The Shaping of Knowledge

Shaping knowledge (Taqi al-Din Ibn Ma’ruf)

Preamble

Geometry & Knowledge

Whether it’s maths, astronomy, or geography, geometry has long driven human discovery — building a proven body of knowledge along the way, and thus establishing itself as an actionable model of knowledge representation. Building on this, ontological frameworks decompose knowledge engineering into three epistemic dimensions: facts as they are observed (extensional knowledge), concepts that structure observations and interpretations (intensional knowledge), and accepted representations (logical knowledge)..

Knowledge Representation

Built upon the Resource Description Framework (RDF), the Web Ontology Language (OWL) has emerged as a dominant standard for knowledge representation, alongside the Simple Knowledge Organization System (SKOS) for thesauri and taxonomies, and the Shapes Constraint Language (SHACL) for constraint specification.

The growing role of knowledge representation in the AI ecosystem has highlighted the need for cross-domain interoperability and, consequently, the benefits of reusing upper or foundational knowledge representations. There is, however, an inherent difficulty in aligning top-down and bottom-up representations — the former compact, stable, and all-inclusive; the latter diverse, changing, and specific.

Ontological Prisms Representation

The aim of ontological prisms is to provide an integrative knowledge engineering framework that distinguishes between knowledge and representation while ensuring the seamless integration of foundational and applied ontologies. To this end, ontological prisms employ an OWL kernel governed by boundaries that enforce an explicit separation of user-defined extensions from the kernel resources. On that account, data properties are exclusively assigned to user-defined domains and applications. Furthermore, constraints and rules are meant to be expressed in line with the Common Logic Interchange Format (CLIF).

By leveraging its RDF foundation, the OWL Kernel can be further extended through SKOS for vocabulary organisation and SHACL for constraint specification.

Ontological Modalities

Objective

Ontological modalities constitute the rational backbone of Prism ontologies. From a philosophical perspective, they may be construed as a declarative counterpart to Aristotle’s taxonomy of substances and accidents. From a knowledge engineering perspective, they provide a principled declarative alternative to imperative inheritance mechanisms.

The aim of modalities is to ascribe intrinsic and functional characteristics to entities targeted for representation. They are defined through predicates and operate within and across ontological realms. Within realms, they enable a seamless integration of foundational and applied representations without coercing the latter into unwieldy inheritance lineages. Across realms, they condition the alignment of ontological designs (categories) with theory (concepts) and empirical experience (facts).

Modalities with OWL

The kernel introduces nine ontological modalities organized into intrinsic (#) and functional (≈) groups on the basis of exclusivity.

For instance, instantiation modality is meant to be uniquely defined for all individuals, compared to the identity principle, which can be combined (e.g. social and temporal) or modified (e.g. from anonymous to social).

Ontological modalities are, notably, optional commitments that knowledge engineers may extend, provided they are consistently defined.

Modalities as Commitments

Unlike foundational types, which impose imperative specifications, modalities are declarative commitments concerning the ontological nature and behaviour of targeted entities. As such, they can be aligned with the relevant upper-level categories and propagated through ontological connectors.

Taking dishes and recipes for examples:

  • The _Recipe concept is characterized by litteral instances and identification.
  • The Dish category, with an intrinsic (#) reference to the _Recipe concept, is characterized by functional identity and digital instance.
  • The [Dish] type is characterized by physical instances and artifact identity.
  • The [CookedDish] type is characterized by reactivity (agency) and timespan (temporality).

Commitments are by design discretionary and may therefore be introduced incrementally at any point during engineering processes. While set across realms, they serve to improve overall consistency, irrespective of levels of abstraction; when set within realms, they serve to ensure coherence across levels of abstraction. For example, instantiation and identification commitments made for [Dish] must apply to its intrinsic (#) subtype [CookedDish], with additional commitments concerning reactivity and timespan.

Representation

The comprehensiveness and versatility of OWL make it the preferred tool for representing complex domains of knowledge, though less so for their validation. However, that can be achieved with two kind of extensions, SKOS and SHACL on the one hand, or CLIF and the Prolog language on the other hand.

