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C00002 00002	approx[f86,jmc]		Approximate theories - epistemological approximation
C00004 00003	approximations
C00006 00004	Qualitatively Approximate theories
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approx[f86,jmc]		Approximate theories - epistemological approximation

We need a formal notion of epistemological approximation of one theory
to another.  In general the inference probably should include non-monotonic
inference.

Let T1 and T2 be two theories, and we want to say that T2 approximates  T1
epistemologically.  Let  T1  and  T2  have distinct vocabularies for
simplicity.

	P1 ∧ P2 ⊃ Q12

Concepts Defined via Approximate Theories

Some important concepts for AI including "it can", "it believes" and
counterfactuals may be precisely definable in theories that approximate
reality in a generalized sense.  Useful approximate theories of action are
typically non-deterministic even when they approximate deterministic
systems.  The concepts are useful to the extent that the approximate
theory answers questions about the real world, but they often become
imprecise when attempts are made to define them directly in real world
terms.  The lecture will discuss the sense of approximation, give
some examples, and make connections with the previous discussion of
contexts.  Some of the material is discussed in my paper "Ascribing
Mental Qualities to Machines".

approximations

the bacteria in the container as an object

the skiiing example

A concept precisely definable in an approximate theory takes its general
thought meaning from this theory.  Natural language meanings are
by-products of thought meanings.

Devika Subramanian asked for a simpler example than skiing.

Pressure and temperature are approximations to statistical mechanics.

The U.S. wants the hostages released.

The Reagan Administration wants the hostages released, so it is
not surprising that the Reagan Administration arranged to get
them money for arms when Congress didn't want to appropriate it.
Saying this does not require knowing of the existence of Lt. Col.
Oliver North or knowing exactly what Reagan and Shultz knew or
thought they were authorizing.

What about an AI example closer to the blocks world?  We abstract
away the shapes of the blocks.

Amarel model of missionaries and cannibals.

General theorems about approximate theories are probably best obtained
in the context of one theory approximating another.

The model of ability in McC and Hayes.  What view should we program
a robot to take of its own abilities?
Qualitatively Approximate theories

The main points:

1. Many concepts that intelligent programs must use are best treated
as defined in approximate theories.  These include causality, can,
and the counterfactuals used in learning from experience.

2. The approximate theory is validated by its many correspondences
with reality.  The single sentences of causality, etc. many not
be independently validatable.  I ascribe many of the philosophical
difficulties to this phenomenon.

3. The main reason for specific approximate theories is epistemological
adequacy and also actions available.  In the skiing example, the
ski instructors (or a future ski instruction robot) don't have
information about what goes on inside the skier, nor can they
expect to influence the skier's internal state directly.  Therefore,
their ability to observe and affect the world makes a certain
approximate theory of skiing appropriate.

4. Many important contexts are based on approximate theories implicitly
assumed.

5. The correct sense of approximation is that under conditions of
validity of the approximation, the theory gives qualitatively correct
conclusions.  However, we often need to store wffs of the approximate
theory including terms that have no definitions outside the approximation
and apply them later to get conclusions in world.