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Re: [ontolog-forum] Ontology, Information Models and the 'Real World': C

To: Waclaw Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Tue, 29 May 2007 15:11:54 -0700
Message-id: <p0623091dc28252e76339@[]>
>John F. Sowa wrote:
>>  If we consider a proposition to be the "language-independent meaning"
>>  of a sentence, then it should also be context independent as well.
>>  That point follows from the fact that different languages have
>>  different means for representing anaphoric references and their
>>  referents (e.g., inflexions, gender, different kinds of articles,
>>  demonstratives, etc.).  Some artificial languages (predicate
>>  calculus, for example) replace all such mechanisms by variables,
>>  which are, in effect, name-like labels.
>>  If all such languages are able to express the "same" propositions
>>  (in whatever sense of "same" seems reasonable), then the simplest
>>  assumption is to assume that the "language-independent meaning"
>>  is converted to a context-independent form by assigning specific
>>  referents to the indexicals.
>This is reasonable;  I agree, and actually hoped for such an answer.
>However, in your (fascinating) book on knowledge representation, you write:
>McCarthy (1993) introduced the predicate ist(c,p), which may be read
>"the proposition p is true in the context c."
>You do not seem to criticize this, though here propositions appear to be
>context-dependent in their truth.    (01)

Not necessarily. Think of ist as simply a 
relation between contexts and propositions. The 
proposition P is in fact either true or false: 
suppose wlog it is true. However, the ist 
relation may not hold between it and a certain 
context C: this means that 'from the C point of 
view' it would be considered 'false'. THis does 
not mean it is in fact false, only that C takes a 
different perspective on things. C's point of 
view, at this juncture, is not veridical. But 
this is entirely to do with the relation between 
P and C, not with the actual truthvalue of P 
(which itself bears no relation to C, and is 
determined by the actual circumstances which 
obtain, regardless of C; unless of course the 
truth of the sentence expressing P depends in 
some way on C.)    (02)

>  It could be thought that
>'proposition' here means the same as 'statement', but of course it is
>not the case, as you also say, explaining an earlier example, "the
>proposition is linked by statement relations (Stmt) to statements of the
>proposition", whereby statements and propositions are clearly distinguished.
>Furthermore, Pat Hayes wrote:
>  > Propositions are not indexical or parameterized in any way. They are
>not sentences, which must be interpreted differently when the names
>which occur in them (actually, occur free in them) are reinterpreted. A
>proposition in IKL is an object which simply has a truth-value: it is a
>'bearer of truth'.
>  > Yet another way to say it is to say that a proposition is like a
>sentence but with all its free names (and indexicals) already
>interpreted to refer to things. This has the consequence that
>propositional expressions are referentially transparent in IKL, so we
>had to invent an 'opaque name' construction to capture the intended
>meaning of opaque contexts.
>It surprises me, then to see in the IKL guide sentences such as
>(ist TemporalContextDay06-16-2006 (that (Dead Osama-Bin-Laden)))
>where apparently it is a proposition and not a sentence that is asserted
>to be true in a context.  (Which in itself is not contradictory with the
>above, unless the hidden meaning is that the proposition is true in that
>context, put may be false in another.    (03)

Yes indeed. And it may be true-in-a-context but 
plain false, or vice versa. Its relationship to 
contexts is completely independent of its 
truth-value. To transcribe the relation ist as 
meaning 'is true in' is purely an aid to 
intuition: it has no bearing on the semantics of 
the language. In IKL, "ist" is merely a relation 
name, not a part of the logical syntax.    (04)

>  To be fully compatible with what
>Pat says above,
>(ist TemporalContextDay06-16-2006 (that (Dead Osama-Bin-Laden)))
>must mean exactly the same as
>(forall (c) (ist c (that (Dead Osama-Bin-Laden)))
>i.e., if a proposition is true in some context (so to speak, conflicting
>Pat's explanation above), it is true in any context whatsoever.    (05)

Not at all. I hope the reason why not is clearer 
now. Bear in mind that IKL assertions are 'simply 
true', not 'true in a universal context' or 'true 
in all contexts'. IKL is not a contextual logic: 
it is simply a logic which we are using to talk 
*about* things called contexts.    (06)

>In the above example from IKL, it seems that the truth of the
>proposition *is* taken to be context-dependent, and that it includes an
>unresolved indexical -- a temporal one.    (07)

No, it is not context-dependent. But the truth of 
P, and the truth of (ist C P) , have nothing at 
all to do with one another, and are determined 
completely independently (as indeed they are in 
most context logics).    (08)

Pat    (09)

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