A Non-concept is Not a ¬Concept
Iaakov Exman
Software Engineering Dept., The Jerusalem College of Engineering, Jerusalem, Israel
Keywords: Non-, Concepts, Identity, Parts, Functionality, Pluggable Ontologies, Abstract Sockets.
Abstract: Often objects with removed parts or functionality also lose their identity. But, there are situations in which
this is not the case: identity is preserved. We refer to such objects, by means of Non- concepts, non-
implying partial negation and concept implying preserved identity. In this work Non- concepts are defined
and pluggable ontologies are proposed for their representation. These ontologies are made pluggable by
sockets, a novel kind of class. These are abstract place-holders for removed/added parts, functionalities or
identities. The space of Non- concepts has been extensively explored. Pragmatic implications of Non-
concepts include manageable design of products with a multitude of models. Non- concepts are also relevant
to the formal controversy whether composition is/isn’t identity. The resolution is not sharp. Identity is
entangled with composition, such that identity is preserved to a certain extent, until further removal causes
identity break-down.
1 INTRODUCTION
When an object is stripped of some of its component
parts or loses functionality it reaches a point where it
is not anymore recognized as such a kind of object:
besides its utility, it loses its identity. But, there are
intriguing situations in which a loss of functionality
or parts does not lead to loss of identity.
We coin a concept assigned to an object in such
situation a “Non-“ concept. It is both Non- as it has
lost some of its characteristics, and it is a concept as
it is still easily recognizable as such.
This paper characterizes Non- concepts, proposes
an ontological representation, explores the space of
possible Non- concepts and deals with its pragmatic
and philosophical implications.
1.1 Related Work
Identity is a widely discussed issue in the literature
e.g. (Kripke, 1977). Literature relevant to this work
relates identity to composition.
There are two roughly opposing positions with
this respect. For one side identity is composition of
parts. Some representative examples are e.g. (Lewis,
1993), (Merricks, 1999) and (Liao, 2005).
Lewis states that the opposite of identity is not
non-identity, but distinctness in the sense of overlap,
things with parts in common (Lewis, 1993) page 33.
This is a suitable starting point for this work.
For the other camp a set of variations on the
composition is not identity. See e.g. (Baker, 1997),
(Elder, 2008). Inquiring deeper one finds that both
camps have more in common than acknowledged.
Systems’ functionality or behavior has been less
under the focus of conceptual approaches.
A gentle introduction to formal ontologies – used
in this work to represent Non- concepts – can be
found in e.g. (Guarino, 1998).
Modular ontologies – composed of sub-
ontologies – have been proposed and extensively
discussed. A few representative pointers include
(Rector, 2008) and (Schlicht, 2008).
Non- concepts do not imply malfunction,
defective or broken objects, or incomplete and/or
inconsistent ontologies. Design problems leading to
incomplete and/or inconsistent ontologies have been
dealt with in the literature, e.g. (Baumeister, 2005).
2 NON-CONCEPTS
Although dictionary-wise “non-“ is a prefix
indicating negation, we shall use it here as a noun,
with the specific meaning of a kind of concept.
2.1 The Non-clock Example
The author of this paper has a non-clock hanging on
401
Exman I..
A Non-concept is Not a Concept.
DOI: 10.5220/0004149704010404
In Proceedings of the International Conference on Knowledge Engineering and Ontology Development (KEOD-2012), pages 401-404
ISBN: 978-989-8565-30-3
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
a wall in the kitchen. It is seen in Fig. 1. It is used to
illustrate the idea of non-clock for guests. It can’t be
used to measure time.
Figure 1: Photo of a Non-Clock – A non-clock as a
concrete instance of its Non- concept. It has a visible scale
– the numbers 6, 12, and marks for other hours. It is
synchronizable by a mechanism in its back. It lacks
periodicity since its battery was removed. Its identity is
clearly recognized, but it is not useful for measuring time.
We have characterized (Exman, 2010) a clock as
a device to measure time with three properties:
1. Periodicity - it has a periodic behavior, based
upon a physical phenomenon;
2. Adjustability – it has a pre-defined scale of
numbers, to which events are assigned;
3. Synchronization – it may send/receive
messages, to synchronize with other clocks.
The non-clock in Fig. 1 has a scale as clearly seen:
the numbers 6 and 12 and marks for other hours. It
may be synchronized and is adjustable, since one
can rotate the non-clock hands to any desired value
in the scale, by a mechanism in its back.
It does not have periodicity, since its battery has
been removed. Thus, it cannot be used to measure
time. It lacks both a component part and its
correspondent functionality.
