A Pragmatic Approach
Ontological prisms are designed to be pragmatic and ecumenical. They are pragmatic in order to avoid definitional debates about the nature of ontologies and to focus on how they can be constructed and utilized. They are ecumenical in that they support various representation semantics throughout the entire lifecycle of ontologies.
Sources
Ontologies are vessels meant to organize knowledge. As far as enterprises are concerned they can be developed from three sources: conceptual Models, databases schemas, or facts (observations, datasets), and documents.
Ontologies: Sources & Consistency
Given the inherent variety and changeability of knowledge, consistency constraints must be addressed upfront, namely at the source level: between conceptual models and facts and documents (thesauri); between facts and documents and databases schemas (taxonomies); and between conceptual models and databases schemas (domains).
Ontological Realms
Extensional Realm: Facts & Documents
Facts encompass whatever can be directly observed in physical or symbolic environments: physical objects, symbolic constructs (time, space, contracts, status, etc.) and documents (text and images).
Facts & Documents
In order to be considered, facts must be labeled, meaning they should be associated with signs that can refer to individuals or groups. Facts can be organized in terms of sets and subsets, as well as composition and aggregation.
Intensional Realm: Concepts
Concepts are mental images which cannot be directly associated with facts in physical or symbolic environments. Typically they stand for abstract entities such as values, intents, or plans.
Ontological Realm: Concepts
Concepts, or more precisely their meanings, can be organized in terms of sets and subsets, as well as through composition and aggregation.
Logical Realm: Categories
Categories are collective symbolic representations meant to be shared across organizations as well as over time.
Ontological Realm: Categories
Contrary to facts and concepts that rely on sets and subsets for representation levels, the representation of category levels depends on abstraction and inheritance.
Avatars
Realms may overlap; for instance, physical objects can also be symbolic and associated with mental images, artefacts are both physical objects and instances of categories, and designs can be viewed as both concepts and categories.
Consistency
Consistency, and more generally alignment and interoperability across domains and over time, represents a major challenge for ontologies, especially if they are to serve as the backbone of agentic collaboration. This objective can be significantly aided if consistency is achieved at the source level with regard to the meaning of words (thesauri), the partitioning of individuals (taxonomies), and the responsibilities on both (domains).
Semantic Consistency: Thesauri
Semantic consistency must be addressed on two levels: first, between domain-specific vocabularies (words), and second, between vocabularies and concepts. With regard to words, lexicons or dictionaries are used to organize the meaning of labels attached to facts, and thesauri are used to align the specific semantic spaces of dictionaries and contexts, as well as to address homonyms or synonyms in cases of overlap.
Semantic Consistency: Thesauri
Ensuring the consistency between the meaning of words (used with facts) and concepts is more challenging because, contrary to flat and grounded vocabularies, thesauri involve multiple semantic levels detached from actual contexts.
Partitions Consistency: Taxonomies
Compared to thesauri, which pertain to meanings, taxonomies relate to individuals. In this context, consistency refers to the alignment of observed partitions (e.g., cattle skin color) with managed ones (e.g., cattle usage).
Partitions Consistency: Taxonomies
The challenge in that case is to map sets and subsets, which are used for facts representation levels, to inheritance of classes and subclasses, which are used for categories representation levels. That can be achieved through taxonomies.
Organizational consistency: Domains
Ontologies, and more generally knowledge, are inherently evolving. Therefore, ensuring their consistency across organizations and over time cannot be achieved without the explicit management of responsibilities regarding concepts and their realization as categories.
Organizational Consistency: Domains
Straddling business-specific boundaries, ontological prisms allow for a distinction between responsibilities: knowledge on one end and engineering on the other.
Ontological Prisms & Enterprise Architecture
The immersion of enterprises in digital environments has undermined traditional gateways and brought their organizations and systems into a single symbolic fold, calling for a redefinition of enterprise architecture in terms of communications and representations.
Languages
Whether it’s for direct (interfaces), or mediated (representations) communication, language is part and parcel of governance for enterprises immersed in digital environments. And the spreading of generative language models (GenLMs) has created a new and powerful momentum that blends communication and representation. The opening of this generative new frontier, has also led to some confusion between language and knowledge. This confusion is further reinforced by the ubiquity of knowledge graphs, which are viewed indiscriminately as both content and containers. Ontological prisms provide a tool to sift through and separate language threads from the fabric of knowledge.
