Ontology Specification

Definition

An ontology for a conceptualization $\mathcal{C}$ with vocabulary $V$ and ontological commitment $K$ is a logical theory consisting of a set of formulas of $\mathcal{L}$, designed so that the set of its models approximates as well as possible the set of intended models $I_K(\mathcal{L})$ according to $K$.

Approximation and Axiomatic Incompleteness

The language of “approximation” is significant. An ontology does not fully capture a conceptualization but rather constrains the space of models to approach the intended models. This is inevitable: the intensional structure of conceptualizations outstrips what can be expressed in first-order logic (or indeed in most formal languages).

The gap between $\text{Mod}(O)$ (models of ontology $O$) and $I_K(\mathcal{L})$ (intended models) is the measure of our axiomatic incompleteness. A “good” ontology minimizes this gap.

Key Characteristics

• Formal: Expressed in a well-defined logical language (FOL, Description Logic, etc.)
• Explicit: States assumptions and constraints clearly
• Shared: Designed for use by multiple agents or systems
• Specification: Describes what exists in the domain and how
• Machine-readable and processable
• Contains vocabulary (terms) and axioms (constraints)
• Multiple ontologies can commit to the same conceptualization

Components of an Ontology

An ontology typically includes:

1. Vocabulary:

   • Concepts/Classes
   • Relations/Properties
   • Individuals/Instances
   • Functions

2. Axioms:

   • Definitions
   • Constraints
   • Rules
   • Theorems

3. Documentation:

   • Natural language descriptions
   • Examples
   • Usage guidelines

Examples

1. SUMO (Suggested Upper Merged Ontology):

   • Domain: General upper-level concepts
   • Language: Higher-order logic
   • Thousands of terms and axioms
   • Covers entities, processes, attributes, relations

2. Gene Ontology (GO):

   • Domain: Biological gene function
   • Three sub-ontologies: molecular function, biological process, cellular component
   • Widely used in bioinformatics

3. DOLCE (Descriptive Ontology for Linguistic and Cognitive Engineering):

   • Domain: Upper-level ontology
   • Focus: Cognitive and linguistic categories
   • Distinguishes between enduring and perduring entities

4. OWL Ontologies:

   • Language: OWL (Web Ontology Language)
   • Based on Description Logics
   • Used extensively in Semantic Web applications

Relationship to Other Concepts

Conceptualization (abstract, intensional)
         ↓
Ontological Commitment (set of allowed models)
         ↓
Ontology Specification (concrete logical theory)

Multiple ontologies can:

• Share the same ontological commitment
• Commit to the same conceptualization
• Differ in axiomatization, language, or granularity

Design Principles

Good ontology specifications should:

• Clearly capture intended models
• Minimize unintended models
• Be consistent (no contradictions)
• Be complete for intended purposes
• Be computationally tractable
• Be modular and extensible
• Include clear documentation

Key References

The modern formal definition of ontology as a specification of conceptualization originates from Gruber (1993, 1995) and was refined by Guarino (1998) and others in the formal ontology community.

Related Concepts

• formal-ontology - The discipline of building ontologies
• conceptualization - What the ontology specifies
• ontological-commitment - The semantic constraints
• intended-models - What the ontology aims to capture
• intensional-relational-structure - The underlying conceptual structure

Bibliography Keys

• gruber1993translation
• gruber1995toward
• guarino1998formal
• guarino1995ontologies
• niles2001towards (SUMO)
• gangemi2002sweetening (DOLCE)