The book will be released in August
Taking a leaf from Stafford Beer’s Brain of the Firm, ontological prisms introduce a 3D geometry of knowledge allowing for a seamless integration of knowledge engineering for enterprise and agentic systems.
Synopsis
The expansion of generative AI has highlighted the limitations of purely neural approaches and the benefits of coupling them with symbolic counterparts epitomized by ontologies. While knowledge graphs emerge as the jack of all trades among agents dealing with language, knowledge, and orchestration, there is little consensus on the sources and roles of ontologies, in other words, knowledge.
The book introduces ontological prisms, a game-changing paradigm that unfolds the geometry of knowledge into a triptych of observed worlds (facts), meanings (concepts), and shared representations (categories). This approach entails three major breakthroughs with regard to:
- Interoperability: by establishing a principled and actionable distinction between communication (language) and representation (knowledge), ontological prisms provide a blueprint for semantic and conceptual layers set across heterogeneous representations.
- Abstraction levels: leveraging the three-pronged paradigm, ontological prisms untangle the abstraction conundrum between upper (or foundational) and lower (or domain-specific) level ontologies. This allows for a smooth, declarative integration of ontological abstractions without imposing unwieldy inheritance hierarchies.
- Temporality: the epistemic distinction between worlds (facts), intents (concepts), and representations (categories), combined with differentiated abstraction semantics, enables diachronic knowledge management alongside concurrent engineering processes, regardless of domain overlaps and misaligned life cycles.
These advances allow for a seamless integration of knowledge engineering between agentic and enterprise systems: facts, categories, and concepts for the former, mapped to data, information, and knowledge for the latter, respectively. That knowledge-driven integration of cognitive and systems capabilities paves the way to a holistic approach to collective learning weaving together individuals, organizations, and systems.
The book is organized into three parts: principles, foundations, and architecture; cognitive functions: language, reasoning, and judgment; and systems and knowledge engineering. The third part introduces the KEOPS (Knowledge Engineering with Ontological Prisms) methodology, accompanied by a kernel developed with OWL/Protégé.
This organization allows for differentiated readings for graduates, engineers, and consultants, ensuring a comprehensive understanding of agentic cognition, knowledge engineering and ontology development, as well as business intelligence and decision-making systems.
Keywords
Ontological prisms, knowledge geometry, knowledge representation, knowledge engineering, agentic AI, complexity, entropy, semantic layers, enterprise architecture, conceptual models, knowledge graphs; data management, owl, cognition, decision-making, thesauri, taxonomies.
Abstracts
Chapter 1
Chapter one examines ontological prisms in the context of the evolution of artificial intelligence (AI), particularly concerning neural and symbolic pathways and the role of language. The section concludes with the rapid and widespread advancements in generative language models along the neural pathway, their inherent limitations, and the necessary complementarity of ontologies along the symbolic pathway. The two main approaches to ontologies are considered: foundational (or upper-level) and empirical (or domain-specific). The challenges of bridging the gap between them, particularly in terms of reusing upper-level abstractions, are also discussed.
The last section introduces ontological prisms in both formal and pragmatic terms. The formal perspective relies on the semiotic distinction between things, signs, and symbols. This distinction provides the foundation for the prism blueprint developed in the book. The pragmatic considerations emphasize the necessity of ensuring the interoperability and temporality of heterogeneous representations.
Chapter 2
Chapter two describes ontological realms: extensional (facts), intensional (concepts), and logical (categories).
Extensional realms encompass all facts (objects, events, or activities) that can be observed in physical or symbolic environments: individuals, datasets, databases (managed individuals), and documents. Generative language models are introduced to explain why documents are best addressed as recorded facts.
Intensional realms pertain to mental representations and correspond to the Aristotelian understanding of ontologies, which aim to address the substance of things, specifically their intrinsic and functional qualities. Aristotelian qualities are used to define ontological modalities.
Logical realms address shared symbolic representations and thus correspond to traditional modeling approaches epitomized by conceptual, logical, and physical models. The chapter emphasizes the differences between the modeling semantics at work in ontological realms: intensional models pertain to abstractions but not to instances; extensional models pertain to instances but not to abstractions; and logical models pertain to both abstractions and instances.
