, while not yet attempted, might also be designed to accept terms from one authority and turn them into the same axioms of another covering the same domain. For example, SOIL.USDA may in the future complement the existing SOIL.WRB authority as an alternative source of soil taxonomy identifiers, producing axioms compatible with the latter. This would enable transparent mediation of competing vocabularies and further expand opportunities for interoperability and reuse of existing annotated data.

2.5. Using the worldview: annotation of data and models

With a common phenomenology, a structured language and validating supporting infrastructure, knowledge engineers can create worldviews with better prospects of consistency, expressiveness and reusability. Yet, the task of building a worldview remains daunting. We can consider the building of the worldview a Tier 3 activity, requiring significant expertise, long-term research investments and a careful vetting process involving consultation and continuing collaboration with a large number of experts. We will briefly summarize challenges and successes of worldview development for ARIES in the discussion and better discuss the topic in forthcoming contributions.

When a suitable worldview is available, it should become possible to compose domain semantic annotations by combining existing concepts from the worldview and its endorsed authorities. We can consider this Tier 2 of difficulty in semantic annotation; it is the scope of many initiatives of which a representative example is the Agrisemantics initiative³⁶. The Agrisemantics vision statement mentions height of corn as an archetypical example of a common observable whose interoperability for existing data resources is desirable. A fitting ontology available in the OBO foundry²⁹ that provides concepts adequate for this task is the Plant Trait Ontology (PTO,³⁷), which draws on the work of many experts and enjoys good community acceptance. The PTO provides a hierarchy of concepts starting at quality (imported from the BFO ontology, also a base ontology for k.LAB) specialized to morphology, then further into size height and plant height. One can assume that identifying height of corn would require a further specialization of plant height, and the corn identity would simply be implied syntactically by using a Corn… prefix in the term assigned to the concept. Further exploration of the PTO reveals that giant embryo (a gene type) is a sibling of plant height, both specialized from whole plant size through is-a inheritance. Further is-a specialization of plant height defines, among others, concept plant height uniformity (a quality not physically commensurable with height) and relative plant height (seemingly adding an observation-related attribute, relativity, out of many possible). The PTO is one of the most advanced domain ontologies in use with respect to phenomenological characterization, and its terms have proved useful to large communities. Yet it is clear from this example that no ontology can force users to adopt cogent annotation practices, ensuring that physical and biological identities are preserved along inheritance chains and attributes retain traceable and stable meaning. These are key requirements to help prevent inconsistencies and better assist annotation in service of the FAIR goals. If the same exercise were replicated in k.IM, for example to annotate a raster map file describing corn height in cm in a given region, the language itself would have driven the specification of the semantics:

model raster(“data/cornheight.tif”)
 as measure im:Height 
   of agriculture:PlantIndividual identified as “c_12332” by AGROVOC.CROPS                  (11) 
   within agriculture:CropField 
 in cm;

Or for increased readability:

agent CornPlant is agriculture:PlantIndividual identified as “c_12332” by AGROVOC.CROPS;

model raster(“data/cornheight.tif”)
 as measure im:Height of CornPlant within agriculture:CropField in cm;                       (12)

The measure (observable) in (unit) syntax (see below and Table 4), one of k.IM’s observer statements (Table 4), embodies the semantics for the how of observation discussed above, and requires that the primary observable, in this case im:Height, be a physical property, simultaneously enforcing the use of units of measurement appropriate for its physical nature. Definitions (11) and (12) intentionally use agriculture:PlantIndividual instead of biology:Individual, as the latter requires a precise species identity (definition 7), while the former references the commonsense taxonomy used in AGROVOC for crop types, reflecting the intended semantics for the data. Most importantly, the adoption of rigorous phenomenological inheritance and specification syntax requires the realization (and the explicit statement) that height is first of all a quality of a plant subject, and that the data refer to plants within a cropfield subject. These logical axioms are a necessary base for any reasoning that can assess their compatibility within applications. While such details still need to be learned by a user, the syntax itself serves as a guide for the annotation workflow: the use of inconsistent observables or the lack of proper inherency would yield ungrammatical statements that are reported as errors. For example, leaving out the of specification would cause height to become abstract, therefore not usable for data annotation; leaving out within would leave the context of inherency for the quality blank, reported as an error for any non-abstract quality. The result is readable by a non-expert and compiles to axioms specifying a single OWL concept, which can be transferred to a remote endpoint in axiomatic form and reconstructed for reasoning or database querying; the shared worldview is the only requirement for its interpretation. The concept as constructed carries information about physical nature, dimensionality, domain of application, agricultural identity, biological identity and context of inherency (plants within a cropfield). These are assembled through consistent logical restrictions and are robust to validation and machine reasoning. On this basis, inferences can be performed that use the annotated dataset to satisfy queries beyond the asserted quality, e.g. for presence of CornPlant as discussed previously. Simply through reasoning on the concept, a query for an observation of the height of generic agriculture:PlantIndividual in any earth:Region (of which agriculture:CropField is a subtype) could be satisfied, in absence of a more specific match, by the same corn height data.

