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Re: [ontolog-forum] A different approach to ontology

To: rick@xxxxxxxxxxxxxx, "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Sun, 11 May 2008 16:05:23 -0500
Message-id: <p06230909c44d0c0b7bff@[]>
At 11:44 AM -0400 5/11/08, rick@xxxxxxxxxxxxxx wrote:
>John, Pat, Chris & All:
>Over the past few months I've been a bit of a bookworm trying to better
>understand interpretation and meaning. I have a few questions about a)
>RDF and CL interpretations and b) what Jospeh Goguen called "a
>relational theory of meaning" here ...
>Many thanks in advance for your time in answering my questions.
>John F. Sowa wrote:
>>  I received the following offline question:
>>>  I don't have it clear in my mind why a formal ontology
>>>  (a particular method of documenting relationships)
>>>  would be "a prerequisite for a formal language that
>>>  says anything meaningful about any subject domain."
>>  The words or other symbols must have some connection to
>>  the world in order to make any statement about any aspect
>>  of the world (i.e., some subject domain).
>The RDF semantics states a) that it restricts meaning to what "can be
>captured in mechanical inference rules" and b) that equates a particular
>world with an interpretation.    (01)

The RDF semantics document tried to be both a 
standards specification and an informal tutorial 
in the basic ideas of model theory, which in 
retrospect was probably a bad idea. Calling an 
interpretation a 'world' was part of the attempt 
to be tutorial. Model theory of course describes 
these 'worlds' mathematically, which succeeds 
because only a tiny part of the actual structure 
of the world is relevant to the truth of formal 
logical sentences, i.e. to model theory.    (02)

>The papers I've seen on possible worlds seem to cover a wide variety of
>other topics like, necessity, possibility, etc ...
>http://www-csli.stanford.edu/~jperry/PHILPAPERS/posswld.pdf    (03)

Yes. Modal logics require a single interpretation 
to encompass many 'worlds' at once, with 
relations on them. Hence the term 'possible 
world' comes up rather often. Each of these 
defines a single interpretation in the 
conventional sense, if you work through the 
semantics: each one determines the truth of all 
non-modal sentences of the language. This is one 
reason why it seems reasonable to refer to an 
interpretation of a non-modal logic as a (single) 
'world'.    (04)

>Would you happen to have a reference to an academic paper the defines an
>interpretation as a world ?
>I've read Tarski's Semantic Conception of Truth which defines truth as
>material adequacy, but this definition seems to require structures
>derived from sentences to "fully interpret" the sentences they represent.    (05)

Yes, exactly, they do. One could define a 
Tarskian interpretation as a mathematically 
described structure which is just sufficient to 
completely define the truth-values of all the 
interpreted sentences, and no more.    (06)

>CL model theory doesn't make the same claim: that an interpretation is a
>world. Why ?    (07)

Because the CL documents weren't trying to convey 
intuitions to a non-logically-trained audience in 
the same tutorial way.    (08)

>>  If the symbols don't have any such connection, you have
>>  a meaningless formal language such as the list of
>>  strings Chris Menzel mentioned:  ab, aabb, aaabbb, ...
>>  Some such strings might be interesting to analyze,
>>  but they don't say anything.  They're formal, but
>>  they're as irrelevant to anything in the world as
>>  a game of chess or a Sudoku puzzle.
>Is it fair to say that vocabularies that satisfy interpretations under
>RDF and CL allow us to extend meaning with to what Goguen called
>representational and relational theories or meaning. For example, in a
>semiotic vocabulary in which various signs without interpretants could
>satisfy a representational theory of meaning, Then interpretants could
>satisfy for relational theory of meaning?    (09)

Sorry, I have no idea what you are asking here.    (010)

Pat    (011)

>Again, many thanks in advance !
>>  John Sowa
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>Thanks Rick,
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