Nonetheless, one easily recognizes its identity.
Ask any guest – what is hanging on the wall? – and
one easily gets a “clock” reply. It takes some time to
explain that it is not a real clock.
The object in Fig. 1 is not a ¬clock, where ¬ is
the logical not sign. The referred object is not the
complement of a clock in any chosen universe of
objects. The very fact of its recognition implies that
it is much closer to be a clock than whatever may be
its complementary ¬clock.
2.2 Non- Concepts Defined
We define a Non- concept as follows.
Non- concepts do not refer gradual change. We
mean discrete removal/addition of parts or
functionalities, leading to a distinct entity of a new
kind. A non- concept is neither a concept, nor a
¬concept.
One can remove/add parts without affecting
identification. In fact, there exist products explicitly
designed to allow such removal/addition.
Nevertheless there are essential parts that once
removed prevent identification of the original object.
Functionalities are quite similar to component
parts. Removal/addition of functionality does not
necessarily prevent identification.
In the above definition there are four elementary
undefined concepts: a) Identity – there may be
several identities of an object, but there is a single
identity in a given context; b) Part – a discrete
structural component of the sub-system that may be
added or removed; c) Functionality – a discrete
behavior of the sub-system, associated with one or
more of its parts; d) Non- - a noun serving as a kind
of identity of a concept.
3 PLUGGABLE ONTOLOGIES
Here we propose sockets, a novel kind of class, to be
added to ontologies in order to represent Non-
concepts. Such ontologies are said to be pluggable,
i.e. parts or functionalities may be plugged-in or out.
Sockets solve the following problem: -How to
fully represent a sub-system’s Non- concept
displaying removable parts which have been actually
removed/added?
3.1 Sockets
Socket is an abstract generic place-holder for any of
the above concepts: identity, part, functionality. It
allows dealing in a neat way with identities, removal
and addition of sub-system parts and functionalities.
Sockets are used as properties of classes. A Socket is
itself a class. Each socket has one or more “plugged-
in” properties, whose respective values are the
respective pluggable part or functionality.
A plugged-in property has a cardinality
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restriction whose value is Boolean. A part or
functionality is either plugged-in with cardinality
value 1, or not plugged-in, with value 0.
A sub-system should have more sockets than the
sum of removable identities, parts or functionalities.
3.2 iSockets
An iSocket, standing for identity socket, is a sub-
class of socket, specialized for identity
removal/addition. The cardinality of the plugged-in
property of an iSocket is omitted, as it is always 1.
Non- is only used as a value of the plugged-in
property of iSockets. There may be only a single
Non- in the iSockets of an object. This is different
from the logical not sign ¬ which can be added to
each proposition, thus appear several times in the
description of a single object.
3.3 Pluggable Ontology Examples
We start with the non-clock of sub-section 2.1. Its
battery was removed, thus it has no periodicity.
Since the adjustability and synchronization were not
modified, they are not represented. The non-clock
pluggable ontology is in Fig. 3.
Figure 3: Non-clock partial pluggable ontology – It has
one iSocket with a Non- value. It is a non-clock as its
battery was removed: it lost its periodicity functionality.
Cardinality values of the plugged-in properties are 0, as
the respective part and functionality were removed.
Let us do a thought experiment. Suppose we add
a new battery to our non-clock. We then synchronize
and adjust the time shown to be the correct current
time. So, now it is just a fine functioning clock.
Next we put an internet video camera in front of
the revived clock. The image of the moving clock is
transmitted through the internet, and seen in another
computer – in a different country.
The image of clock through the internet is now
an Internet-Video non-clock. It has a scale and
periodicity. Its identity is easily recognized as an
instrument to measure time and can be used to do so.
But the video itself cannot be synchronized. So,
by the demand of the three properties above it is not
a plain clock. Nonetheless it is a useful non-clock, as
long as the actual clock which is the video image
source works well. Its partial pluggable ontology is
seen in Fig. 4. It differs from the previous ontology
by a plugged-in addition.
Figure 4: Internet-Video Non-clock partial pluggable
ontology – It is a non-clock as we see its video through the
internet: it lost its synchronization functionality. The
cardinality values of the plugged-in synch-part and
synchronization functionality are 0. On the other hand, an
internet-video property has been added with cardinality 1.
Next, we do a second thought experiment. We
keep the internet video camera, but again remove the
clock’s battery. The image now is static. This new
non-clock is not very useful. It certainly has a scale,
but no periodicity and no synchronization ability.