The simplest examples of usage (Tier 1) exploit pre-defined concepts from the worldview to annotate resources. In such cases, knowledge of the syntax and simple search tools allow a user to produce annotations that can accompany informational assets for automated discovery and indexing:

worldview im;
model raster(“elevation.tif”) as measure geography:Elevation in m;                        (13)

Specifications such as (13) are simple enough to be added to metadata or “sidecar files” – files with a “.kim” extension that accompany data files with the same name - which may be automatically detected and indexed by specifically designed web crawlers, so that indexes of web-accessible, annotated datasets can be built and maintained. Specification (13) is complete and correct, as geography:Elevation is fully characterized in terms of inherency within the worldview, as seen in statement (1). The statement of the worldview name is enough to load the web-accessible worldview and use it to interpret the specification that follows. To annotate qualities, which encompass a majority of data artifacts, the syntax for observer statements (such as measure in the example above) is enough to represent all observation semantics known to k.IM. The set of available observer statements (Table 4) is small and has proven easy to learn and use in ARIES coursework and test user communities.

While this article does not fully describe modeling and annotation features of k.IM and k.LAB, we note that data annotation is not restricted to qualities. Subjects can also be annotated with ease using a slightly different syntax:

model each vector(“data/roads.shp”) as infrastructure:Road;                              (14)

As subjects are observed directly (without needing units or other known observations for comparison), the simple acknowledgement of the semantics is enough to annotate a source of objects, such as roads in a vector file. The keyword each, only applicable to countable observables, reflects the fact that such sources can produce one or more subjects with the specified semantics; the model statement also allows annotation of semantics for any attributes of the observed subjects (not shown). The k.IM language and k.LAB infrastructure build on these semantic foundations to enable a distributed modeling infrastructure, in which the resulting observations can be complemented, through further extension to the model syntax, with procedural information to create “live” observations interacting on a networked infrastructure, in compliance with their semantics. Such features, briefly described for the ARIES application in 5, will be more thoroughly illustrated in forthcoming contributions and documentation.

2.6. Assessing compatibility

FAIR+ interoperability requires the unsupervised assessment of compatibility between semantically annotated resources. We use the term compatibility to refer to concepts and interoperability to refer to observations of compatible observables. In k.LAB, compatibility enables interoperability in two fundamental ways:

Using the notion of interoperability illustrated in Section 1.2 and the semantic foundations illustrated so far, the assessment of compatibility for interoperability can be defined as follows.

Two observables (O1, O2) are compatible if and only if:

If observables are compatible, their observations are interoperable. They are FAIR+ interoperable if and only if:

This definition is amenable to being incorporated in an unsupervised algorithm. Mediation may engender information loss (e.g. aggregation error) and other uncertainties (e.g. when bridging different classification systems), which should be recorded as provenance³⁸ in separate records kept with the dataflow. In queries, when more than one interoperable observation may be returned, any potential information loss can become part of the criteria used to rank the appropriateness of each candidate observation that matches the observable. On a semantic level, the match may also be incomplete. For example, some traits of the matching observation may not be stated in the query, e.g. a vertical length could match an unspecified one. This offers a base to develop ranking strategies considering, among other criteria, metrics of semantic accuracy or distance; the latter is an important criterion in k.LAB and will be discussed in detail in further contributions.