Danny:
May I point out the essence of my message in a more
specific way: relations are fundamental to any robust knowledge modeling
system, since what it knows about the class of relations and how it models this
elusive kind of entity are the crucial indicants of its quality and commercial
usage. It must be noted that the extant literature on
the ontology of relations is poor comparing with the formal calculi (algebra and
logic) of relations, mostly due to the pioneering works of De Morgan and Peirce;
as far as we know, there is no systematic classification of the fundamental
species of relations. Despite of this, the reason to have a
fundamental theory of relations is perfectly clear; not having developed a
general ontology of relations may result in a variety of schemes
mostly based on practical purposes or everyday intuition, as systems like
RDF/OWL and UML avoiding, or rather unable, to define and
classify relations, considering them as the class of
things having formal existence.
Now, carefully researching the matter, we found out
that the universal class of
relations consists of sixteen classes of ordered classes of the
world variables (objects O, states S, changes
C, and relations R) arrayed in a matrix
structure:
|
O : O |
O :
S |
O :
C |
O :
R |
|
S :
O |
S :
S |
S :
C |
S :
R |
|
C :
O |
C :
S |
C :
C |
C :
R |
|
R :
O |
R :
S |
R :
C |
R :
R |
Depending on the nature of correlatives, the general
relational formula allows for a complete extent of possible relations, so richly
listed, but not properly ordered, in the WordNet' lexical
database:
=> social relation (communication (message, language, spoken and
written, infection or contagion,), relations or dealings, professional relation,
politics, interpersonal chemistry or
alchemy)
=> position, spatial relation (inclination,
slope, placement, point of view, coincidence, centrality, marginality,
anteriority, posteriority, outwardness, inwardness, malposition, northerness,
southerness, horizontality, verticality, way, direction, angular position)
=> ownership (community, severality, property right, proprietorship,
employee ownership, landholding, stockholding)
=> causality
=> relationship, human relationship
(personal relation: bonding, obligation)
=> function
=> association
(colligation: generalization, induction)
=> logical relation (contradictory, contrary,
transitivity, reflexivity, modality or mode, implication or conditional
relation)
=> mathematical relation (function (inverse, Kronecker
delta, metric, transformation, mapping, map, or correspondence, operator,
trigonometric, threshold, exponential), parity, transitivity,
reflexivity)
=> foundation (footing, basis, or ground; grass
roots)
=> connection, connexion, connectedness
(series, bond, linkage, communication, concatenation, bridge, involvement, iclusion
or containment, relevance (materiality, cogency, point, reference, regard,
respect, relation to, applicability), relatedness (bearing))
=> unconnectedness
(irrelevancy,
unrelatedness)
=> linguistic relation (grammatical
relation, agreement, transitivity, intransitivity, coreference, conjunction,
complementation, coordination, subordination, modification, mood, anaphoric
relation, voice, inflection, aspect; semantic relation, subordination or
hyponymy, superordination or hypernymy, synonymy, antonymy, whole to part
relation or holonymy, part to whole relation or meronymy, troponymy)
=> part, portion, component part, component
(linguistic or language unit; item or point; basis or base; detail, particular,
or item; unit; member; substance; remainder, balance, residual, residuum, or
rest; subpart)
=> affinity, kinship (rapport;
sympathy)
=> kinship, family relationship, relationship
(affinity or phylogenetic relation; descent, line, lineage, or filiation;
affinity or kinship by marriage; consanguinity or blood kinship; parentage or
birth; fatherhood or paternity; motherhood or maternity; brotherhood;
sisterhood; marital relationship)
,
=> magnitude relation, quantitative relation
(scale; ratio (profit margin, abundance, efficiency, frequency, productivity,
quotient; rate (acceleration, fertility, mortality, flow rate, flux, frequency,
growth rate,
speed)
=> control
=> business relation
(competition; clientage)
=> reciprocality, reciprocity (complementarity,
correlation, mutuality or interdependence (commensalism, parasitism, symbiosis,
sharing), mutualness, reciprocal)
=> interrelation,interrelationship, interrelatedness
=> temporal relation (antecedent, chronology,
synchronism,
asynchronism)
=> comparison (imaginative comparison:
simile, metaphor, allegory)
=> opposition, oppositeness
(antipode, antithesis, conflict, contrast, mutual opposition or polarity,
ungradable opposition, conradictoriness, contradiction, contrary, contrariety,
tertium quid, reverse, inverse, antagonism)
=> change (difference,
gradient)
As one can see, the
mathematical (logical) relations between sets (classes) so actively used by
OWL make only small part of an enormous universe of relations, real, ideal, and
formal or external and internal. Here emerges the conclusion that
'proposing a general conceptual scheme by using the class /property distinction,
the data type languages like OWL are missing the meat of things',
accordinly, using such a language is harmful with badly constructed
Web-based applications.
