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 ...
>
>http://cse.ucsd.edu/~goguen/pps/notn.ps
>
>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,
>blog http://spout.rickmurphy.org
>web http://www.rickmurphy.org
>cell 703-201-9129
>
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