-----Original Message-----
From: Pat Hayes [mailto:phayes@xxxxxxx]
Sent: Thursday, August 02, 2007 1:12 PM
To: Obrst, Leo J.
Cc: [ontolog-forum]
Subject: Re: [ontolog-forum] Current Semantic Web Layer Cake (01)
>Aaargh. The real meaning of the symbolism is defined by its semantics.
>The symbolism of a language, right? The symbols of a language. The
>language has a syntax and a semantics. The syntax enumerates the
>symbols and then gives the rules on how they can combine to form
>expressions (sentences, groupings, etc.) The semantics is the
>interpretation of those symbols and those syntactically legitimate
>groupings of symbols (02)
Right. But... (03)
>(in a formal model). (04)
No, in a MODEL (in the model-theory sense). There
is nothing in model theory which says that
interpretations (a model is just an
interpretation which makes the sentences true, so
I'll use the I-word rather than the M-word to
avoid engineer/logician confusion) are "formal".
There is no reason to suggest that
interpretations come in two flavors, "formal" and
(I guess) "informal". Model theory is itself a
formal - that is, mathematical - theory of
structures called interpretations, but the fact
that the theory is formal does not imply that the
things it is a theory OF are 'formal', in the
sense of 'not really real'. When I count some
change and announce that I have a dollar, I'm
using arithmetic, a formal theory, to talk about
pieces of metal. We do this all the time. I'm not
required to only talk about Platonic things when
using the formal language of arithmetic. (05)
LEO: Ok, I was unclear. In model theory, one does have some kind of
set-theoretic structure, i.e., interpretations. The objects in those
structures can be real things, as you say. (06)
>This is formal semantics for formal languages. (07)
It is a semantic theory, formally expressed,
which can be applied to both formal and natural
language. (08)
LEO: Agree. I just didn't want to fight the NL vs. formal language
battle now. (09)
>Ontology is different. It is the content of a language (languages), or
>equivalently is represented in the language(s). Most often this
content
>is called a collection of "non-logical constants", to set it apart
from
>the "logical constants" of the language (a logic is a language).
>
>As such, the ontology content has formal models in that language
>(languages), and those models are approximately constrained to be
those
>that the ontologist had in mind under his/her conceptualization of a
>portion of the world. So, for example, an ontology that contains cars
>and dogs will hopefully not license models which contain Fido and
>JimBob's1957CandyAppleRedChevyTruck in the same set. The logical
>ontologist is interested in formulating axioms
(class/relation/property
>and instance statements typically) about the content, e.g., Animal is
a
>Class, Person is a Class, the Person Class is a Subclass of the Class
>Animal, etc. Subclass is a Transitive relation. Spouse_of is a
>Symmetric relation. Part_of is more complex and is defined by a set of
>(usually) mereotopological axioms that define Part_of by defining
>Proper_Part_of, etc. These are "content" or "non-logical" axioms (010)
True, but for the benefit of readers not yet
familiar with this usage, all this means is that
these axioms are not logically VALID (ie true in
ALL possible worlds). Which is kind of required
if they are to be of any use at all in describing
a world, since logically valid axioms such as (if
(and p (if p q)) q) only tell you things about
the world that you already know. (011)
LEO: Yes, agree. (012)
>which
>attempt to constrain the set of permitted models (allowed by the
>semantics of the language) to a set of models that approximate the
>conceptualization of the world that the ontologist had in mind. (013)
Right, exactly. And this 'constrain' relationship
between axioms and interpretations is exactly
what model-theoretic semantics is about, and what
it makes precise. (014)
LEO: Agree. (015)
>This is formal ontology, or at least formal ontology refracted by
>ontology engineering. (016)
But the mathematical theory of it, whose results
it depends on, is model-theoretic semantics. (017)
LEO: I agree, but tried to state the usual view of the formal
ontologist, which leads to the following "heartburn". (018)
>Is this clear as water or as mud?
>
>This is why too often ontologists and logicians go at each others'
>throats. (They both have large prehensile mouths that talk around each
>other).
>
>Formal ontologists have heartburn because they see "elephants" and not
>sets. (019)
They *shouldn't* have heartburn. There can be sets of elephants. (020)
>Their focus is on the things of the world, as opposed to the
>things of language (logics, in particular).[1]
>
>There are other definitions of "model". I am only talking about formal
>models here. (021)
Ie models in the model-theory sense, what Im
calling interpretations. Not model airplanes. (022)
LEO: Yes. Model-theoretic: interpretations. (023)
>My guess is that those other definitions of "model"
>largely lead back to this formal definition, whether those "modelers"
>know this or not. (024)
I think in many cases they lead back to an
inverse of it. See Kathryn's recent message in
this thread. (025)
LEO: I think we will see eventual violent agreement. (026)
Pat (027)
>
>Thanks,
>Leo
>
>[1] Languages (logics) have at least a bi-partite "model" (I hesitate
>to say that): syntax and semantics. When you factor in stuff that
we've
>learned from the philosophy of language/linguistics, we think that
>languages have a tri-partite "model": syntax, semantics, and
>pragmatics. (028)
Yes, and maybe more. But the pragmatics only
applies to language used in a certain way, by
intentional agents like you and me. Its not clear
that ontology-language has pragmatics in the same
sense. (029)
>This stuff also suggests that for at least natural
>languages (potentially formalizable as formal languages), there are
two
>notions (relations): 1) sense (a relation between the word and the
>"semantic sense" or "word sense", e.g., "tank" as wordsense1, military
>vehicle), and 2)denotation (what the word refers to once the sense is
>chosen, in the real world). Pragmatics adds a third notion: what did
>the user intend? I.e., semantics in context.
>_____________________________________________
>Dr. Leo Obrst The MITRE Corporation, Information Semantics
>lobrst@xxxxxxxxx Information Discovery & Understanding, Command and
>Control Center
>Voice: 703-983-6770 7515 Colshire Drive, M/S H305
>Fax: 703-983-1379 McLean, VA 22102-7508, USA
>
>
>-----Original Message-----
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Waclaw
>Kusnierczyk
>Sent: Wednesday, August 01, 2007 3:50 PM
>To: [ontolog-forum]
>Subject: Re: [ontolog-forum] Current Semantic Web Layer Cake
>
>Christopher Menzel wrote:
>>> The scopes and subject matters of Ontology and Logic shouldn't be
>>> mixed.
>>> The real semantics or meanings of any symbolism or notation is
>>> defined by
>>> ontology;
>>
>> Silly me, I've been thinking that the real semantics of any
symbolism
>
>> is defined by, you know, its *semantics*.
>
>silly you. i have recently been introduced to a newly designed
>language
>for summarizing the content of scientific publications; when i asked
>about the semantics, the answer was 'the semantics are provided by the
>bioontologies'.
>
>vQ
>
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