Abstract for AISB 2000: How to Design a Functioning Mind
AUTHOR Dr. Zippora Arzi-Gonczarowski, Typographics, Ltd.,Jerusalem
TITLE: A blueprint for a mind by a categorical commutative diagram
A unified ontology that is applied to various intelligent
capabilities and skills may help combine them in a fully
functioning mind. That ontology should be able to capture some
essence of mind processes, yet it should avoid over determinism
and be general enough for its eclectic purpose. Mathematical
category theory typically provides formal tools to capture a
structural essence without being over deterministic. Based on
these tools, the category of artificial perceptions has been
conceived and proposed as an infrastructure for a theory of AI
processes, and it is further proposed to design a high level AI
architecture on the basis of the ontology provided by that
The basic objects of the category are snapshots of perceptual
states. Each consists of perceiving an environment, producing
responses, and recording the experience in an internal structure.
The internal structure serves as a basis for further processes,
thoughts and deliberation. Streams of perceptual states are
formed through transitions that are formalized by morphisms (and
further categorical constructs such as natural transformations).
Any one of the elements that make a perceptual state (i.e. the
internal structure, the environment, or the responses) could be
modified along paths to other perceptual states.
The schema has already been applied to model, besides the
perceptual states themselves, various cognitive-affective
processes. These include, among others: adaptations,
interpretations, analogy making, communications, joining
perceptions (with various degrees of partnership and trust). A
significant family of transitions involves the formation of
complex internal structures, such as acutely perceptive mental
representations that could layer on top of basic observations.
These complex structures provide a bridge for scaling up to
higher-level, rational and emotional, capabilities (e.g.
reasoning, creative planning, integrated behaviour management,
and autonomous regulatory control).
The unified theoretical standard underlying the various processes
enables a rigorous interweaving and integration of all of them in
one formal `mind'. Distinct processes and capabilities enhance
one another rather than interfere with one another, making a
whole that is more than the sum of its parts. The technical tool
for the integration is the category theoretical typical way to
describe equational reasoning: a commutative diagram. This
highlights the computational nature of the formalism. The
commutative diagram provides a tentative high level `blueprint'
for the eventual programmed design of a functioning `mind'. A
study of the mathematical properties of the commutative diagram
provides further systematizations of intuitions about minds and
intelligence: boundary conditions, terminal objects, and a
categorical fixed point show how perception, in its broadest
sense, both enables and bounds the capabilites of the `mind'.
Structural symmetries provide insights into similarity of
Autonomous action tendencies, e.g. emotions, are fomalized as the
natural engines of mind vitality: they impel actual performance
of transitions between perceptual states. If the diagram provides
a `blueprint of the circuits', then this is the actual `current'.
The rather minimalistic categorical setting provides a unified
ontology. Like a reduced instruction set for a computer, it
conflates the types of building blocks that are required for a
high level architecture, but not necessarily the spectrum of mind
processes that are modeled. The formalism enables a rigorous
distinction between quite a few types of mind processes and
autonomous action tendencies, yet they are all integrated in a
The research is in progress, and part of it has already been
2. CV and publications.
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Orlando, Florida, October 1998. (AAAI Press technical report
Introducing the Mathematical Category of Artificial Perceptions.
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