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Re: [ontolog-forum] Current Semantic Web Layer Cake

To: "Obrst, Leo J." <lobrst@xxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 2 Aug 2007 12:11:36 -0500
Message-id: <p06230904c2d79ee4a4aa@[]>
>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    (01)

Right. But...    (02)

>(in a formal model).    (03)

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.    (04)

>This is formal semantics for formal languages.    (05)

It is a semantic theory, formally expressed, 
which can be applied to both formal and natural 
language.    (06)

>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    (07)

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.    (08)

>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.    (09)

Right, exactly. And this 'constrain' relationship 
between axioms and interpretations is exactly 
what model-theoretic semantics is about, and what 
it makes precise.    (010)

>This is formal ontology, or at least formal ontology refracted by
>ontology engineering.    (011)

But the mathematical theory of it, whose results 
it depends on, is model-theoretic semantics.    (012)

>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
>Formal ontologists have heartburn because they see "elephants" and not
>sets.    (013)

They *shouldn't* have heartburn. There can be sets of elephants.    (014)

>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.    (015)

Ie models in the model-theory sense, what Im 
calling interpretations. Not model airplanes.    (016)

>My guess is that those other definitions of "model"
>largely lead back to this formal definition, whether those "modelers"
>know this or not.    (017)

I think in many cases they lead back to an 
inverse of it. See Kathryn's recent message in 
this thread.    (018)

Pat    (019)

>[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.    (020)

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.    (021)

>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
>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
>for summarizing the content of scientific publications;  when i asked
>about the semantics, the answer was 'the semantics are provided by the
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>    (022)

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