Re: comments on current version BLD document: symbols, datatypes, semantics

>> Just one more remark:
> 
> Could not resist an urge to reply, below :-)

 Of course, I could not resist to reply to that :-)

> 
> 
>>>>> The standard way is to first define an alphabet (which includes all the
>>>>> symbols, connectives, etc.) and then define the rules for putting the
>>>>> alphabet symbols together into formulas.  This is not explicitly mentioned
>>>>> -- an omission. It is mentioned now. In fact, there was a bad typo, which
>>>>> said "The language of RIF ..." while it should have been "The alphabet of
>>>>> RIF ...".
>>>> As I understand, the standard way is to let the alphabet vary; the user
>>>> can choose an alphabet, and the logic defines which formulas can be
>>>> obtained from this alphabet and the logical connectives (i.e. the
>>>> language). in my example above, the alphabet A is chosen by the user,
>>>> and LA is the language obtained from A and the logical connectives and
>>>> syntax formation rules in logic.
>>> Nope. When you define a logic, you would normally say that you have a set
>>> Const, Var, etc., without giving out many details.
>>>
>>> But when you are specifying a ***concrete language*** then you must state
>>> what your alphabet is, and it is fixed. An analogy is to say that Java
>>> should not have a fixed alphabet and each user should be able to decide
>>> which sequences of characters are to be allowed as variables, integers, etc.
>>>
>>> We are defining a concrete language, not just a logic.
>> I would argue that the RDF and OWL are concrete languages.  In both
>> languages, the alphabet is not fixed; the symbols simply have to be of a
>> specific shape (e.g. URI or literal).
>> However, as I said, I gave up my resistance to fixing the alphabet :-)
> 
> I claim that OWL alphabet does include all symbols in the lexical spaces of
> its data types, since one can write any literal of the right "shape", and
> it is supposed to be accepted by OWL.
> 
> Now, if you look at their semantics, they define it with respect to an
> unspecified "vocabulary", which is probably the basis for your claim.  In
> the grand schema of things it really does not matter because one could
> always say it is a matter of style.  But I would argue that this was
> actually a mistake.
> 
> An interpretation is supposed to be a structure where one should be able to
> interpret any statement, S, in a given concrete language (OWL). But the way
> it is defined in OWL (http://www.w3.org/TR/owl-semantics/direct.html), if S
> contains a literal that is not in the vocabulary of one particular
> interpretation, I, then S has no meaning with respect to I.

Right, so I does not satisfy S.

> 
> The normal way to define things is to say that a logic language has an
> alphabet (vocabulary + a small set of special symbols, like parentheses)
> and then go from there. By this measure, OWL does not define a language but
> rather a group of languages (I am not talking about Lite vs DL, etc. -- OWL
> DL can be said to be a group of languages according to this view).

Yes.  This is actually the textbook way of defining a logic (at least in
the textbooks I read).  A language is determined by a specific set of
symbols (the vocabulary), and there can be many different languages
which have different sets of symbols.  The logic defines how, using the
symbols in the vocabulary and some auxiliary symbols such as
connectives, punctuation, and variables, formulas can be written.

> Given
> two OWL statements, S1 & S2, there might be an OWL language which
> contains S1 but not S2; there is one that contains S2 but not S1, and there
> is one that contains both.

Right.

> Another analogy is to view C as a group of languages that vary in their
> alphabets.
> 
> As I said, this all can be seen as a matter of style, but I'd rather stick
> with the standard way of doing things in logic and CS.

Well, there can be disagreement about what the "standard" way is of
doing things. Some textbooks may use the one style, whereas others use
the other style.

> In any case, your
> claims that this is "highly undesirable" is a slight exaggeration :-)

I agree :-)

Best, Jos

> 
> 
> 	--michael  
> 

-- 
Jos de Bruijn            debruijn@inf.unibz.it
+390471016224         http://www.debruijn.net/
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