Difference between revisions of "Directory talk:Jon Awbrey/Papers/Cactus Language"

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* http://stderr.org/pipermail/inquiry/2005-February/002360.html
 
* http://stderr.org/pipermail/inquiry/2005-February/002360.html
 +
 +
==Alternate Version?  Editing Fragment?==
 +
 +
<pre>
 +
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
 +
 +
In this Subsection, I finally bring together many of what may
 +
have appeared to be wholly independent threads of development,
 +
in the hope of paying off a percentage of my promissory notes,
 +
even if a goodly number my creditors have no doubt long since
 +
forgotten, if not exactly forgiven the debentures in question.
 +
 +
For ease of reference, I repeat here a couple of the
 +
definitions that are needed again in this discussion.
 +
 +
| A "boolean connection" of degree k, also known as a "boolean function"
 +
| on k variables, is a map of the form F : %B%^k -> %B%.  In other words,
 +
| a boolean connection of degree k is a proposition about things in the
 +
| universe of discourse X = %B%^k.
 +
|
 +
| An "imagination" of degree k on X is a k-tuple of propositions
 +
| about things in the universe X.  By way of displaying the kinds
 +
| of notation that are used to express this idea, the imagination
 +
| #f# = <f_1, ..., f_k> is can be given as a sequence of indicator
 +
| functions f_j : X -> %B%, for j = 1 to k.  All of these features
 +
| of the typical imagination #f# can be summed up in either one of
 +
| two ways:  either in the form of a membership statement, stating
 +
| words to the effect that #f# belongs to the space (X -> %B%)^k,
 +
| or in the form of the type declaration that #f# : (X -> %B%)^k,
 +
| though perhaps the latter specification is slightly more precise
 +
| than the former.
 +
 +
The definition of the "stretch" operation and the uses of the
 +
various brands of denotational operators can be reviewed here:
 +
 +
055.  http://suo.ieee.org/email/msg07466.html
 +
057.  http://suo.ieee.org/email/msg07469.html
 +
 +
070.  http://suo.ieee.org/ontology/msg03473.html
 +
071.  http://suo.ieee.org/ontology/msg03479.html
 +
 +
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
 +
</pre>

Revision as of 22:00, 22 January 2009

Fragmata

Cactus Language, Operator Variables, Reflection

NKS Forum (Mar 2005)

Cactus Rules

Inquiry List (Mar 2004)

Ontology List (Mar 2004)

Cactus Town Cartoons

Arisbe List (Dec 2001)

  1. http://stderr.org/pipermail/arisbe/2001-December/001214.html
  2. http://stderr.org/pipermail/arisbe/2001-December/001217.html

Extensions Of Logical Graphs

Ontology List (Dec 2001)

Arisbe List (Dec 2001)

Logic In Graphs

NKS Forum (Feb 2005)

Propositional Equation Reasoning Systems

Arisbe List (Mar 2001)

  1. http://stderr.org/pipermail/arisbe/2001-March/000380.html
  2. http://stderr.org/pipermail/arisbe/2001-April/000407.html
  3. http://stderr.org/pipermail/arisbe/2001-April/000409.html
  4. http://stderr.org/pipermail/arisbe/2001-April/000411.html
  5. http://stderr.org/pipermail/arisbe/2001-April/000412.html
  6. http://stderr.org/pipermail/arisbe/2001-April/000413.html
  7. http://stderr.org/pipermail/arisbe/2001-April/000416.html
  8. http://stderr.org/pipermail/arisbe/2001-April/000417.html
  9. http://stderr.org/pipermail/arisbe/2001-April/000421.html
  10. http://stderr.org/pipermail/arisbe/2001-April/000427.html
  11. http://stderr.org/pipermail/arisbe/2001-April/000428.html
  12. http://stderr.org/pipermail/arisbe/2001-April/000430.html
  13. http://stderr.org/pipermail/arisbe/2001-April/000432.html
  14. http://stderr.org/pipermail/arisbe/2001-April/000433.html
  15. http://stderr.org/pipermail/arisbe/2001-April/000434.html
  16. http://stderr.org/pipermail/arisbe/2001-April/000435.html

Inquiry List (Mar 2003)

Theme One Program : Logical Cacti

Inquiry List (Mar 2003)

Inquiry List (Feb 2005)

Alternate Version? Editing Fragment?

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

In this Subsection, I finally bring together many of what may
have appeared to be wholly independent threads of development,
in the hope of paying off a percentage of my promissory notes,
even if a goodly number my creditors have no doubt long since
forgotten, if not exactly forgiven the debentures in question.

For ease of reference, I repeat here a couple of the
definitions that are needed again in this discussion.

| A "boolean connection" of degree k, also known as a "boolean function"
| on k variables, is a map of the form F : %B%^k -> %B%.  In other words,
| a boolean connection of degree k is a proposition about things in the
| universe of discourse X = %B%^k.
|
| An "imagination" of degree k on X is a k-tuple of propositions
| about things in the universe X.  By way of displaying the kinds
| of notation that are used to express this idea, the imagination
| #f# = <f_1, ..., f_k> is can be given as a sequence of indicator
| functions f_j : X -> %B%, for j = 1 to k.  All of these features
| of the typical imagination #f# can be summed up in either one of
| two ways:  either in the form of a membership statement, stating
| words to the effect that #f# belongs to the space (X -> %B%)^k,
| or in the form of the type declaration that #f# : (X -> %B%)^k,
| though perhaps the latter specification is slightly more precise
| than the former.

The definition of the "stretch" operation and the uses of the
various brands of denotational operators can be reviewed here:

055.  http://suo.ieee.org/email/msg07466.html
057.  http://suo.ieee.org/email/msg07469.html

070.  http://suo.ieee.org/ontology/msg03473.html
071.  http://suo.ieee.org/ontology/msg03479.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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