Concurrent Ontology and the Extensional Conception of Attribute
Vaughan R. Pratt
Stanford University
January 2009
Abstract
By analogy with the extension of a type as the set of individuals
of that type, we define the extension of an attribute as the set of
states of an observer of that attribute, observing concurrently with
observers of other attributes. The attribute-theoretic counterpart of
an operation mapping individuals of one type to individuals of another
is a dependency mapping states of one attribute to states of another.
We integrate attributes with types via a symmetric but not self-dual
framework of disheaves amounting to a type-theoretic notion of Chu
space over a family of sets of qualia doubly indexed by type and
attribute, for example the set of possible colors of a ball or heights
of buildings. We extend the sheaf-theoretic basis for type theory to a
notion of disheaf on a profunctor, and give a universal representation
of disheaves as dilimits, as an extension of the representation of
presheaves as colimits. Applications for this framework include
the Web Ontology Language OWL, UML, relational databases, medical
information systems, geographic databases, encyclopedias, and other
data-intensive areas standing to benefit from a precise ontological
framework coherently accommodating types and attributes.
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