Connectors are defined at the ontological level (intrinsic or functional) using parthood semantics for facts and concepts, object oriented semantics for categories.
The last section introduces ontological modalities as a declarative alternative to the imperative inheritance of foundational approaches. Ontological modalities are stereotypical commitments regarding foundational qualities such as the identification principle, instantiation, life cycle, agency, or veracity. As such, they can be uniformly applied to domain-specific (extensional), organizational (intensional), or systems (logical) constructs.
Chapter 3
Chapter 3 delves into the mechanics of ontological prisms and examines the roles played by thesauri, taxonomies, and domains in ensuring the alignment, integration, and interoperability of heterogeneous ontologies. Heterogeneity is addressed from three perspectives: semantic layers (nominal, formal, deontic, empirical), abstraction models (parthood, inheritance), and engineering processes (knowledge life cycle).
Alignment is discussed at domain level in relation to emerging changes (abstraction), designed changes (realization), and organizational changes (temporality). Interoperability is discussed at the enterprise level in terms of transparency, traceability, and accountability. The focus is thus placed on the interoperability of knowledge engineering processes achieved through perceptions (facts and concepts), projections (concepts and categories), and experience (categories and facts). The chapter concludes with the benefits of a holistic approach to interoperability for collective learning and intelligence.
Chapter 4
Chapter 4 addresses the governance issues associated with ontological prisms in relation to four key dimensions: the institutional status of environments and enterprise architecture layers, value chains, regulatory compliance, and complexity management.
Exchanges with environments are categorized based on status, scope, and modalities of change: institutional, professional, corporate, social, and personal. Conversely, enterprise architectures are examined from an ontological perspective, with the traditional layers—platform, system, and organization—neatly aligned with the ontological dimensions of data (facts), information (categories), and knowledge (concepts), respectively.
Value chains are analyzed through ontological prisms, allowing for their segmentation based on knowledge contributions, which are defined by transaction costs. These costs are used to compare the expense of resources—whether priced internally or by markets—with expected returns. The issue of knowledge value chains is illustrated through intellectual property. In the case of copyrights, the benefits of ontological prisms arise from representing creative works as singular entities, based on taxonomies, and nominal entities, based on thesauri. For patents, the representation of patents leverages three ontological crossroads: thesauri, which differentiate between the actual and symbolic scope of patents; domains, which distinguish between intent and patented content; and taxonomies, which separate patented content from its utilization.
Finally, ontological prisms are used to assess governance in terms of extensional (2D) and intensional (3D) complexity management. The former addresses facts only, while the latter addresses both facts and objectives. Drawing from cybernetics, entropy is then introduced to characterize the objectives of complexity management.
Chapter 5
Chapter 5 examines the role played by language in the development of knowledge.
First, ontological prisms are used to clarify the fundamental traits of language: signs vs. symbols, communication vs. representation, direct vs. mediated communication, and grammars vs. semantics.
Next, ontological prisms are employed to introduce a functional approach to generative language models (GenLMs). Two main issues are considered: the inherent limitations of GenLMs, which are designed to process pre-defined words (tokens) detached from reality and cannot be expected to go beyond nominal reasoning; and the need for GenLMs to collaborate with cogent and cognizant agents to whom they can delegate knowledge-intensive tasks. Both cases highlight the benefits of a knowledge-based architecture with ontological prisms at its core.
The last segment addresses the role of language in knowledge-based architectures. Returning to the distinction between direct and mediated communication, semantics are analyzed through ontological prisms, redefining layers in terms of conversational and contextual semantics.
Chapter 6
Chapter 6 uses ontological prisms to deconstruct reasoning processes in relation with evidences, intents, and logic.
The chapter begins by framing the scope and paths of reasoning in terms of facts, concepts, and categories, and then provides a quick overview of nominal, propositional, and predicate logic.
Reason is addressed at a functional level, typically distinguishing between correlation and causation, and at a cognitive level, typically distinguishing between interpretation, explanation, and comprehension. This two-pronged analysis is used to assess the reasoning capabilities of generative language models and to explain their hallucinations.
