Dear Joe,
You are racing way ahead of me, and maybe down a couple different roads,
but I'll be making a dogged effort to stick with my math-bio-graphical
narrative this time around, and try to tell how I came to climb down
from logical trees and learned to love logical cacti.
As far as the logical ballpark goes, this is all just classical propositional
logic, what my old circle used to call “zeroth order logic”, alluding to its
basemental status for every storey built on it. (But I have since found that
others use that term for other things, so usage varies as it usually does.)
When it comes to semantics, the class of formal or mathematical objects residing
among the referents of our propositional signs, I'm content for most purposes to
say they're all the same, namely, Boolean functions of abstract type f : B^k → B,
where B = {0, 1} and k is a non-negative integer. Although we're likely to have
other sorts of meanings in mind, this class of models suffices for a ready check
on logical consistency and serves us well, especially in practical applications.
The upshot is — I'm aiming for innovation solely in the syntactic sphere,
the end being only to discover/invent a better syntax for the same realm
of logical objects.
To be continued ...
On 12/17/2018 8:36 PM, joseph simpson wrote:
> Jon:
>
> Very interesting.. I look forward to the continuing story...
>
> A common theme that runs through "expert systems", large group discussions,
> and system design discussions is the idea of "cognitive complexity"
> overload.
>
> William Combs addressed the rule explosion associated with binary expert
> systems using a different type of logical rule base (union rule
> combination.)
>
> Lotfi Zadeh addressed a similar issue associated with binary logic using
> fuzzy logic (continuous logical value set.)
>
> Warfield addressed a similar issue in large scale system component
> composition using the concept of controlling dimensions (describe a space -
> enumerate the objects in the space.)
>
> Your work with differential logic appears to blend discrete values and
> continuous values depending on the context of interest.
>
> I would like to see if I can apply your deferential logic to the insurance
> problem outlined by Combs. I am looking for a simple, concrete example
> that I can use to explore your concepts.
>
> One area of interest is the idea of definition. Warfield outlines four
> types of definitions:
> 1: Definition by naming (weakest type of definition.)
> 2: Definition by extension
> 3: Definition by intension
> 4: Definition by relationship (strongest form of definition.)
>
> Definition by relationship creates natural clusters and conceptual
> dimensions.
>
> When we engage and unknown area and start to define this new unknown area
> (or system), we are engaged in the activity of definition.
>
> As pointed out by Kevin Dye, last Saturday, current structural modeling
> techniques have a natural complexity barrier. The structural modeling
> process, for large scale activities, needs to incorporate the concepts
> associated with dimensions, quads and tapestries (all concepts developed by
> Warfield.).
>
> Groups of objects are encapsulated in a quad (identifiable objects.)
>
> Quads may be "woven" into tapestries that depict and define the area of
> interest.
>
> I am working on a new set of code for the January 5th structural modeling
> session.
>
> Some of these more advanced techniques will hopefully make it into one of
> the future versions of the open source structural modeling software.
>
> Take care, be good to yourself and have fun,
>
> Joe
>