Connectionists: Ontologies and Neural Networks

[mjhealy@ece.unm.edu]

The paper

M. J. Healy and T. P. Caudell,
"Ontologies and Worlds in Category Theory: Implications for Neural Systems",
Axiomathes, vol. 16, no. 1, 2006

 is available for download at http://www.ece.unm.edu/~mjhealy .

Please let me know if you have a problem with the download.

Abstract:
We propose category theory, the mathematical theory of structure, as
a vehicle for defining ontologies in an unambiguous language with analytical
and constructive features.  Specifically, we apply categorical logic and
model theory, based upon viewing an ontology as a sub-category of a
category of theories expressed in a formal logic.  In addition to providing
mathematical rigor, this approach has several advantages.  It allows the
incremental analysis of ontologies by basing them in an interconnected
hierarchy of theories, with an operation on the hierarchy that expresses the
formation of complex theories from simple theories that express first
principles.  Another operation forms abstractions expressing the shared
concepts in an array of theories.  The use of categorical model theory makes
possible the incremental analysis of possible worlds, or instances, for the
theories, and the mapping of instances of a theory to instances of its more
abstract parts.  We describe the theoretical approach by applying it to the
semantics of neural networks.

Key words:
category, cognition, colimit, functor, limit, natural transformation, neural
network, semantics


Regards,
Mike