SUO: RE: Re: Direct and Indirect Use of Axiom Systems
Dear Jon,
See comments below.
Matthew West
Principal Consultant
Shell Information Technology International Limited
Shell Centre, London SE1 7NA, United Kingdom
Tel: +44 20 7934 4490 Other Tel: +44 7796 336538
Email: matthew.west@shell.com
Internet: http://www.shell.com
> -----Original Message-----
> From: Jon Awbrey [mailto:jawbrey@att.net]
> Sent: 05 July 2003 04:24
> To: SUO
> Subject: SUO: Re: Direct and Indirect Use of Axiom Systems
>
>
>
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
> After some thought, I think that it might be
> good to elaborate on a few of these points,
> especially to point out certain implications
> of the indirect approach.
>
> JA: 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.
>
> JA: For example, consider the case of common sense belief systems
> and the performance systems that depend on them for guidance.
>
> JA: 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 occurring "in the head" or in external action.
>
> JA: 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.
MW: This sounds closer to what we are attempting.
>
> As a matter of fact, the indirect approach allows us to deal with
> a much wider range of object systems than just those that conduct
> themselves like literal deductive systems. For instance, we might
> be dealing with systems of belief and behavior that are configured
> at several different levels and that are composed of many diverse
> components, not all of which are consistent with each other, and
> that interact in non-deterministic ways. Indeed, many of these
> components may not even have all the structure of axiom systems
> but may operate more like automatic associative complexes or
> even very primitive reactive processes.
MW: But I think we are trying to produce one consistent system, rather
than many different views.
>
> For instance, systems of heuristics often have this structure, with
> one sage maxim contradicting the next deep truth, it all depending
> on practical judgment, what the Greeks called "phronesis", I think,
> to decide which rule of thumb applies in which immediate instance.
>
> In light of these possibilities, it might be better
> to revise my description of the indirect approach
> in something like the following way:
>
> 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 literal representations of the initial conditions and the
> transitional processes that take place in the object system.
MW: OK.
>
> JA: 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.
>
> Of course, it is also perfectly conceivable that we will be
> using a mixture of both direct and indirect modalities in
> our models and theories.
MW: I think what we are attempting is a single consistent indirect
model - from your description above.
>
> Jon Awbrey
>
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
>