Avril and Ferenc, (01)
AS> Always when it is said that a real-life application uses something
> infinite, it in fact uses only the potential infinite. (02)
Yes, indeed. Unless I am specifically talking about Cantor's work
and later developments based on it, I always use the term 'infinite'
in its original sense of 'without boundary'. No computer program or,
in fact, nothing in the universe can contain anything that remotely
resembles a Cantorian set -- not even a countable set, let alone the
hierarchies of infinities. (03)
The only point I was trying to make is that there are good reasons
for explicit boundaries as small as 1, 8, or 64 bits. And the Common
Logic standard avoids any commitment to any choice of boundary. (04)
FK> What is the grammar of logic? You consider those two
> representations to be leading the same conclusion, but they do
> not have the same content. Or is content conclusion? (05)
The terms 'form' and 'content' are informal terms, which can be made
precise only within a formalism of some kind. (06)
If you want to get into the details, we have to make the topic
specific by formulating it in a more detailed framework. The most
general framework for such issues is Peirce's semiotic, but I'll
just present a brief summary: (07)
The two terms 'form' and 'content' are the beginning of a triad.
Form is the first, which addresses only the pattern on the page
-- either linear or graphic. It does not consider anything beyond
what you see immediately in front of you. Content is second, which
addresses the relations between that pattern and whatever subject
matter it refers to. The third is the purpose or the pragmatics
of why you are making that statement and what goals you hope to
achieve by means of it. (08)
FK> What is the grammar of logic? (09)
If you want to address that issue in general, you need to use
category theory (in the mathematical sense). For specific examples,
I'll use Common Logic, which is defined in terms of an abstract
syntax that is independent of any concrete realization. (010)
The simplest logical operator is the conjunction of two statements
p and q. The grammar of the CLIF dialect represents it as (011)
(and p q) (012)
The grammar of the CGIF dialect is even simpler, because it follows
Peirce's graphs, which assert the conjunction of everything written
on a "sheet of assertion". Therefore, conjunction in CGIF is just (013)
p q (014)
In this example, p and q represent abstract (notation independent) CL
statements, each of which has some content that must be realized in
whatever concrete notation is used -- in this example, CLIF or CGIF. (015)
The abstract syntax of CL states that conjunction applies to a *set*
of arguments -- i.e., there is no implicit ordering among them. In
a 2-dimensional graph notation, there is no implicit order. But in
a linear notation, such as CLIF or CGIF, the arguments are listed
in some order. But the CL semantics does not depend on that order
in any way -- all possible permutations are logically equivalent. (016)
We can continue in this way to describe the form of all the features
of CL. The model theory in the CL standard defines how the abstract
form of a CL statement is related to some abstract model M of the
subject S. That model consists of abstract sets, whose elements
represent actual entities in the subject domain. (017)
The content of a CL statement p is a pattern of relationships in
the subject S, which is determined by the CL model theory. If that
pattern happens to be in S, then p is true. If not, p is false. (018)
However, the CL standard does not address the pragmatics of the
statement -- i.e., what do you intend to do with it and why.
That is very important, but it's outside the scope of the
ISO/IEC International Standard 24707. (019)
FK> Before the Big Five were merged I worked for all of them separately.
> I had a piece of software (under DOS) of my own development to align
> those terms being party different with each. It was especially
> important in translating Financial Statements to and from English/
> Hungarian. But that is not the main issue. (020)
That is excellent background for anybody who is working on practical
problems of using ontologies in real applications. (021)
FK> The main issue is synchronization and not just the alignment of
> data.... (022)
Those are very important issues, but they don't affect the distinction
between form and content. (023)
John (024)
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