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Re: [ontolog-forum] What is logic?

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Fri, 09 Mar 2007 13:27:35 -0500
Message-id: <45F1A717.1080702@xxxxxxxx>
John F. Sowa wrote:    (01)

> I changed the subject line of this thread.    (02)

To put it mildly. ;-)    (03)

>> Ontology and logic are different subjects.      (04)

Fully agree, which apparently doesn't prevent us from discussing the latter 
without regard to the former.    (05)

>> But I
>> would add that *every* precise declarative notation that is
>> capable of making statements that are judged true or false
>> *is* a version of logic.    (06)

This makes "version of logic" a subcategory of "notation", which we must 
understand to be "the formal representation of a meaning", as distinct from 
the "expression" part of the representation (relationship).    (07)

The notion of "logic" as "a process of reasoning" is, therefore, a *different* 
concept from John's "version of logic".  These two ideas are related, in the 
sense that certain elements in the notation (language) are needed in order to 
enable certain reasoning processes (and the presence of certain combinations 
of elements in the notation can render the reasoning process meaningless).    (08)

Aristotle carefully coupled these two notions.  John seems to be deliberately 
separating them.  But wait, there's more...    (09)

>> UML diagrams, for example, are a version of logic.     (010)

Yes, as a set of formal declarative sentences.
The question, however, is what reasoning process is *defined to be* coupled to 
the UML formal notation.  If you look at the UML standard (and discard the 
noise), you will find that there is a defined reasoning process, but it is 
almost entirely based on subsumption -- there is no general support for modus 
ponens, for example, until you add OCL.    (011)

>> The declarative subset of natural languages forms a version of
>> logic -- and in fact, NL (actually Greek) was Aristotle's
>> inspiration for the first formal logic.     (012)

Yes.  And (most?) natural languages support many reasoning processes, because 
they have if/then structures and type/instance notions, and so on.    (013)

>> And *every*
>> statement in *every* version of logic that anyone has
>> ever invented can be translated into natural language.
>> So anyone who is doing any work on ontology is stating
>> their results in some version of logic (but possibly in
>> a rather imprecise and insufficiently understood version).    (014)

 From the above, I read this to say:  Anyone doing any work on capturing 
meaning as a set of formal relationships among concepts denoted by terms is 
stating their results in formal declarative sentences.    (015)

I don't have a problem agreeing with that.  I wonder why John bothered to say 
it.  When John uses the word "formal", perhaps it carries baggage other than 
"having carefully defined and specialized meanings", such as the ability to 
express certain concepts fundamental to a reasoning process, and an 
interpretation that supports that process.    (016)

> PD> My, what a large definition of logic you have.    (017)

My sentiments exactly.    (018)

> That's the traditional definition, which goes back to Aristotle.    (019)

As I mentioned above, Aristotle definitely coupled the reasoning process to 
the careful use of the language that supports it.  John's definition above 
failed to mention that, but apparently he meant to:    (020)

> Historically, logic evolved from language.  Its name comes from
> the Greek logos, which means word or reason and includes any
> language or method of reasoning used in any of the -ology fields
> of science and engineering.  Aristotle developed formal logic as
> a systematized method for reasoning about the meanings expressed
> in ordinary language.    (021)

And in particular, from declarative statements that involved certain 
particular constructs, like if/then and type/instance associations and 'every 
X <verb> Y' and so on.    (022)

And on the other side of the world, in the same time frame, one sees the 
introduction of reasoning from natural language that Aristotle would have 
found very confusing.  About 330 B.C., Gung-Sun Ze wrote:
"'A white horse' is not 'a horse'.  Not every statement that is true of a 
horse is true of a white horse.  A horse can be black."    (023)

The point is that the formalism of the natural language depends on the 
intended interpretation under a reasoning process.  And this is true of any 
formal declarative language, including those which report observations with no 
clearly intended reasoning process at all.    (024)

> In modern terms, a logic may be defined as any precise notation
> for expressing statements that can be judged true or false.  To
> clarify the notion of "judging," Tarski defined a model as a set
> of entities and a set of relationships among those entities.
> Model theory is a systematic method for evaluating the truth
> of a statement in terms of a model.    (025)

Yes, one can smuggle in the concept of interpretation under a process as 
"judging truth or falsity", but I think Tarski called it "interpretation".    (026)

> But Tarski quoted Aristotle as a basis for his approach, and
> he claimed that he was formalizing the informal methods.    (027)

Hardly a surprise, since Tarski provided a formalization for validating the 
results of the Aristotelian reasoning process.    (028)

> John the Evangelist had an even larger definition:
>     "In the beginning was the logos, and the logos was with God,
>     and God was the logos.  It was in the beginning with God.
>     All things (panta) came into being through it, and without it
>     nothing that has come to be came into being."
> In short, being (to on) depends on the logos.  Therefore, the
> study of being (ontology) must depend on logic (the study
> of the logos).    (029)

In spite of certain elements of my education, I would never presume to 
interpret the intent of 'logos' in John 1:1.  As I remember it, John 1:1 said: 
"THE/THAT logos was THE theos" = That Concept was God.  Fortunately, we don't 
have to believe that, or even understand it, in order to work on the 
development of ontologies and reasoning systems.    (030)

-Ed    (031)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                FAX: +1 301-975-4694    (032)

"The opinions expressed above do not reflect consensus of NIST,
  and have not been reviewed by any Government authority."    (033)

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