SUO: Direct and Indirect Use of Axiom Systems
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SUO Working Group,
There are two different ways of using axiom systems to describe an object system,
like common sense, domain knowledge, intelligent conduct, linguistic competence,
linguistic performance, and so on. It has taken three years for this recognition
to precipitate out of a suspension of nagging senses that we are talking in ways
that are radically skew to one another, but I think that I can safely describe it
now as a difference between the "direct" and the "indirect" use of axiom systems.
For example, consider the case of common sense belief systems
and the performance systems that depend on them for guidance.
1. Common sense belief and behavior might be represented directly
as an axiom-based inference system, where the axioms give us
the starting points of belief and behavior and the inference
rules and proof chains provide us with literal simulations
of the processes that apply this knowledge in practice,
whether "in the head" or in external action.
2. Common sense belief and behavior might be regarded as arising
from the states and transformations of an object system, and
this object system might be described by an axiomatic theory,
and yet the relationship of theory to model is more indirect,
in that the axioms and inferences occurring in the theory are
not the axioms and inferences occurring in the object system.
I think that it would help to clarify many of our discussions
if we able to reflect on which implicit model we were using
in each case, and to make a point of making that explicit.
Jon Awbrey
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