Ontological Prisms & The Geometry of Knowledge

The book will be released in August

Preamble

The rapid and pervasive expansion of generative artificial intelligence (GenAI) technologies has highlighted the inherent limitations of purely neural approaches, as well as the benefits of coupling them with symbolic counterparts, epitomized by ontologies. While knowledge graphs have long been recognized as a jack-of-all-trades in symbolic representation, there is little consensus regarding the roots and roles of ontologies. In practice, operational ontologies are typically developed as extended conceptual models or abstracted from logical ones. Both approaches come with key caveats, such as siloed knowledge, a one-size-fits-all abstraction model, and a lack of diachronic representation.

Ontological prisms intend to address these challenges introducing a game-changing geometric approach that combines observations (facts), intents (concepts), and shared symbolic representations (categories).

Related readings:

A Paradigm Shift

From 2D to 3D Geometry 

As noted above, the main drawback of foundational ontologies is their limited conceptual perspective: ontological categories are directly defined from semiotic triangles that associate things (an hospital) with signs (‘Hopital’) to denote them, and logographic (H) or literal (Hospital) symbols representing concepts and/or categories; such a two-dimensional (2D) representation of things conflates models (categories) and ontologies (concepts). Hence the benefits of shifting to a three dimensional representation of things, concepts, and categories

Unfolding a third dimension for categories enables an explicit distinction between universals (concepts) and their representations (categories). It also allows for an explicit representation of designed and/or symbolic objects and their corresponding categories. As a corollary, the partitioning of objects can be carried out independently of the naming of concepts; the former is realized through taxonomies (things/categories), while the latter is achieved through thesauri (signs/meanings). The third intersection pertains to domains, sometimes referred to as ontologies, which are used to align the management of concepts (for knowledge) and categories (for representations).

Unfolding 2D Representations

The significance of the interplay between realms, and the role of thesauri, taxonomies, and domains as gears realising their alignment, appears fully through a simple sleight of hand that rearranges the pyramids into prisms.

A Shift in Perspective

Ontologies & Philosophy

Despite their roots in classical philosophy, ontologies are usually understood as upgraded conceptual models, often without further consideration of epistemic issues—the branch of philosophy that studies the nature, sources, validity, and edges of knowledge. Ontological prisms can reconcile these issues with classical philosophy.

Philosophical schools of thought can be broadly categorized into three main perspectives introduced by ancient Greek philosophers

  • Empiricism, for knowledge achieved through the observation of physical, social, and political facts.
  • Idealism, for knowledge achieved through conscientious conceptual (aka mental) judgment.
  • Rationalism, for knowledge achieved through reason applied to agreed upon symbolic constructs.

These mainstays can be further refined through their overlaps, typically:

  • Phenomenology, for knowledge achieved through the mental representation of perceived physical, social, and political facts.
  • Relativism, for knowledge achieved by projecting judgment on reason.
  • Positivism, for knowledge achieved by experiencing facts through reason.
Philosophical Perspectives

As they stand, these perspectives can also be aligned with Kant’s works on Practical Reason (things), Power of Judgment (concepts), and Pure Reason (categories); or with Spinoza’s learning taxonomy of Senses, Judgment, and Reason, respectively. As a practical counterpart to that philosophical versatility, ontological prisms can also serve as an agnostic knowledge engineering platform.

Ontologies & Reason

Unfolding the shapes of knowledge breaks the opacity of generative AI operations, allowing for transparency (the maps), traceability (the paths), and explainability (from maps to paths).

Explanations bring together correlations (observed facts), causations (based on categories), and interpretations (driven by concepts). Comprehension puts explanation at work in dialogs.

The Shapes of Knowledge

Ontologies & Enterprises

Ontologies are vessels meant to organize knowledge. At enterprise level they can be developed from three sources: conceptual Models, databases schemas, or facts (observations, datasets), and documents.

Ontological prisms are designed to be pragmatic and agnostic. Pragmatic, in order to avoid definitional debates about the nature of ontologies and to focus on how they can be constructed and utilized. Agnostic, in that they support ontologies regardless of representations semantics and lifecycles.

The transition from foundational approaches is materialised by the shift from things to facts, and the mapping of ontologies to systems by the dual representation of facts, categories, and concepts, on the one hand, data, information, and knowledge, on the other hand. While the views are isomorphic and can be switched depending on the issues, the distinction is particularly relevant with regard to knowledge engineering processes.

Management & Engineering of Ontologies & Systems

Processes

Ontological prisms allow for three generic processes supporting:

  • Aristotle’s foundational ontologies, focused on essential concepts (“ur-elements”).
  • Engineering approaches, focused on the categories and taxonomies supporting the representation of specific domains of concern.
  • Frameworks, the primary objective of ontological prisms, focused on the sharing of concepts and representations.
Generic Processes

Language & Representation

Language has always been the underlying subtext of artificial intelligence (AI), whether it’s for implementation (computer languages), communication (user interfaces), or truthfulness (knowledge representation). The comprehensive surge of generative language models (GenLMs) has created a new and powerful momentum that blends communication and representation. The confusion between language and knowledge is further reinforced by the ubiquity of knowledge graphs, which are viewed indiscriminately as both content and containers. Ontological prisms unfold the two roles of languages, communication and representation, allowing for the mapping of semantic layers with knowledge shapes.

Setting apart communication and representation

Forms & Functions

Interfaces

Communication interfaces can be supported by various symbolic and natural languages according to realms:

  • Facts: XML, JSON, DMS
  • Concepts: OWL/RDF, SKOS, SHACL
  • Categories: UML, SysML, Archimate

With language models, Prolog, and SQL supporting natural, logical, and Query languages, respectively.

Likewise, ontological prisms can support functional interfaces addressing:

  • Facts: Data analytics or requirement analysis
  • Concepts: Business analysis and intelligence, strategic planning
  • Categories: Systems modeling and engineering

The Wheel of Knowledge

On a broader perspective, ontological prisms provide both an universal compass and a comprehensive thinking wheel across a wide range of issues, e.g.,:

  • Agents: people, devices, systems
  • Languages: natural, digital, symbolic
  • Cognition: judgement, observation, reasoning
  • Systems: control, boundaries, memory
  • Time: futur, past, present
  • Philosophy: idealism, empiricism, rationalism
A Grid, a Wheel, a Compass

That will ensure the consistency and interoperability of representations.

FURTHER READING

Language, Intelligence, Knowledge

Enterprise Architecture

Modeling Templates