From:
Danny Ayers
Sent: Sunday, February 15, 2004 6:42
PM
Subject: RE: Re: W3C approves RDF and OWL
as recommendations
Asha:
The OWL project undoubtedly comes under
a great technological undertaking, but the course of action embarked on makes
it a dubious venture, raising doubts
about the whole enterprise, although there is no question about the
technological enormity of the target
pursued. To our feelings, the administrators running the World Wide Web
Consortium rushed the matter by recommending the
OWL
as an ontology language standard fit for structuring the Web
data, documents, and applications. Since, beside the
well-knowing merits, the language
has bad conceptual faults which make it falling short of a wide
commercial use.
First, any ontology formal
language designed to formulate classes and their relationships has to
include an ontology of relations describing their real
features accompanied with the formal attributes.
Danny:
I'm afraid I'm unclear about what you mean by "real
features" in this context, do you have any examples of these in other
languages?
As I see it the OWL language attempts to find the
sweet-spot between expressive capability and decidability in the context of
the web. From my own little experiments, I'd suggest it does quite a good
job.
----- Original Message -----
Asha:
This is not the case with the OWL
created as adding better vocabulary than developed by XML, RDF, RDF Schema,
DAML+OIL in formal description of classes,
individuals and properties, like cardinality, equality, and other
formal characteristics. The language is lacking many significant features of
relations, both formal and real.Among real, first of all, the relation of
cause and effect is fatally missing.
Danny:
Cause
and effect can be modelled using OWL - this is something found in
OWL-S:
http://www.daml.org/services/owl-s/1.0/owl-s.html
Note too that the languages (RDF and OWL) are
designed to be extensible, so additional constraints could be added as
required.
Asha:
Such defects come from the
approach used, purely set-theoretical and formal logical, while any
content-based (world) ontology distinguishes internal and external
relations, avoiding their reduction to relational properties.'Being a
parent' is merely a relational property, while 'parentage' (parenthood, but
not the act or process of parenting) is a relation of parent to child. Or,
more generally, the relational property of being a cause is just a monadic
reduction of causality, the relation of cause to effect.
Danny:
I can't actually see any part of that which
couldn't be represented fairly directly using RDF/OWL As to the processing
of the material thus represented, maybe what you describe falls outside of
the capability of OWL's Description Logic - but that doesn't mean such logic
couldn't be layered on top.
Asha:
So, instead of classes and relational
properties, we have rather to speak of classes and their relationships as
two sorts of distinct entities.
Danny:
Within
OWL DL, yes. Within OWL Full (which encompasses 'generic' RDF) properties
are classes too. Instantiation of properties isn't possible directly, that
is lacking - but given that tractability is a key aim, there's a potential
Pandora's box of undecidability if this were
possible.
Asha:
Besides, it will make a poor language
to use the class/property distinction, where all properties are reduced to
relational properties as a substitute of the relations of classes. In
fact, there are several sorts of property, substantial (material,
structural), stative (qualitative, quantitative), active (functional), along
with relational (causal, spatial, temporal) properties, all such
properties of a substantial class (genus) are to be the properties of its
species and individuals. With such distinction, it makes a difference
whether we just state that 'a class (a thing) have attributes (properties)'
or that 'a thing has the properties to be a substance, to be in a state, to
be acted or acting upon, and to be related to something else'. The later is
a universal ontological statement, while the former is a general logical
proposition. That is, from one side, to build a formal ontology language,
one may develop a set-theoretic (logical) ontology constructed as a formal
logical system composed of its objects-primitives, classes, individuals, and
properties, logical syntax (notation techniques, formation and
transformation rules), and formal semantics (model theory), as the OWL is
doing.
