ONT Re: Apposite Purposes Of Logical Languages Objectified (APOLLO)
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Communication is about sharing experience.
Experience being everything from ecstasy
and enthusiasm to passion and suffering,
its exchange from moment to moment can
amount to the most ambivalent of gifts.
At this particular moment in time, I am trying to share with you
my experiences with a particular family of objects, not all that
exciting in and of themselves, but interesting and useful if you
consider what all they are nevertheless capable of leading up to.
Are nine languages enough to talk about these experiences, these objects?
No, as it happens, I omitted to mention one of the more important of the
bunch, so let me now mention S_0 = Par, the sign domain that consists of
the parse graph data structures, as they form in our mechanical memories
when we parse the RefLog text strings in S_4 = Ref. Now, I cannot write
out here, in this medium, the actual data structures of this sign domain,
and so I shall need to invoke the device of yet another graphical syntax
in order to convey a rough-fitting approximation to their abstract forms.
The species of graphs used is dubbed "painted and rooted cacti" (PARC's).
Here is a Table of corresponding syntax, in Par and in Ref,
for the propositional forms on two variables, in ZOL(p, q).
Table. Painted And Rooted Cacti (PARC's) & RefLog
o---------o----------o------------------o----------o
| Par | Ref | Eng | Tra |
| | | | |
| S_0 | S_4 | S_5 | S_6 |
o---------o----------o------------------o----------o
| | | | |
| o | | | |
| | | | | |
| @ | () | false | 0 |
o---------o----------o------------------o----------o
| | | | |
| p q | | | |
| o o | | | |
| \ / | | | |
| @ | (p)(q) | neither p nor q | ~p & ~q |
o---------o----------o------------------o----------o
| | | | |
| p o | | | |
| | | | | |
| @ q | (p) q | not p but q | ~p & q |
o---------o----------o------------------o----------o
| | | | |
| p o | | | |
| | | | | |
| @ | (p) | not p | ~p |
o---------o----------o------------------o----------o
| | | | |
| o q | | | |
| | | | | |
| p @ | p (q) | p and not q | p & ~q |
o---------o----------o------------------o----------o
| | | | |
| o q | | | |
| | | | | |
| @ | (q) | not q | ~q |
o---------o----------o------------------o----------o
| | | | |
| p q | | | |
| o---o | | | |
| \ / | | | |
| @ | (p, q) | p not equal to q | p + q |
o---------o----------o------------------o----------o
| | | | |
| p q | | | |
| o | | | |
| | | | | |
| @ | (p q) | not both p and q | ~p v ~q |
o---------o----------o------------------o----------o
| | | | |
| p q | | | |
| @ | p q | p and q | p & q |
o---------o----------o------------------o----------o
| | | | |
| p q | | | |
| o---o | | | |
| \ / | | | |
| o | | | |
| | | | | |
| @ | ((p, q)) | p equal to q | p = q |
o---------o----------o------------------o----------o
| | | | |
| q | | | |
| @ | q | q | q |
o---------o----------o------------------o----------o
| | | | |
| p q | | | |
| o---o | | | |
| | | | | |
| @ | (p (q)) | not p without q | p => q |
o---------o----------o------------------o----------o
| | | | |
| p | | | |
| @ | p | p | p |
o---------o----------o------------------o----------o
| | | | |
| q p | | | |
| o---o | | | |
| | | | | |
| @ | ((p) q) | not q without p | p <= q |
o---------o----------o------------------o----------o
| | | | |
| p q | | | |
| o o | | | |
| \ / | | | |
| o | | | |
| | | | | |
| @ | ((p)(q)) | p or q | p v q |
o---------o----------o------------------o----------o
| | | | |
| @ | | true | 1 |
o---------o----------o------------------o----------o
Note. The constant true function 1 : B^2 -> B takes as its
simplest representation in RefLog the blank expression " ",
whose parse graph is the unmarked node "o", or "@" at root,
thus it will often be convenient to render it more visible
in a textual context by using the equivalent form "(())".
That's all that fits for the moment ...
Jon Awbrey
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