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"Top-level categories of an ontology are derived from contrasting features that distinguish the entities of a subject domain. Each
distinctive feature is associated with axioms that are inherited by every entity or category of entities that have that feature. A hierarchy of categories can
then be derived as a lattice formed as a product of the fundamental distinctions. This paper develops such a lattice based on philosophical distinctions taken
primarily from the theories of Charles Sanders Peirce and Alfred North Whitehead.
1. Categories, distinctions, and axioms
Ontology is the study of existence, of all the kinds of entities - abstract and concrete - that make up the world. It supplies the predicates
of predicate calculus and the labels that fill the boxes and circles of conceptual graphs. Logic and ontology are prerequisites for natural language semantics
and knowledge representation in artificial intelligence. Without ontology, logic says nothing about anything. Without logic, ontology can only be discussed and
represented in vague generalities. Logic is pure form, and ontology provides the content. The most general categories of an ontology are the framework for
classifying every thing else.
More fundamental than the categories themselves are the criteria for distinguishing categories and determining whether a particular entity
belongs to one or another. Those distinctions are the basis for Aristotle's method of definition by genus and differentiae. Each distinction
contributes a pair of primitive features or differentiae, and the conjugation of all the differentiae for all the genera or supertypes of a compound concept
constitutes its definition.
In his efforts to automate Aristotle's logic, Leibniz assigned a prime number to each primitive feature. Then he represented each composite
concept by the product of the primes in its definition. Leibniz's method of combining primitives generates highly symmetric hierarchies called
lattices. That symmetry, by itself, is not essential to an ontology, but it is an important guide to knowledge acquisition: every combination that is
generated theoretically should be tested empirically to determine whether entities of that type happen to exist. If so, then the combinatorial method may
predict new types of entities and aid in their discovery. If no entities of the predicted type are found, then the combinatorial method may aid in the
discovery of axioms or constraints that rule out those combinations. In either case, the method helps to ensure completeness by directing attention to
possibilities that may have been overlooked or by suggesting new scientific principles that explain their absence.
2. Philosophical foundations
The last two great ontological system builders were Charles Sanders Peirce and Alfred North Whitehead, both of whom were also pioneers in the
development of symbolic logic during the late nineteenth and early twentieth centuries. Although their logic has flourished, their ontologies have been
neglected. Yet the ontologies of Peirce and Whitehead, when combined with logic, can serve as a foundation for AI knowledge representation and natural language