Empirical and analytical reasoning processes are then discussed in relation with driving profiles: evidence, interpretative, and controversial reasoning.
Finally, the last segment examines the interplay of reason and knowledge from two key perspectives. First, reasoning through heterogeneous ontologies, defined in terms of empirical, semantic, and deontic inferences. Second, collective reasoning, defined in terms of collaboration, supporting systems, and learning organizations.
Chapter 7
Chapter 7 considers the benefits of harnessing ontological prisms in enterprises’ decision-making processes.
Decision-making is first defined in relation to reasoning and problem-solving. Unlike reasoning, which pertains solely to symbolic realms, decision-making is intended to affect environments, whether or not it is supported by reasoning. Unlike problem-solving, confined to atemporal and bounded spaces, decision-making operates within open contexts, carries ambivalent semantics, and involves interested parties who are committed to and accountable for actual operations and time frames. Intrinsic dimensions of decision-making can thus be outlined in terms of issues, parties, processes, problem and solution spaces, and time frames.
Intrinsic dimensions are then put through ontological prisms and used to address transparency, traceability, and accountability, leading to decision-making templates characterized by processes (one-sided, collaborative, adversarial) and the predictability of environments (deterministic, stochastic, strategic).
The OODA (Observation, Orientation, Decision, Action) loop serves as a reference for the integration of iterative decision-making processes with knowledge management, a key component of the agentic AI collaborative architecture.
The chapter concludes with the assessment of the proposed approach with regard to learning curves and complexity management.
Chapter 8
Chapter 8 considers the benefits of ontological prisms for enterprises embedded in digital ecosystems.
Using the Pagoda blueprint as a reference for enterprise architecture, four levels are identified for requirements capture and elicitation: business, function, user, and system. Requirements units are then defined according to Aristotle’s three unities principle for action (roles), time (events), and space (location). These requirements units are anchored to ontological prisms, and taxonomies used to untangle variants and rules, mapping rules’ conditions (the rules’ domain) and actions (the rules’ co-domains) with empirical (facts), deontic (concepts), or logical (categories) realms.
Addressing engineering processes through ontological prisms enables a flow-based definition of work units, and thereby bottom-up, model-based engineering workflows. In line with the imperative of continuous change, processes can thus conciliate two different time frames. One, driven by changes in architectural assets that are intended to be shared and stable; the other, driven by specific business opportunities. Stand-alone developments, which do not affect shared resources, are set in time capsules.
Finally, using ontological prisms allow for a distinction between intentional validation of models (between concepts and categories), and extensional verification of systems (between categories and facts). Test cases can be designed accordingly, aiming at endogenous flaws (scripted tests) or exogenous disruptions (generative tests).
Chapter 9
Chapter 9 describes the Knowledge Engineering with Ontological Prisms (KEOPS) methodology.
First, KEOPS’ core principles are established: an iterative process that traverses the extensional, intensional, and logical realms; and incremental development that weaves intrinsic and functional threads into the knowledge fabric.
Second, the chapter examines how ontological modalities provide a declarative alternative to imperative inheritance in addressing abstractions, ensuring a seamless integration of foundational and domain ontologies without resorting to cumbersome and ineffective lineages. This is achieved by combining modalities into blueprints (intensions), profiles (extensions), and templates (categories).
The third major issue addressed by KEOPS relates to the unstructured, porous, and shifting nature of knowledge deliverables. The KEOPS solution is to revisit use cases in relation to their impact on knowledge architecture, and more specifically, ontological prisms. Actionable knowledge can thus be framed by the nature of commitments made by use cases: committed (domain-specific or unbounded, homogeneous or heterogeneous) or uncommitted (exploratory or functional).
Finally, KEOPS resets the engineering of knowledge from the perspective of agentic architectures that support the collaboration of AI agents. Assuming that knowledge-driven collaboration cannot operate sequentially, agentic AI must rely on conversational loops, which combine direct conversation (experience), integration of contexts (perceptions), and anticipations of further developments (projections).
Chapter 10
Chapter 10 introduces an online OWL/Protégé kernel that supports the KEOPS methodology. This kernel relies solely on core OWL features, allowing for maximum flexibility for users’ customized extensions without the risk of confusing overlaps.