4 THE NON-CONCEPTS SPACE
4.1 Non-concepts by Design
There are products a priori designed to fit Non-
concepts: a) lacking parts; b) downgraded
components (see Fig. 5); c) lacking functionality.
Figure 5: Non-printer with downgraded toner partial
pluggable ontology – It is a non-printer since the standard
toner was removed – plugged-in cardinality=0. It is sold
with downgraded toner – plugged-in cardinality=1.
4.2 Non-concepts, Obsolescence and
their Cemeteries
The most widespread object cemeteries are car
ANon-conceptisNota¬Concept
403
cemeteries, see Fig. 6. They are impressive and have
been the subject of literary works and a theatre play.
Figure 6: Yellow non-car in Car cemetery photo – All the
cars in a cemetery are identifiable as such. Although one
cannot tell that the yellow one is for sure a non-car, its
overall condition leads us to think so.
Photo: Norbert Aepli, published under the license "Creative
Commons Attribution 3.0".
A non-car’s ontology for a car rescued from the
cemetery – say the bright yellow little car – to be a
collector’s item is shown in Fig. 7.
Figure 7: Collector’s Non-car partial pluggable ontology –
It is a non-car since the driving functionality was removed,
perhaps by removing the battery – plugged-in
cardinality=0. It serves only as a collector’s item – as
shown plugged-in in the iSocket.
5 DISCUSSION
The pragmatic implications of non- concepts refer to
design of systems of a few kinds: a) variety of
models; b) removable parts. In such cases, one could
use abstract sockets to explicitly manipulate parts
with differing status, viz. to label the respective parts
along design, manufacturing and delivery stages.
The formulation of Non- concepts and sockets in
this work and the examples given lead us to a unique
position about whether identity is/isn’t composition.
We say that identity and composition are
entangled. To a certain extent, composition changes
by parts’ removal/addition do not affect identity.
Beyond further removal/addition of parts,
identity breaks down. This is not marked by a fixed
quantitative limit; it depends on the part types and
order of removal/addition.
5.1 Future Work
Among the open questions regarding Non- concepts:
Do we need additional accessories to
characterize non- concepts? While it is satisfactory
that with a minimal set of generic classes – Sockets
and iSockets – one still needs a more comprehensive
investigation to provide a more definitive answer.
Are pluggable ontologies completely equivalent
to modular ontologies? Sockets seem to be the
natural mechanism to attach ontology modules.
REFERENCES
Bacon, J., Campbell, K. and Reinhardt, L., 1993.
Ontology, Causality and Mind, Cambridge University
Press, Cambridge, UK.
Baker, L. R., 1997. “Why Constitution is Not Identity”,
The Journal of Philosophy, Vol. 94, (12), pp. 599-621.
Baumeister, J. and Seipel, D., 2005. “Smelly Owls –
Design Anomalies in Ontologies”, in Proc. 18
th
Int.
Florida Artificial Intelligence Research Society Conf.,
AAAI Press, pp. 215-220.
Elder, C., 2008. “Against Universal Mereological
Composition”, Dialectica, Vol. 62, (4), pp. 433-454.
Exman, I., 2010. “Software is Runnable and Composable
Ideas – 1. Persistent Systems”, in Proc. SKY’2010
International Workshop on Software Knowledge,
Herzlia, Israel, pp. 29-35.
Guarino, N., 1998. “Formal Ontology and Information
Systems”, in Proc. Of FOIS’98, Amsterdam, IOS
Press, pp. 3-15.
Kripke, S., 1977. “Identity and Necessity”, pp. 66-101, in
Schwartz, S.P. (ed.) Naming, Necessity and Natural
Kinds, Cornell University Press, Ithaca, NY, USA.
Lewis, D., 1993. “Many, But Almost One”, in ref. (Bacon,
1993), pp.23-37.
Liao, Shen-yi, 2005. “Things are Their Parts”, Logos, Vol.
II, Issue 2, pp. 44-61 (Spring 2005).
Merricks, T., 1999. “Composition as Identity,
Mereological Essentialism, and Counterpart Theory”,
Australasian Journal of Philosophy, 77, pp. 192-195.
Rector, A., Horridge, M., Iannone, L. and Drummond, N.,
2008. “Use Cases for Building OWL Ontologies as
Modules: Localizing, Ontology and Programming
Interfaces & Extensions”, in Proc. 4
th
Int. Conf.
SWESE Semantic Web Enabled Software Engineering.
KEOD2012-InternationalConferenceonKnowledgeEngineeringandOntologyDevelopment
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