Re: Expressions versus the value they represent

On Apr 12, 1:51 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> Keith H Duggar wrote:
> > On Apr 12, 7:09 am, David BL <davi..._at_iinet.net.au> wrote:
>
> >>On Apr 12, 2:37 pm, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
>
> >>>Hopefully we can agree that since there is no interpretation defined
> >>>in the RM nor FOL that there are not "multiple phases" nor "playing
> >>>around" nor any other of the problems above.
>
> >>Yes I agree with that, but I actually want to consider the problems
> >>that arise under interpretations.
>
> > Ok, cool. Thanks for this and the other clarifications. Now I'm
> > a bit clearer on understanding what you are exploring. However,
> > are we agreed that in the context of RM this is what we would
> > call the "physical" layer?
>
> > For example, suppose that we define a particular interpretation
> > that maps the ellipse and circle terms to particular structures
> > say sets over which we define various other axioms (perhaps even
> > including axioms referring to natural (as in physical world)
> > observations. Then I would argue that even though these sets
> > are not bits and bytes they are, none-the-less, "physical" in
> > so far as the RM is concerned. Would you agree?
>
> Are you conflating physical and conceptual?

Maybe. I don't know.

In my thinking from the perspective of the logical layer both the conceptual and physical layers are just "models" ie valid interpretations for the logical layer.

Of course we imagine some "precedence" among them in that we often say the logical layer "implements" the conceptual layer and the physical layer "implements" the logical layer. But, this is just an artificial albeit useful ordering of what are flat role relationships.

Anyhow, it seemed to me that DBL was focussing on a layer used to "implement" certain functions such as equality etc and that layer is not necessarily identical to the conceptual layer.

For example, in the DirectedGraph example I posed it may be the case that the concept domain is optimizing airline schedules, or power distribution, etc and as part of implementing those concepts we choose a relation that has DirectedGraph valued attributes. And we find that isomorphism is the notion of equality we need to implement the functions we need to solve the problems we are interested in.

So in that scenario I would think the "conceptual" layer is the airline schedules or power distribution, the logical layer is the various relations such as the one having DirectedGraph, and the physical layer are the bits and bytes and/or imagined sets (for example integers) and algorithms used to implement the various functions we need.

But, from the perspective or logic, both the airline schedules and the bits and bytes or sets are "interpretations" or "models" of the logical layer.

Anyhow, that's just how I was thinking of the layers in DBLs context. Please let me know if and how this is far off the accepted definitions.

Thanks!

KHD Received on Mon Apr 12 2010 - 20:20:52 CEST