Re: What do the ontologists want

At 05:02 PM 5/15/01 -0500, pat hayes wrote:
>>Something that I very much wish to be able to do is something like this:
>>
>>  'Jon says "The sky is blue"'
>>  'I believe Jon'
>>=>
>>  'I believe (the sky is blue)'
>
>Careful, those are two different senses of 'believe'. You don't believe 
>Jon is TRUE, right? You believe that what he SAYS is true. Write that out 
>and your example looks more, er, logical:
>
>Says(Jon,  (the sky is blue))
>Says(Jon, ?p) implies ?p.
>=>
>(the sky is blue)

I knew you'd be able to formulate this more precisely than I ;-)

>Notice that I havnt quoted the internal sentence, since there is no need 
>to do so. Says(...) here is a modal operator, not a predicate on 
>sentences.  If you want it to really be a predicate on sentences then the 
>second assumption (about Jon's veracity) needs to be restated using a 
>truth predicate:
>Says(Jon, ?y) implies true(?y)
>Notice that ?y here ranges over reified sentences - syntactic things - 
>while ?p ranges over propositions - semantic things, the things that the 
>?y's refer to. 'true' maps the former to the latter. The inference then 
>goes like this:
>Says(Jon, "the sky is blue")
>Says(Jon, ?y) implies true(?y)
>=>
>true("the sky is blue")
>=>
>the sky is blue

Excellent explanation!  Before proceeding, I'd like to test my 
understanding of "modal operator":

M is a "modal operator" if M(?p) can be used to determine the truth of ?p 
in the presence of some additional information.  Thus, from the above 
example, M(?p) == Says(Job,?p), and determines the truth of ?p when we also 
know the assertion M(?p) => ?p.  Brief reading suggests that modality is 
often associated with temporal assertions, so another example would be 
M(?p) == AtTime(?time,?p), which allows us to deduce the truth of ?p given 
the additional information that the current time is ?time.


[...]
>>Maybe there is a way of formulating this that doesn't rely on logical 
>>exotica.  But it does seem to rely on some form of "reflexion" -- a 
>>statement is used both as an object about which other statements are 
>>made, and as an assertion in its own right.
>
>To me, attribution seems better modelled as a modality. Certainly belief 
>is best modelled that way. If you do it that way, you never need to use 
>reification or reflexion, and the logic is... well, not transparent 
>exactly, but reasonably well-behaved and thoroughly understood.

I think this is exactly the kind of direction I hoped this discussion might 
go...

Returning to the example:

     Says(Jon,  (the sky is blue))
     Says(Jon, ?p) implies ?p.
   =>
     (the sky is blue)

How are we to express these statements in our logical language without 
quotation?

Could it be that the construction that we have been calling 'reification' 
is not so much a device for quoting statements as values [that may be bound 
to some quantified variable], but as a syntactic mechanism for introducing 
the proposition represented by a statement of the formal language?

If I may use the term 'reification' to mean "the construction that we have 
been calling 'reification'", as something distinct from 'quotation':

The difference between quotation and reification is (given an applicable 
model theory):
- the interpretation of a quotation in a domain of discourse is 
itself:  the domain of discourse must then necessarily include wffs of the 
formal language itself, but
- the interpretation of a reification is the proposition that it represents 
in the domain of discourse.  This tells us that reification may be applied 
only to wffs of the formal language that are interpreted as propositions in 
the domain of discourse.

>PS. There seems to be an implicit assumption in some of the RDF literature 
>that the only two things to do with a sentence (triple) are to either 
>assert it or to reify it, so any use that doesnt involve asserting a 
>triple must reify it. This is just wrong. Logical notation is full of 
>examples of sentences being used but not being asserted. The simplest is 
>probably negation: when one writes (not P), P is being used (not mentioned 
>or reified), but it is not being asserted: on the contrary, in fact. Now, 
>it might be that RDF is incapable of making this distinction. So much the 
>worse for RDF, if so.

If I haven't slipped a cog, I think the above view of reification validates 
this implicit assumption.  The "notation" that is RDF graph syntax has the 
property that direct expression of a statement entails its 
assertion.  Thus, any mention of a statement that does also assert it must 
be indirect.  The construct we have been calling 'reification' seems to do 
this.

(I won't claim here that this is better than standard logical notation, 
which as has been pointed out by others, employs different conventions for 
distinguishing assertion from mention.)

#g


------------
Graham Klyne
(GK@ACM.ORG)

Received on Thursday, 17 May 2001 05:40:23 UTC