John F. Sowa wrote: (01)
> 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. (02)
This is reasonable; I agree, and actually hoped for such an answer. (03)
However, in your (fascinating) book on knowledge representation, you write: (04)
"
McCarthy (1993) introduced the predicate ist(c,p), which may be read
"the proposition p is true in the context c."
" (05)
You do not seem to criticize this, though here propositions appear to be
context-dependent in their truth. 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. (06)
Furthermore, Pat Hayes wrote: (07)
> 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'. (08)
> 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. (09)
It surprises me, then to see in the IKL guide sentences such as (010)
(ist TemporalContextDay06-16-2006 (that (Dead Osama-Bin-Laden))) (011)
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. To be fully compatible with what
Pat says above, (012)
(ist TemporalContextDay06-16-2006 (that (Dead Osama-Bin-Laden))) (013)
must mean exactly the same as (014)
(forall (c) (ist c (that (Dead Osama-Bin-Laden))) (015)
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. (016)
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. (017)
vQ (018)
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