From the other side, one can
develop a true ontological system involving as its primitives Entity or
Thing and the kinds of entities or things along with fundamental
definitions, axioms and real-world semantics seeking the interpretation of
the theory and its truth conditions in the world of things, entities, or
beings.
Danny:
The only difference I see there
is in the 'real-world semantics' part. Like I said, I'm not
entirely sure what you mean by
this.
Asha:
Next demerit is tightly connected with
the first. Any general theoretical model or conceptual scheme or description
framework is built with some kinds of concepts, individuals, predicates,
attributes, or relations. If the model represents the traits and features of
the real world, its predicates represent real properties. In so far as the
scheme describes formal objects, its predicates give description of formal
properties, attributes, or predicates. As a consequence, there are two sorts
of predicates: formal, logical attributes or real-valued, ontological
predicates. Failing to see such difference can result in another conceptual
mess and confusion. Proposing a general conceptual scheme by using the class
(object)/property (relation) distinction, the data type languages like OWL
are missing the meat of things. For such a formal data structure
might not adequately represent the whole gamut of the world entities with
their various interrelationships. We must clearly differentiate between
classes, properties, definitions as logical forms and entity types as
ontological classes; for the definition and class and property will always
be in one of these thing types represented by the classes of ontological
predicates and signified by the generic terms and expressions, such as
thing, being or entity, substance or object, state, property or quality
and quantity, change or action or process, and relation, like
causality, time, space. Any meaningful statements or propositions is always
about one or another of these types of entity, in two principal ways. If the
same type of predicate is asserted of its kinds (a quantity predicated of
magnitudes), it signifies its genus, a thing's essence. On the other side,
if one type of predicate is asserted of another type, as equality and
inequality relations are predicated of quantity, sameness or
difference relations, of substances, it signifies rather a property than an
essence.
Danny:
That appears to be
the same point again, that somehow the Semantic Web languages are lacking
'reality'. Most things we do in this field are very approximate models, and
grounding in the real world is limited. Having said that, I don't see
any problem in creating the kinds of predicates you describe
here.
Asha:
Thus, to construct a high quality Web
ontology language as a computational ontology incorporating the basic
rules of reasoning about the world and its generic
entities, we first need to formulate the universal entity framework
supporting all the major classes and relations in the single hierarchy of
things, as it is implicitly intended to achieve by the SUO project, how
successfully or unsuccessfully, this is another topic. And
designing such a (machine processible) ontology language system
requires a formal inquiry into the world's objects, states, changes, and
relations as the fundamental classes of ontological predicates specifying
diverse kinds of entity and realms of the world.
Danny:
Ok, and
while that magnum opus continues, the crude approximations of RDF
and OWL can be used to carry out useful work on the web. OWL most certainly
is not perfect, but there is enough for it to useful, and
significantly, be comprehensible to most web developers. Whether there
is a single universal ontology is a moot point. There's certainly a lot
more that can be done in the field, but I would suggest that we can learn a
lot from applying what we have already, approaching the problem from the
direction of what we do know, rather than that of what we
don't.
But
whatever, I don't see any reason to reject the Semantic Web languages on the
grounds that they can't fully describe the universe, any more than you might
reject the relational model for storage of census data. The Object Oriented
programming paradigm often involves a crude modelling of real-world
objects, yet it is still useful. Your argument begins by suggesting that OWL is
unfit for commercial application because of its conceptual shortfalls. If
anything its shortfalls, which are on the whole simplifications, put it more
in reach of commercial developers away from the Ivory
Towers.
The
bottom line is that the W3C's initiatives and the loftier aims you describe
aren't mutually exclusive. I'd go further and suggest that the former may
indeed help bootstrap development of the latter.
Cheers,
Danny.
----
http://dannyayers.com
Azamat:
The OOP paradigm case illustrates quite opposite what your intended. As
any sophisticated knowledge artefact is based on great ideas and
principles, implicitly or explicitly, so OOP, as a piece of virtual reality,
involves the classical concepts of inheritance relation and substance as a
class and object [an entity involving identity, state (data), and
behavior (methods, functions, procedures)]. Otherwise it would hardly been
so useful.
All the
best,
Azamat
Abdoullaev
EIS
LTD
Russia,
Moscow
Cuprus,
Pafos
http://www.eis.com.cy
|