SUO: Defining words (was Problems in SUMO)
Ian,
I think that we both understand what can and cannot be
expressed in languages like KIF or CGs.
What we are disagreeing about is the definition of what
constitutes a natural language, such as English. My claim
is that all natural languages are equally expressive in the
same sense that KIF and CGs are equally expressive:
1. The syntactic and semantic features of KIF and CGs are
equivalent in the sense that any statement in one could
be translated to a logically equivalent statement in the
other, provided that all the nonlogical constants (i.e.,
the vocabulary) were defined by suitable definitions and
axioms.
2. The syntactic and semantic features of English and any
other natural language are equivalent in the sense that
any statement in one could be translated to a logically
equivalent statement in the other, provided that all the
words outside some "core vocabulary" were suitably defined.
I certainly agree that "suitably defined" for most human
speakers requires much more than giving them some axioms
stated in the core vocabulary. But that is a question
of how people learn -- they learn best from examples, not
from abstract statements.
JFS>> All natural langauges have the full expressive power of
>> first-order, modal, higher-order, and metalevel logics.
>> Any ontology that can be encoded in those logics can be
>> encoded in any NL.
IN>This doesn't follow. The fact that natural languages have at least the
>degree of syntactic expressiveness of the logics you mention does not imply
>that natural languages can express any ontology and, hence, any semantic
>content whatsoever.
My claim is that the core vocabulary of any NL is capable of
stating the definitions and axioms for any terms that could be
defined in either KIF or CGs (or any other system of logic).
I admit that there is a very serious question of whether the
native speakers of that NL could understand those axioms
without a large amount of traing.
But you don't have to go to a stone-age tribe. Just try to
explain the notion of a charmed quark to somebody who has
never taken a course in physics. Or try to explain the
concept of puts and calls to somebody who has never made any
kind of financial investments.
The fact that certain terms exist in "the English language"
doesn`t mean that a typical English speaker of average
intelligence can understand them without a great deal of
extralinguistic training.
JFS>> It is simply impossible to encode anything in KIF (e.g.
>> SUMO) that could not be recoded in any stone-age language.
>> How would you define book in KIF without assuming a lot of
>> primitives that no stone-age reader would understand?
IN>I don't follow you here. I was arguing that the concept of book presupposes
>a set of concepts that are not available in many languages, e.g. those of
>stone-age cultures, and that inculcating those concepts in the mind of
>someone who is familiar only with one of those cultures would require
>non-linguistic training, and, hence, that your claim that all natural
>languages are fully expressive is false.
My claim was that any term in English could be defined in any
other NL by means that are similar to the way that term was
introduced into English. But the fact that any particular
term was introduced into any NL (including English) does not
imply that an average speaker of that NL can understand it
without a great deal of training.
John