The book is available on Amazon
Related readings:
- KEOPS
- KEOPS Kernel
- Ontological Prisms & The Geometry of Knowledge
- Enterprise’s New Brains
- Conversations with Claude: #2
A Pragmatic Approach
Ontologies are vessels used to manage knowledge representations; they can be defined using Davis, Shrobe, and Szolovits five basic functions:
1. Surrogates: manage the symbolic representation of objects, events and relationships identified in context and pertaining to concerns.
2. Ontological commitments: maintain a set of consistent statements about the categories represented.
3. Fragmentary theory of intelligent reasoning: support an actionable representation of what the things can do or can be done with.
4. Medium for efficient computation: make representations understandable by computers and support smooth learning curves.
5. Medium for human expression: improve the communication between specific domain experts and generic knowledge managers.
As far as enterprises are concerned ontologies 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).
An Epistemic Frame
Knowledge is meant to be framed by epistemic dimensions: extensional, intensional, or logical. Extensional dimension pertains to reality as it can be observed, intensional dimension to the concepts used to make sense of reality, logical dimension to the symbolic categories used to represent reality.
This frame can be aligned with a revisited Peirce’s semiotic triad of things, signs, and symbols to define models and ontologies, mapping symbolic categories and concepts to things labelled with signs, respectively.
Combining 2D models and ontologies into 3D ontologies introduces overlaps, and thus potential conflicts:
- Between the signs used to map things to concepts and things to categories
- Between the symbols attached to concepts and those attached to categories
Where signs overlap, the conflict is functional: the same sign may label a thing in a taxonomy and name a concept in a thesaurus. Where symbols overlap, the conflict is territorial: the same symbol may fall within different organizational domains.
When these overlaps are dealt with, ontological prisms emerge from a single geometric rearrangement of the things-concepts-categories triad.
An Effective Framework
Despite broad consensus on their pivotal role in agentic AI, the development of ontologies has been caught between two irreconcilable perspectives: the bottom-up, trying to build ontologies from data models, and the top-down, trying to force siloed ontologies into foundational concepts.
The way out of this conundrum is found in two sentences from Wittgenstein’s Tractatus Logico-Philosophicus that prove uniquely relevant here.
“The world is the totality of facts, not of things” shifts the ground of inquiry from philosophical essence — what things are — to practical observation — how facts are registered.
“The limits of my language mean the limits of my world” deals a fatal blow to any attempt to model the world from the outside: there is no view from nowhere, no language-independent vantage point from which such models could be built.
Ontological prisms thus become knowledge engineering devices, dynamically aligning:
- categories with symbolic languages
- facts with domain-specific vocabularies
- concepts with natural languages
Concomitantly, ontological prisms rest on two built-in distinctions — knowledge versus language, concrete versus conceptual semantics — critical, respectively, for interoperability across heterogeneous representations and seamless integration between abstraction levels.