Fully recognizing the danger of fools rushing in... (01)
The discussions of what constitutes a definition, how to modularize ontologies,
and how to state the relations among ontological components seems (to me) to be
so similar to discussions 20-25 years ago in the Abstract Data Type (ADT) and
algebraic specification communities that I would like to mention some of the
decisions we made in the Larch Shared Language (Cf.
http://www.sds.lcs.mit.edu/spd/larch/,
http://www.cs.cmu.edu/afs/cs/usr/wing/www/publications/LarchBook.pdf). (02)
The details of Larch's specification technique (signatures, equations,
non-equational axioms, etc.) need not concern us here. Suffice that it was a
formal system with precise proof and model theories, and that terms were
"defined" only in the sense of specifying their relations. (03)
Larch's (textual and logical) module of specification was called a "trait." (04)
A trait could introduce names and axioms, but it could also refer to other
traits in three distinct ways: (05)
- "includes" The theory associated with the including trait is the theory
associated with the union of its text and that of the included trait. (06)
- "implies" An assertion that the theory associated with the implying trait
includes the theory associated with the implied trait. (07)
"It is not possible to prove the 'correctness' of a specification, because
there is no absolute standard against which to judge correctness. But since
specifications can contain errors, specifiers need help in locating them. ...
Specifications can be augmented with redundant information to be checked during
validation." (08)
We also found this information to be very valuable in allowing human readers to
develop and check their understanding of the "meaning" of a specification. (09)
- "assumes" Whenever a trait with assumptions is itself included or assumed,
its assumptions must be discharged (i.e., implied by the incorporating trait). (010)
I think "assumes" is close to at least one meaning of "context" that has been
thrown around on this list in the last few days. (011)
Any "stratification" or "level of entrenchment" in LSL was a consequence of the
ways a particular collection of traits used in a specification referred to each
other. It was in not built into the language, nor was it a property of
individual traits in isolation. (012)
One of our ways of "remembering the poor human" was to keep individual traits
small, typically fewer than ten axioms, often only a couple. Another was to
explicitly record cross-implications. (E.g., the trait Boolean has 9 explicit
axioms and 13 implications, Set has 3 inclusions, 9 explicit axioms, and 20
implications.) I refer you to the Larch Shared Language Handbook for examples.
http://nms.lcs.mit.edu/Larch/handbook/toc.html (013)
Incidentally, we found in Larch (and most other algebraic specification
researchers have agreed) that it is essential to be able to rename signs
appearing in an external trait when it is included, implied, or assumed.
Modularity and reusability suffer enormously if this ability is omitted. (014)
Jim H. (015)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
Sent: Wednesday, February 14, 2007 11:33 AM
To: Olken, Frank
Cc: [ontolog-forum]
Subject: Re: [ontolog-forum] Role of definitions (Remember the poor human) (016)
>Concerning the issue of definitions, I am inclined to mostly agree
>with Barry Smith (although he will probably object to "concepts".
>
>1) In recent terminology/metadata standards names
>(or more commonly terms - since (proper) names may designate
>individuals)
>designate concepts which have "definitions" - either in natural
>language and/or formal definitions. There is some shift to
>using "signs" as a generalization of "names" in recent standards. (017)
FWIW, the Common Logic standard is explicit in
allowing non-lexical entities to count as 'names'
(in CL, a sign which refers), so that one could
in principle define a CL dialect which used, say,
images to refer to entities or concepts. (018)
>Often a given concept will have multiple "names" in several
>languages. (019)
Indeed, or even in the same language. (020)
>2) The formal definitions are just collections of axioms
>which constrain a particular concept (represented by a symbol
>in the axiom). (021)
Er... which collection? Suppose A 'defines'
concept C in this sense and B 'uses' C. Then both
A and B are collections of axioms involving C.
Nothing in the semantics gives A a different role
than B in constraining which interpretations of
A+B satisfy the axioms. This is one reason I see
no utility in making this distinction between
'definition' and mere assertion. There is
considerable danger in trying to strengthen the
semantics to make the distinction more
meaningful, and as far as I can see, almost no
pragmatic utility. The entire SWeb apparatus for
example does not seem to need it. Issues of
updating, truth maintenance and so on are handled
by such devices as issue dates, assertions of
deprecation and so on, rather than by appeal to
'definitions'. (There is a good engineering
reason for this. Definitions are created early in
the life-cycle, but during the history of any
long-lived ontology, one gets a better ability to
decide which parts should be modified later
rather than earlier. So if B updates A, then B
should be able to modify anything in A.) (022)
> As Barry (and others) have noted,
>it is generally more convenient for the human
>users of such ontologies if they can readily examine the collection
>of axioms which constrains the semantics of a particular concept. (023)
True, but what if they are distributed all over
the Web? One can say it would be better for
people if all the webpages relevant to any query
were all found in one place, which is probably
true in the same, but isn't a useful guide to Web
architecture. We have to manage with the facts of
how information is distributed. (024)
>It may also help some reasoning systems if the axioms relevant to
>a concept are grouped together. (025)
But a lot more is relevant to reasoning than simply a definition. (026)
>However, if several "concepts" are defined by a collection
>of axioms it may be difficult to untangle the collection of axioms
>into individual "definitions". (027)
It may be *impossible*. In fact, it *usually* is.
And even when it can be done, setting out to do
so is counter to one of the basic intuitions of
the Sweb view, which is that one might find
useful information about a concept from many
sources, not all of which have been found at any
given moment. One should think of the 'normal'
case being that in which the set of axioms is
open-ended and may be extended at any time. (028)
>3) There is the problem of reconciling natural language definitions
>used in conjunction with formal definitions. (029)
Indeed. (030)
Pat Hayes (031)
>
>
> Frank Olken
>
>National Science Foundation
>Computer and Information Science and Engineering Directorate
>Intelligent Information Systems Division
>Information Integration and Informatics
>Suite 1125
>4201 Wilson Blvd.
>Arlington, VA 22230
>
>Tel: 703-292-8930 (main)
>Tel: 703-292-7350 (direct)
>Email: folken@xxxxxxx
>-----Original Message-----
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Smith,
>Barry
>Sent: Tuesday, February 13, 2007 11:01 AM
>To: [ontolog-forum]
>Cc: [ontolog-forum]
>Subject: [ontolog-forum] Role of definitions (Remember the poor human)
>
>
>>
>>I would prefer that we don't say that names are "defined". Very few
>>ontology languages provide for actual definitions of names, and several
>
>>that once did (notably KIF) no longer do. Explicit definitions are
>>semantically troublesome, practically of no actual use, create
>>paradoxes, and generally have negative utility. The entire SWeb
>>apparatus has no definitions in it anywhere, nor is it likely to in the
>
>>future. It is very hard to even see what it would mean to define a
>>globally useable name. Let us just say that names occur in ontologies,
>>and ontologies constrain the meaning of names.
>>
>>Pat
>
> From my experience working with biologists and medical researchers on
>ontologies, definitions (ideally both natural language definitions and
>equivalent formal definitions) play a very useful role when it comes to
>ensuring that ontologies are populated in consistent ways across
>disciplines and subsequently used correctly (or indeed at all) in
>practical applications. Most of those involved in such use will not have
>logical or computer science expertise. Where else should they turn to
>find out what a term means?
>BS
>
>
>
>
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