Modalities as Shapes

Leveraging the shared RDF basis, OWL modalities could be jointly represented by SHACL shapes, for instance:

ex:∆Agency
	a owl:Modality .

ex:AgencyShape
	a sh:NodeShape ;
	sh:targetClass ex:Entity ;
	sh:property [
	...
	] .
However, while that would allow for a conceptual alignment of modalities and shapes, it would come with redundancies between OWL and SHACL representations, and significant additional programming. Using the Prolog language would mitigate both.

Modalities as Predicates

Set with the OWL kernel, modalities can be represented as predicates such as modality(_Recipe, instance, digital) or modality(Dish, agency, reactive). Such predicates could be defined according to the Common Logic Interchange Format (CLIF) and implemented through the Prolog language.

modality(opLog,#,dish,idenMod,funct).
modality(opLog,#,dish,instMod,digit).
modality(opInt,#,recipe,idenMod,litter).
modality(opInt,#,recipe,instMod,litter).
modality(opExt,#,[dish],idenMod,artif).
modality(opExt,#,[dish],instMod,phys).
modality(opExt,#,[cookDish],idenMod,artif).
modality(opExt,#,[cookDish],idenMod,phys).

Shapes & Patterns

Shapes can be defined from two perspectives: empirical, where they are observed, and formal, where they are defined by symbolic constructs. Patterns occupy the crossroads between them — empirical shapes that admit formal representation.

Individual Patterns

Ontological prisms introduce three empirical shapes — profiles, blueprints, and templates — anchored respectively to facts, concepts, and categories. Formal shapes are uniformly defined in terms of modalities.

For instance, a ∆Role blueprint would be committed to symbolic identity and instance, as well as some agency and temporality. It will also come with an intrinsic reference to _Organization and functional ones to _Actor.

These four levels of commitment — specific modality, open modality, intrinsic connector, functional connector — allow for fine-grained sharing and reuse of verified elements.

Crossed Patterns

Individual patterns are not necessarily hierarchical and can be defined indirectly through elements partially committed. For instance, a ∆LegalEntity blueprint entails direct commitments for ∆SymbolicInstance, ∆SocialIdentity, and ∆SymbolicCom; the blueprint is exclusively decomposed into _Organization and _HumanAgent concepts characterized by non ∆PhysicalInstance and ∆PhysicalInstance commitments, respectively.

Combined Patterns

Combined patterns are containers used to characterize domain-specific, conceptual, or logical contexts. They are composed of individual patterns and may also include specific elements. In the case of combined patterns, the commitments are not about individual modalities but about their consistency.

While the targets of combined patterns are meant to be set in the same realm, their branches can be set across. For instance, a business transaction profile is meant to be applied to domain-specific contracts with providers. The type [contract] is meant to be aligned with a ∆Contract profile while the type [Provider] is meant to be defined in reference to an existing Party category, itself characterized by a ∆LegalEntity blueprint.

Benefits

The benefits of modality-based patterns for knowledge engineering operate at two levels — global learning, in terms of plasticity and versatility, and local reliability, in terms of quality and resilience.

Versatility & Plasticity

Versatility and plasticity are the modality counterparts of specialization and generalization in abstraction.

Versatility allows domain-specific ontologies to be developed without disturbing foundational commitments. This can be achieved in two ways: by completing partially defined patterns — adding temporality to ∆LegalEntity, for instance — or by extending the scope of modalities already defined, such as adding natural language to the symbolic communication of human legal entities.

Plasticity is the ability to widen foundational commitments without affecting existing domain-specific ontologies. Where versatility operates on the refinement of modalities, plasticity operates on the consolidation of patterns — for instance, introducing a ∆Party pattern to integrate the representation of [Provider] and [Customer] types

Furthermore, versatility and plasticity — as declarative alternatives to the specialization and generalization of imperative inheritance — deliver on the promises of object-oriented design more effectively than inheritance itself.

Quality & Resilience

Leveraging modalities and patterns to achieve OO objectives would ensure that representations have only one reason to change — through versatility and fine-grained modality changes — and remain open for specialization but closed for modification — by enforcing the distinction between modality changes (specialization) and pattern changes (generalization).

This would allow the semantics of higher levels — enterprise or corporate — to be defined independently of those at lower levels — domains — ensuring that domain semantics, consistently though not necessarily uniformly defined, remain interoperable.

Finally, applying these principles separately to environments (facts), intents (concepts), and realizations (categories) would enable diachronic knowledge representations, supporting the integration of engineering processes regardless of their life cycles.life cycles.

References

Caminao

External