Re: FW: Meaning: 'natural language semantics' vs 'formal semantics'
In comment on my note below, Michael wrote:
There is indeed a formal way to ensure that what one person (say Alice)
chooses to assert is a sale is what the authors of the EO would agree is a
sale.
There are two aspects to this --
1. Is Alice's use of the EO correct with respect to the axioms of the EO?
2. Do the axioms of the EO fully capture the intuitions of its designers?
I have no problem with the first part of this. I think the answer to the
second is that given the nature of the real world, no ontology can ever
fully capture the intuitions of the designers for all the classes of
interest. I assert this in the sense that given a set of classes of
structures, any user of the ontology will not be constrained, by virtue of
conforming with the axioms, to represent a particular real world situation
by the same set of members of those classes as would the designer.
I support this assertion first by the discussion in Lakoff, as I have
previously referenced, for example of the meaning of the word "ball", which
on the surface looks trivially easy, but rapidly reveals difficult
complexity. Second, because of the inherent limitations of the formal
semantics. Yes, we can add ever more complex axioms about the classes of
structures, and we can add more classes to the structure, but each of these
is inherently open to different intuitive interpretations. Taken to
extreme, we would be limited to enumerating all the permissible members of
every class, an obviously impractical and useless conclusion.
Any SUO published for widespead use will have to succeed or fail on
whatever semantics it contains, formal or informal, as in general, after
release, there will be no opportunity for its designers to review what
Alice chooses to assert, let alone revise the SUO in response to every
mis-interpretation. As far as it supports interoperability among systems,
this will be limited to things which do conform with the formal axioms. As
far as the users of these interoperatiing systems are concerned, it will be
limited to how closely their intuitive interpretations of the formal and
informal semantics match those of the SUO designers.
Clearly, during any development of an SUO, we can and should review
different interpretations of the informal semantics, and do our best to
eliminate ambiguities, while recognizing the practical limitations of this.
e-business Services PHONE: +44-1707-363090 (Int 7-453090)
Rosanne House (RH2A) FAX: +44-1707-338732
Welwyn Garden City Internet: martin_king@uk.ibm.com
GB - AL8 6UB IBMMAIL: GBIBM3WS
Michael Gruninger <gruning@cme.nist.gov> on 02/08/2000 16:45:01
Please respond to Michael Gruninger <gruning@cme.nist.gov>
To: Martin King/UK/IBM@IBMGB
cc: standard-upper-ontology@ieee.org
Subject: Re: FW: Meaning: 'natural language semantics' vs 'formal
semantics'
martin_king@UK.IBM.COM wrote:
> I suggest:
>
> 1. If we wish to build reliable and consistent systems, or reliable and
> consistent ontologies, we need a precise and accurate set of rules. For
> the Enterprise Ontology, these rules are contained in the formal KIF
> statements. For example there are rules about SALE and about DATE, and
> about how a DATE may be related to a SALE. These rules could be applied
by
> a proof engine that processed KIF directly or translated into some other
> language that could be used to validate updates to SQL tables intended to
> hold data about SALES.
>
> 2. As and when anyone wishes to use the Enterprise Ontology definition of
> SALE and DATE, there is no formal way to ensure that what such a person
> chooses to assert is a SALE is what the authors of the EO would agree is
a
> SALE. Informally, if the authors of the EO have done a good job of
writing
> their natural language definition, most users will choose the right
> interpretation most of the time. If the user wishes to relate what he
has
> chosen to call a SALE to what he has chosen to call a DATE, he may be
> prevented by the application of the formal rules, and hence the formal
> rules may assist users in conforming with the EO authors intentions, but
> there can never be any formal proof of the correctness of the
> interpretation.
This issue is the motivation for my earlier notes on language and models.
There is indeed a formal way to ensure that what one person (say Alice)
chooses to assert is a sale is what the authors of the EO would agree is a
sale.
There are two aspects to this --
1. Is Alice's use of the EO correct with respect to the axioms of the EO?
2. Do the axioms of the EO fully capture the intuitions of its designers?
If Alice writes a sentence in KIF that is consistent with the axioms of the
EO,
then it must be considered correct with respect to the EO. If such a
sentence
does not correspond to the intuitions of the EO designers, then the EO must
be
modified/extended so that Alice's use of the ontology becomes inconsistent.
One problem is that in general, this may require a second-order
axiomatization
to rule out such unintended interpretations by Alice.
Now the axioms of the EO may not fully capture the intuitions of its
designers,
and you say that the natural language definition provides assistance in
this.
Although this may be adequate if the ontology is being used to facilitate
communication among people, if we want to use the EO to support
interoperability among software applications (or agents), then it may not
be
enough.
The second aspect of this discussion has to with whether the EO designers
can
ever prove that the axioms capture their intuitions. Since intuitions are
by
their nature informal, we can't directly prove that the axioms are correct
with respect to their intuitions. However, as I have discussed in earlier
messages, we can formally specify classes of structures and formally prove
that the ontology axiomatizes these classes of structures (i.e. all these
structures are models of the ontology, and all models of the ontology are
isomorphic to one of these structures).
This approach pushes the problem back to the relationship between the
intuitions and these structures, i.e. do the structures correspond to the
designers' intuitions? Although this relationship cannot be proven
formally, I think that we can take an approach analogous to a scientific
methodology. For example, from a Popperian view, scientific theories
cannot be validated, but they can be falsified. Similarly, the
characterization
of the models of an ontology cannot be validated, but we can try to find
counterexamples that can be used to falsify the ontology.
Such counterexamples would either
be intuitive scenarios that are inconsistent with the axioms, or
counterintuitive scenarios that are consistent with the axioms.
- michael