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Re: [ontolog-forum] syntax & semantics

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>, Richard H.McCullough <rhm@xxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Tue, 5 May 2009 21:40:25 -0500
Message-id: <1058BDEA-3F20-4190-B8F1-9A1FD1358F2B@xxxxxxx>

On Apr 28, 2009, at 3:52 AM, Richard H. McCullough wrote:

----- Original Message -----
From: "Christopher Menzel" <cmenzel@xxxxxxxx>
> So philosophers, logicians, computer scientists, linguists, and
> mathematicians since Tarski have all *thought* that what they were
> studying under the rubric "formal semantics" was indeed semantics.  But
> they have in fact all been mistaken; they've only been studying syntax
> all along.  A remarkable discovery!
> Just for the record, since this is a public forum: You haven't the
> slightest idea what you are talking about.
>> Formal semantics looks at the properties of the syntax of a language
>> which do not depend on the actual semantics of the language.
> Utter nonsense.
>> That is why I associate syntax with "possible meaning" and semantics
>> with "real meaning".
> Actually, the main problem is with its missing semantics, as explained
> to you, patiently, on numerous occasions.
> -chris
As you, John, and Pat continue to say -- you don't understand what I mean.
So, I will speak of specifics, instead of abstractions.
Here is a very simple example to illustrate what I mean.
My reference for "formal semantics" is the IKL specification document.

You would probably do better with a textbook or the ISO Common Logic documentation. IKL is rather exotic, and the documentation is minimal. BUt whatever, it probably doesn't really matter.

Consider the English sentence, "Fido is a dog."
[The mKR translation is "Fido isu dog;" ]
The "real symantics" of English [and mKR] tell us that
    a "dog" is a domesticated carnivious mammal, Canis familiaris
    "Fido" is the dog identified by Napa, CA animal control license # 1234.

No, the semantics of English does not tell us that. Not in any sense of "semantics". A competent human native English speaker would not know that about Fido. As for the English meaning of "dog", its not at all clear that it necessarily refers to Canis Familiaris. For example, a competent native speaker of English is not obliged by that competence to know the LInnaean system of biological classification, or even to have the modern concept of species entirely clear. Some English speakers might think that cats can interbreed with dogs: they can still know what "dog" means. 

But I expect that your point is, unless you know what 'dog' means (in some sense), you havn't grasped the full English meaning - the English semantics - of sentences involving the word "dog". And this is of course quite true. And, as you go on to point out, such knowledge (of the meanings of open-class words) is not part of the formal semantics of logics like CL or FOL or IKL. Also completely true. The model theory of FOL is entirely concerned with the meanings of the words that FOL sets out to formalize, which are, pretty much, the English words and, not, or and every, together with what linguists call the cupola, which is one of the common meanings of the verb to be, although that particular verb has a host of other uses as well. 

The IKL translation of this sentence is
(and   (isu_rel Fido dog)   (dog Fido)   (individual Fido)  (property dog))
The "possible semantics" of IKL tell us that
    "dog" is a member of the set of all possible property names.
    "Fido" is a member of the set of all possible individual names.
    "Fido" is an individual which has the property "dog".

No, it tells us that Fido has the property of being a dog. (Note, no quotes.) Indeed - what I expect is your rhetorical point - it tells us nothing about the meaning of "dog" beyond that it is something a thing can be. Which is not a lot, but at least gets us started: if you want more, you have to write some axioms. You have to provide an ontology of dogginess, in fact. Or, more ambitiously, you have to invent a logic of dogginess, a formal language in which the English semantics of "dog" is somehow incorporated into the formal semantic conditions of the logical notation itself. The meta-theory of this dog-logic will have to provide a mathematical theory of dog-hood, and give the semantic conditions as mathematical properties or constraints on the structure of a canine interpretation, so that all valid conclusions about dogs will be entailed, relative to this notion of canine interpretation. That is to say, if B is true in every canine-interpretation which satisfies A, then B is a valid canine-conclusion from A. That is a very tall order, and one that I for one have absolutely no idea how to even begin approaching. Its much easier to stick with the logic we have and try writing some canine ontology axioms in it. 

What you seem to have with mKR is an ad-hoc semi-formal notation (I say semi- because you have never given us a grammar for it) which has no semantic conditions at all, yet which you claim has the same meaning as English. But claims like this are meaningless unless supported by actual content, and you havn't given any such support. Your notation comes without even a notion of an interpretation, let alone semantic conditions on an interpretation, so you aren't providing a canine logic. And you havn't shown us any mKR ontologies, or any actual axioms which might pin down the meanings you claim to be capturing. It is trivial to make claims of 'real meaning' like this. In fact, I will now do so. In my ontology of dogginess, the predicate "dog" means being a member of the species Canis Familiaris when applied to names of mammals other than human beings, and it means worthless and unregarded when applied to human beings, and it means of less than normal functionality when applied to pieces of machinery. And it means all this because I say it does, and I am in charge here because it's my ontology. There: that was easy. In fact, defining meanings this way is so easy, I wonder why anyone ever tries to do it any other way. Who needs axioms, in any case? Right? 


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