Communication vs Representation
On the communication end the relevant distinction is between the capabilities of collaborating agents: digital, symbolic, or natural languages. On the representation end the distinction is between the content addressed: thesauri (words), models (systems), and ontologies (ideas). Ontological prisms allow for an explicit integration of representations (models, neural networks, and knowledge graphs) and communication (empirical, natural, and formal languages).
Integration
Regarding enterprise architectures, the primary objective of ontological prisms is to ensure a technical and functional integration of heterogeneous representations shared across business units.
Technical integration can be achieved with OWL and RDF (concepts), UML or SQL (models), and XML (documents). Leveraging its shared RDF implementation, the Shapes Constraint Language (SHACL) can complement OWL in ensuring the consistency of representations. More specific interfaces could also be supported with RDF-based ontologies (e.g., DOLCE, UFO, or BFO), Documents management systems (DMS), general modeling methods and tools (e.g. SysML, Archimate, or BPMN/BPEL), or specific ones (e.g. SAS/SPSS or MATLAB). Regarding interoperability, besides generative language models (GenLMs), four languages can serve as references: SKOS (Simple Knowledge Organization System), implemented with RDF, for the meaning of facts and concepts, and Common Logic Interchange Format (CLIF) and Prolog for formal reasoning. ORM (Object-role Modeling) can also be mentioned with regard to the mapping of facts into categories.
Technical interfaces & Functional Integration
Ontological prisms provide the symbolic backbone of enterprise architectures allowing for the integration of their key functions:
- Requirements, as expressed from users’ perspective and set in actual contexts.
- Data analytics, from a business perspective aiming at virtual contexts.
- Business analysis, for the alignment of data analytics and business models and objectives.
- Business intelligence for the definition of business models and objectives.
- Strategic planning, for the alignment of business models and objectives with organisation and supporting systems.
- Systems modeling, for the alignment of planned, legacy, and currently required systems.
- Systems engineering, for the realisation of system models.
Such a backbone can be best implemented using OWL.
Utilization
Ontological prisms provide an ecumenical framework for a three-pronged management and engineering of knowledge addressing extensional (facts), intensional (concepts), and logical (categories) realms.
Extensional realms address whatever can be observed about symbolic or physical environments: direct observations, systems, processes, documents, or datasets. Intensional realms pertain to mental representations, addressing values, intents, and plans. Logical realms pertain to collective representations, addressing the management of shared entities. Overlaps between realms are managed through thesauri, taxonomies, and domains, which address the meaning of words, the partitioning of observations, and the governance of ontologies, respectively.
Ontological Prisms & Knowledge
Ontological prisms can be applied to both ontological and systems views, the former in terms of facts, categories, and concepts, and the latter in terms of data, information, and knowledge, respectively. Since these views are isomorphic, they can be switched at will depending on the issues at hand, which is particularly relevant in knowledge engineering processes. In this context, knowledge engineers can act on three rods, one for each realm, moving each rod parallel to the corresponding boundaries of the prisms. First, the inward movements select candidate facts, categories, or concepts from nondescript entries. Then, perceptions, projections, and returns from experiences are used to consistently translate facts, categories, and concepts into data, information, and knowledge, respectively.
OWL Kernel
A kernel prototype has been developed as a proof of concept using OWL with the Protégé platform. This allows for both online and on-site standalone utilization, as well as seamless portability for projects.
In line with the objectives of ecumenism of ontological prisms, the kernel relies solely on core OWL features, leaving as much room as possible for users’ customized extensions without the risk of confusing overlaps.
Ontological Prisms Kernel (OWL/Protégé)
On that account the Protégé hierarchy of classes is solely used to organize entries, without bearing particular semantics. The kernel introduces two significant distinctions: on one hand, it introduces Aspect to represent edges with properties, making a step towards labeled property graphs; on the other hand, the kernel does not assign any particular meaning to the Protégé hierarchy, except for the management of entries, and instead relies on stereotyped connectors.